GENERATION OF ENTANGLED STATES OF TWO DISTANT CAVITY MODES VIA JOSEPHSON JUNCTION BASED DEVICES

We present a simple scheme for the preparation of entangled states of the e.m. modes of two spatially separated microwave cavities exploiting their interaction with two superconducting SQUID rings embedded within them. The scheme requires that the two SQUID qubits are initially prepared in an entangled state and the possibility of controlling both the coupling strengths and the interaction times. We also briefly discuss the importance of such a theoretical scheme in view of possible applications in the context of quantum computing and its experimental feasibility.

Notulae to the Italian alien vascular flora: 13

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions. Nomenclatural and distribution updates published elsewhere are provided as Suppl. material 1.

Second quantization and atomic spontaneous emission inside one-dimensional photonic crystals via a quasinormal-modes approach

An extension of the second quantization scheme based on the quasinormal-modes theory to one-dimensional photonic band gap (PBG) structures is discussed. Such structures, treated as double open optical cavities, are studied as part of a compound closed system including the electromagnetic radiative external bath. The electromagnetic field inside the photonic crystal is successfully represented by a new class of modes called quasinormal modes. Starting from this representation we introduce the Feynman's propagator to calculate the decay rate of a dipole inside a PBG structure, related to the density of modes, in the presence of the vacuum fluctuations outside the one-dimensional cavity.

Effects of Cavity damping on the oscillatory photon exchange between two modes coupled to a two-level atom

On applications of non-point and discrete symmetries for reduction of the evolution-type equations

Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation

Abstract The detailed construction of a prefixed fundamental set of solutions of a linear homogeneous difference equation of any order with arbitrarily variable coefficients is reported. The usefulness of the resulting resolutive formula is illustrated by simple applications to the Hermite polynomials and to the Fibonacci sequence.

Microscopic description of dissipative dynamics of a level-crossing transition

We analyze the effect of a dissipative bosonic environment on the Landau-Zener-Stuckelberg-Majorana (LZSM) level crossing model by using a microscopic approach to derive the relevant master equation. For an environment at zero temperature and weak dissipation our microscopic approach confirms the independence of the survival probability on the decay rate that has been predicted earlier by the simple phenomenological LZSM model. For strong decay the microscopic approach predicts a notable increase of the survival probability, which signals dynamical decoupling of the initial state. Unlike the phenomenological model our approach makes it possible to study the dependence of the system dynamics…

Obituary in memory of Prof. Franco Persico

Genuine tripartite entanglement in a spin-star network at thermal equilibrium

In a recent paper [M. Huber {\it et al}, Phys. Rev. Lett. {\bf 104}, 210501 (2010)] new criteria to find out the presence of multipartite entanglement have been given. We exploit these tools in order to study thermal entanglement in a spin-star network made of three peripheral spins interacting with a central one. Genuine tripartite entanglement is found in a wide range of the relevant parameters. A comparison between predictions based on the new criteria and on the tripartite negativity is also given.

On the merit of a Central Limit Theorem-based approximation in statistical physics

The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved as well as its inadequacy to disclose quantum criticalities at fixed temperatures. Its high temperature predictions are in addition shown to coincide with those stemming from straightforward appropriate expansions up to (k_B T)^(-2). Our results are clearly illustrated by comparing the exact and approximate temperature dependence of the free energy of some exemplary physical systems.

Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets a…

Estimation of the Repeatedly-Projected Reduced Density Matrix under Decoherence

Decoherence is believed to deteriorate the ability of a purification scheme that is based on the idea of driving a system to a pure state by repeatedly measuring another system in interaction with the former and hinder for a pure state to be extracted asymptotically. Nevertheless, we find a way out of this difficulty by deriving an analytic expression of the reduced density matrix for a two-qubit system immersed in a bath. It is shown that we can still extract a pure state if the environment brings about only dephasing effects. In addition, for a dissipative environment, there is a possibility of obtaining a dominant pure state when we perform a finite number of measurements.

Generating and Revealing a Quantum Superposition of Electromagnetic Field Binomial States in a Cavity

We introduce the $N$-photon quantum superposition of two orthogonal generalized binomial states of electromagnetic field. We then propose, using resonant atom-cavity interactions, non-conditional schemes to generate and reveal such a quantum superposition for the two-photon case in a single-mode high-$Q$ cavity. We finally discuss the implementation of the proposed schemes.

Bounds on the entanglement of two-qutrit systems from fixed marginals

We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of candidates for maximally entangled mixed states with respect to fixed marginals for two qutrits. These states are extremal in the convex set of two-qutrit states with fixed marginals. Moreover, it is shown that they are always quasidistillable. As a by-product we prove that any maximally correlated state that is quasidistillable must be pure. Our observations for two qutrits are supported by numerical analysis.

Distilling angular momentum nonclassical states in trapped ions

In the spirit of Quantum Non-Demolition Measurements, we show that exploiting suitable vibronic couplings and repeatedly measuring the atomic population of a confined ion, it is possible to distill center of mass vibrational states with well defined square of angular momentum or, alternatively, angular momentum projection Schr\"odinger cat states.

Resonant Transitions Due to Changing Boundaries

The problem of a particle confined in a box with moving walls is studied, focusing on the case of small perturbations which do not alter the shape of the boundary (\lq pantography\rq). The presence of resonant transitions involving the natural transition frequencies of the system and the Fourier transform of the velocity of the walls of the box is brought to the light. The special case of a pantographic change of a circular box is analyzed in dept, also bringing to light the fact that the movement of the boundary cannot affect the angular momentum of the particle.

Tomographic approach to the violation of Bell's inequalities for quantum states of two qutrits

The tomographic method is employed to investigate the presence of quantum correlations in two classes of parameter-dependent states of two qutrits. The violation of some Bell's inequalities in a wide domain of the parameter space is shown. A comparison between the tomographic approach and a recent method elaborated by Wu, Poulsen and Molmer shows the better adequacy of the former method with respect to the latter one.

Unitary reduction of the Liouville equation relative to a two-level atom coupled to a bimodal lossy cavity

The Liouville equation of a two-level atom coupled to a degenerate bimodal lossy cavity is unitarily and exactly reduced to two uncoupled Liouville equations. The first one describes a dissipative Jaynes-Cummings model and the other one a damped harmonic oscillator. Advantages related to the reduction method are discussed.

Time-dependent perturbation treatment of independent Raman schemes

The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur.

Analytic estimation of transition between instantaneous eigenstates of quantum two-level system

AbstractTransition amplitudes between instantaneous eigenstates of a quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions. In particular, the condition under which the transitions are suppressed is examined analytically. It is shown that the analytic expression of the transition amplitude enables us, not only to confirm the adiabatic theorem, but also to derive the necessary and sufficient condition for quantum two-level system to remain in one of the instantaneous eigenstates.

Entropy production and information fluctuations along quantum trajectories

Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an additional, non-thermal contribution to the entropy flux, which is shown to be a direct consequence of quantum fluctuations. These features lead to a quantum definition of single trajectory entropy contributions, which accounts for the difference between classical and quantum trajectories and results in a quantum correction to the standard form of the integral fluctuation theorem.

Symmetry-based canonical dressing of a bidimensionally trapped and laser-driven ion

Abstract We present a detailed and exact construction of a unitary operator accomplishing the diagonalization of an effective quadratic radiation-matter interaction model describing a bidimensionally trapped and appropriately laser-driven ion. The possibility of applying the same mathematical method to other effective radiation-matter interaction model is briefly put into evidence.

Perturbative Treatment of the Evolution Operator Associated with Raman Couplings

A novel perturbative treatment of the time evolution operator of a quantum system is applied to the model describing a Raman-driven trapped ion in order to obtain a suitable 'effective model'. It is shown that the associated effective Hamiltonian describes the system dynamics up to a certain transformation which may be interpreted as a 'dynamical dressing' of the effective model.

Quantum light depolarization: the phase-space perspective

Quantum light depolarization is handled through a master equation obtained by coupling dispersively the field to a randomly distributed atomic reservoir. This master equation is solved by transforming it into a quasiprobability distribution in phase space and the quasiclassical limit is investigated.

Entanglement of distant SQUID rings

ELECTROMAGNETIC CONTROL OF DYNAMICAL LOCALIZATION CONDITIONS IN 1D LATTICES WITH LONG-RANGE INTERSITE INTERACTIONS

In this paper we investigate the possibility of controlling dynamical localization conditions for a charged particle confined in a 1D lattice biased with a dc-bichromatic field and long-range intersite interactions. We derive the quasi-energy spectrum of the system proving that the tunneling dynamics of the particle can be destroyed provided that the parameters of the external irradiating electric field are properly chosen.

Gruppo umano di età ellenistica di Polizzi Generosa (PA). Antropologia e paleopatologia

Dynamical behavior of a XX central spin model through Bethe ansatz techniques

Electromagnetically induced tunnelling suppression in a flux qubit

Motivated by recent experiments wherein Josephson devices are irradiated by microwaves fields or are coupled to LC resonators, we theoretically investigate the dynamics of a flux qubit coupled to a monochromatic bosonic mode. We define strong coupling conditions under which the qubit tunnelling frequency between the localized flux states can be controlled and even suppressed. The practical realization of such a regime leading to this hindered dynamics is discussed.

Generation of Entangled Two-Photon Binomial States in Two Spatially Separate Cavities

We propose a conditional scheme to generate entangled two-photon generalized binomial states inside two separate single-mode high-Q cavities. This scheme requires that the two cavities are initially prepared in entangled one-photon generalized binomial states and exploits the passage of two appropriately prepared two-level atoms one in each cavity. The measurement of the ground state of both atoms is finally required when they exit the cavities. We also give a brief evaluation of the experimental feasibility of the scheme.

Quantum superpositions of clockwise and counterclockwise supercurrent states in the dynamics of a rf-SQUID exposed to a quantized electromagnetic field

The dynamical behavior of a superconducting quantum interference device (a rf-SQUID) irradiated by a single mode quantized electromagnetic field is theoretically investigated. Treating the SQUID as a flux qubit, we analyze the dynamics of the combined system within the low lying energy Hilbert subspace both in the asymmetric and in the symmetric SQUID potential configurations. We show that the temporal evolution of the system is dominated by an oscillatory behavior characterized by more than one, generally speaking, incommensurable Rabi frequencies whose expressions are explicitly given. We find that the external parameters may fixed in such a way to realize a control on the dynamical repla…

Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath

We apply the time-convolutionless (TCL) projection operator technique to the model of a central spin which is coupled to a spin bath via nonuniform Heisenberg interaction. The second-order results of the TCL method for the coherences and populations of the central spin are determined analytically and compared with numerical simulations of the full von Neumann equation of the total system. The TCL approach is found to yield an excellent approximation in the strong field regime for the description of both the short-time dynamics and the long time behavior.

A Realistic Proposal for the Observation of Zeno Phenomena in the Dynamics of Trapped Ions

A realistic experimental scheme for the observation of a continuous measurement Quantum Zeno Effect in the contest of single trapped ions is proposed. Our method relies on the nonlinearities characterizing the ionic Rabi frequency far from the Lamb-Dicke regime.

Landau-Majorana-Stuckelberg-Zener dynamics driven by coupling for two interacting qutrit systems

A time-dependent model of two interacting spin qutrits is analyzed is analyzed and solved. The two interacting qutrits are subjected to a longitudinal field linearly varying over time as in the Landau-Majorana-St\"uckelberg- Zener (LMSZ) scenario. Although a transverse field is absent, we show the occurrence of LMSZ transitions assisted by the coupling between the two spin-qutrits. Such a physical effect permits us to estimate experimentally the coupling strength between the spins and allows the generation of entangled states of the two qutrits by appropriately setting the slope of the ramp. Furthermore, the possibility of local and nonlocal control as well as the existence of dark states o…

A Possible Time-Dependent Generalization of the Bipartite Quantum Marginal Problem

In this work we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced states (marginals). The compatibility of such choice with a global unitary evolution is considered. For the non unitary case we propose a systematic method to reconstruct examples of master equations and address them to different physical scenarios.

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.

Coherent control of stimulated emission inside one-dimensional photonic crystals

In this paper, the quasinormal mode (QNM) theory is applied to discuss the quantum problem of an atom embedded inside a one-dimensional (1D) photonic band gap (PBG) cavity pumped by two counterpropagating laser beams. The e.m. field is quantized in terms of the QNMs in the 1D PBG and the atom modeled as a two-level system is assumed to be weakly coupled to just one of the QNMs. The main result of the paper is that the decay time depends on the position of the dipole inside the cavity, and can be controlled by the phase difference of the two laser beams.

Greenberger-Horne-Zeilinger-state Generation in Qubit-Chains via a Single Landau-Majorana-Stückelberg-Zener π/2-pulse

A protocol for generating Greenberger-Horne-Zeilinger states in a system of (Formula presented.) coupled qubits is proposed. The Hamiltonian model assumes (Formula presented.) -wise interactions between the (Formula presented.) qubits and the presence of a controllable time-dependent field acting upon one spin only. The dynamical problem is exactly solved thanks to the symmetries of the Hamiltonian model. The possibility of generating GHZ states simulating our physical scenario under both adiabatic and non-adiabatic conditions is within the reach of the experimentalists. This aspect is discussed in detail.

Unitary transfer of entanglement in multipartite two–level systems

Quantum-state manipulation via quantum nondemolition measurements in a two-dimensional trapped ion

The quantum nondemolition measurement is applied to a two-dimensional (2D) trapped-ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level system of the ion. The information about the ionic vibrational energy can be detected by the occupation probability of the internal electronic level. The substantial difference of the 2D model from the one-dimensional one is that two orthogonal beams have a fixed phase shift instead of statistical independence. As a result, the atomic Rabi oscillation is involved in the coherent superposition of two sub-Rabi oscillations induced by the corresponding driving beams. This means that, in the …

Breakdown of separability due to confinement

A simple system of two particles in a bidimensional configurational space S is studied. The possibility of breaking in S the time-independent Schrodinger equation of the system into two separated one-dimensional one-body Schrodinger equations is assumed. In this paper, we focus on how the latter property is countered by imposing such boundary conditions as confinement to a limited region of S and/or restrictions on the joint coordinate probability density stemming from the sign-invariance condition of the relative coordinate (an impenetrability condition). Our investigation demonstrates the reducibility of the problem under scrutiny into that of a single particle living in a limited domain …

STUDIO SU ALCUNI RESTI UMANI ENEOLITICI PROVENIENTI DAL SITO DI MAREDOLCE SAN CIRO (PALERMO)

Distillation of entanglement between distant systems by repeated measurements on an entanglement mediator

A recently proposed purification method, in which the Zeno-like measurements of a subsystem can bring about a distillation of another subsystem in interaction with the former, is utilized to yield entangled states between distant systems. It is shown that the measurements of a two-level system locally interacting with other two spatially separated not coupled subsystems, can distill entangled states from the latter irrespectively of the initial states of the two subsystems.

Geometric Phase Accumulation-Based Effects in the Quantum Dynamics of an Anisotropically Trapped Ion

New physical effects in the dynamics of an ion confined in an anisotropic two-dimensional Paul trap are reported. The link between the occurrence of such manifestations and the accumulation of geometric phase stemming from the intrinsic or controlled lack of symmetry in the trap is brought to light. The possibility of observing in laboratory these anisotropy-based phenomena is briefly discussed.

Heat Capacity and Entanglement Measure in a simple two-qubit model

A simple two-qubit model showing Quantum Phase Transitions as a consequence of ground state level crossings is studied in detail. Using the Concurrence of the system as an entanglement measure and heat capacity as a marker of thermodynamical properties, an analytical expression giving the latter in terms of the former is obtained. A protocol allowing an experimental measure of entanglement is then presented and compared with a related proposal recently reported by Wie\'sniak, Vedral and Brukner

Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems

We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical treatment transparently unveils the physical reasons for the occurrence of such a phenomenon, relating it to the dynamical invariance of the X structure of the initial state. The quantum correlations which asymptotically emerge in the system are investigated in detail in terms of the time evolution of the fidelity of the initial Werner state.

Coupling-assisted Landau-Majorana-Stückelberg-Zener transition in a system of two interacting spin qubits

We analyse a system of two interacting spin-qubits subjected to a Landau-Majorana-Stuckelberg-Zener (LMSZ) ramp. We prove that LMSZ transitions of the two spin-qubits are possible without an external transverse static field since its role is played by the coupling between the spin-qubits. We show how such a physical effect could be exploited to estimate the strength of the interaction between the two spin-qubits and to generate entangled states of the system by appropriately setting the slope of the ramp. Moreover, the study of effects of the coupling parameters on the time-behaviour of the entanglement is reported. Finally, our symmetry-based approach allows us to discuss also effects stem…

Measuring the mean value of vibrational observables in trapped ion systems

The theoretical foundations of a new general approach to the measurement problem of vibrational observables in trapped ion systems is reported. The method rests upon the introduction of a simple vibronic coupling structure appropriately conceived to link the internal ionic state measurement outcomes to the mean value of a motional variable of interest. Some applications are provided and discussed in detail, bringing to light the feasibility and the wide potentiality of the proposal.

Conditional generation of non-classical states in a nondegenerate two-photon micromaser: single-mode Fock states preparation. II

Abstract A conditional generation of single-mode Fock states in the framework of a non-degenerate two-photon micromaser theory is reported. The exact expression for the probability of success of the experiment is obtained. We show that it is possible to conjugate experimentally interesting values of this probability, with the generation of number states having a controllable high intensity. This objective is reached by constructing analytically detailed rules about the cavity state at t = 0 as well as the atom–field interaction times as functions of the available operating conditions. These rules play a central role in our Fock-state-building process, leading to an essential countering of t…

Driven Appearance and Disappearance of Quantum Zeno Effect in the Dynamics of a Four-level Trapped Ion

An example of constrained unitary quantum dynamics in the context of trapped ions is given. We study a laser driven four-level ion system confined in an isotropic three-dimensional Paul microtrap. Our main result is that when two independent controllable continuous measurement processes are simultaneously present, the unitary quantum dynamics of the system can be parametrically frozen into a one-dimensional Hilbert subspace (Quantum Zeno Effect) or constrained into a two-dimensional one, at will. Conditions under which one of the two processes acts upon the physical system inhibiting the effects due to the other one, are explicitly found and discussed (Hierarchically Controlled Dynamics).

Microscopic derivation of the Jaynes-Cummings model with cavity losses

In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.

A criterion for entanglement in two two-level systems

We prove a necessary and sufficient condition for the occurrence of entanglement in two two-level systems, simple enough to be of experimental interest. Our results are illustrated in the context of a spin star system analyzing the exact entanglement evolution of the central couple of spins.

Exactly solvable relativistic model with the anomalous interaction

A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron'ko-Stroganov model.

Entangling a Three High-Q Cavity System in a GHZ State

Generation of Non-Classical States through QND-like Processes

In the spirit of quantum nondemolition measurement we show that repeatedly measuring the atomic state of a trapped ion subjected to suitable vibronic couplings it is possible to extract interesting nonclassical states. The possibility of generating angular momentum Schrödinger cat is demonstrated.

Balance equations-based properties of the Rabi Hamiltonian

A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrodinger equation. The knowledge of such properties in the case of Rabi Hamiltonian is exploit to provide arguments to make easier the variational engineering of the ground state of this model.

Entanglement of distant superconducting quantum interference device rings

We consider two distant mesoscopic SQUID rings, approximated with two-level systems, interacting with two-mode microwaves. The Hamiltonian of the system is used to calculate its time evolution. The cases with microwaves which at t = 0 are in separable states (classically correlated) or entangled states (quantum mechanically correlated) are studied. It is shown that the Josephson currents in the two SQUID rings are also correlated.

Decoherence and robustness of parity-dependent entanglement in the dynamics of a trapped ion

We study the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion, Under particular conditions this entanglement depends on the parity of the total initial vibrational quanta. We study the robustness of this quantum coherence effect with respect to the presence of non-dissipative sources of decoherence, and of an imperfect initial state preparation.

Dzyaloshinskii-Moriya and dipole-dipole interactions affect coupling-based Landau-Majorana-Stückelberg-Zener transitions

It has been theoretically demonstrated that two spins (qubits or qutrits), coupled by exchange interaction only, undergo a coupling-based joint Landau-Majorana-St\"uckelberg-Zener (LMSZ) transition when a linear ramp acts upon one of the two spins. Such a transition, under appropriate conditions on the parameters, drives the two-spin system toward a maximally entangled state. In this paper, effects on the quantum dynamics of the two qudits, stemming from the Dzyaloshinskii-Moriya (DM) and dipole-dipole (d-d) interactions, are investigated qualitatively and quantitatively. The enriched Hamiltonian model of the two spins, shares with the previous microscopic one the same C2-symmetry which onc…

Step-by-Step Control of the Dynamics of a Superconducting QED-like System

We discuss the modus operandi of a theoretical scalable coupling scheme to control step by step the time evolution of a pair of flux qubits embedded in a lossy resonant cavity. The sequential interaction of each qubit with the quantized cavity mode is controlled by externally applied magnetic fluxes. Our analysis indicates that indirect qubit-qubit interactions, with the electromagnetic mode acting as a data bus, can be selectively performed and exploited both for the implementation of entangling gates and for the generation of states with a priori known characteristics.

Exact treatment of operator difference equations with nonconstant and noncommutative coefficients

We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.

Simulating quantum Brownian motion with single trapped ions

We study the open system dynamics of a harmonic oscillator coupled with an artificially engineered reservoir. We single out the reservoir and system variables governing the passage between Lindblad type and non-Lindblad type dynamics of the reduced system's oscillator. We demonstrate the existence of conditions under which virtual exchanges of energy between system and reservoir take place. We propose to use a single trapped ion coupled to engineered reservoirs in order to simulate quantum Brownian motion.

Dissipation and entanglement dynamics for two interacting qubits coupled to independent reservoirs

We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.

Theoretical analysis of a recent experiment on mesoscopic state superpositions in cavity QED

Quite recently quantum features exhibited by a mesoscopic field interacting with a single Rydberg atom in a microwave cavity has been observed [A. Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)]. In this paper we theoretically analyze all the phases of this articulated experiment considering from the very beginning cavity losses. Fully applying the theory of quantum open systems, our modelization succeeds in predicting fine aspects of the measured quantity, reaching qualitative and quantitative good agreement with the experimental results. This fact validates our theoretical approach based on the fundamental atom-cavity interaction model and simple mathematical structure of dissipative…

Population trapping due to cavity losses

In population trapping the occupation of a decaying quantum level keeps a constant non-zero value. We show that an atom-cavity system interacting with an environment characterized by a non-flat spectrum, in the non-Markovian limit, exhibits such a behavior, effectively realizing the preservation of nonclassical states against dissipation. Our results allow to understand the role of cavity losses in hybrid solid state systems and pave the way to the proper description of leakage in the recently developed cavity quantum electrodynamic systems.

Simulating open quantum systems with trapped ions

This paper focuses on the possibility of simulating the open system dynamics of a paradigmatic model, namely the damped harmonic oscillator, with single trapped ions. The key idea consists in using a controllable physical system, i.e. a single trapped ion interacting with an engineered reservoir, to simulate the dynamics of other open systems usually difficult to study. The exact dynamics of the damped harmonic oscillator under very general conditions is firstly derived. Some peculiar characteristic of the system’s dynamics are then presented. Finally a way to implement with trapped ion the specific quantum simulator of interest is discussed.

N-qubit states as points on the Bloch sphere

We show how the Majorana representation can be used to express the pure states of an N-qubit system as points on the Bloch sphere. We compare this geometrical representation of N-qubit states with an alternative one, proposed recently by the present authors.

Single and two-qubit dynamics in circuit QED architectures

In this paper we overview our researches on the generation and the control of entangled states in the framework of circuit quantum electrodynamics. Applications in the context of quantum computing and quantum information theory are discussed.

General Solution of a Second-Order Nonhomogenous Linear Difference Equation with Noncommutative Coefficients

The detailed construction of the general solution of a second-order nonhomogenous linear operator-difference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by studying some applications belonging to different mathematical contexts.

Bounds on mixed state entanglement

In the general framework of d 1 &times

Perturbative Treatment of the Evolution Operator Associated with Raman Couplings

Polynomial method to study the entanglement of pure N-qubit states

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the number of unentangled qubits of pure N-qubit states.

Superradiant Quantum Phase Transition for an Exactly Solvable Two-Qubit Spin-Boson Model

A spin-boson-like model with two interacting qubits is analysed. The model turns out to be exactly solvable since it is characterized by the exchange symmetry between the two spins. The explicit expressions of eigenstates and eigenenergies make it possible to analytically unveil the occurrence of first-order quantum phase transitions. The latter are physically relevant since they are characterized by abrupt changes in the two-spin subsystem concurrence, in the net spin magnetization and in the mean photon number.

Parametrizations of density matrices

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some r…

Master equations for two qubits coupled via a nonlinear mode

A microscopic master equation describing the dynamics of two qubits coupled via a nonlinear mediator is constructed supposing that the two qubits, as well as the nonlinear mode, interact, each with its own independent bosonic bath. Generally speaking the master equation derived in this way represents a more appropriate tool for studying the dynamics of open quantum systems. Indeed we show that it is more complex than the phenomenological master equation, constructed simply adding ad hoc dissipative terms.

Coarse grained and fine dynamics in trapped ion Raman schemes

A novel result concerning Raman coupling schemes in the context of trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems (in the interaction picture) can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamics. The second is a suitable correction restoring the {\em fine} dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level.

Resonant effects in a SQUID qubit subjected to nonadiabatic changes

By quickly modifying the shape of the effective potential of a double SQUID flux qubit from a single-well to a double-well condition, we experimentally observe an anomalous behavior, namely an alternance of resonance peaks, in the probability to find the qubit in a given flux state. The occurrence of Landau-Zener transitions as well as resonant tunneling between degenerate levels in the two wells may be invoked to partially justify the experimental results. A quantum simulation of the time evolution of the system indeed suggests that the observed anomalous behavior can be imputable to quantum coherence effects. The interplay among all these mechanisms has a practical implication for quantum…

Entangling two spatially separate cavities

A scheme for the transfer of entanglement among systems via successive coupling with an intermediate system is described. This method is applied to a simple experimental realizable situation for entangling two spatially separated cavities. In this scheme entanglement, initially stored in two modes of the first cavity, is transferred by an atom interacting successively with the cavities, into entanglement between two non resonant modes of the different cavities.

Radial coherent states for Dirac hydrogen-like atom

In this paper we use an su(2) representation of the radial eigenfunction of the Dirac hydrogen-like atom and we build the Glauber coherent states and the displacement operator coherent states. We also calculate the average values of some observables corresponding to these states.

Lindblad- and non-Lindblad-type dynamics of a quantum Brownian particle

The dynamics of a typical open quantum system, namely a quantum Brownian particle in a harmonic potential, is studied focussing on its non-Markovian regime. Both an analytic approach and a stochastic wave function approach are used to describe the exact time evolution of the system. The border between two very different dynamical regimes, the Lindblad and non-Lindblad regimes, is identified and the relevant physical variables governing the passage from one regime to the other are singled out. The non-Markovian short time dynamics is studied in detail by looking at the mean energy, the squeezing, the Mandel parameter and the Wigner function of the system.

Coherent control of stimulated emission inside one-dimensional Photonic Crystals

In this paper, the quasinormal mode (QNM) theory is applied to discuss the quantum problem of an atom embedded inside a one-dimensional (1D) photonic band gap (PBG) cavity pumped by two counterpropagating laser beams. The e.m. field is quantized in terms of the QNMs in the 1D PBG and the atom modeled as a two-level system is assumed to be weakly coupled to just one of the QNMs. The main result of the paper is that the decay time depends on the position of the dipole inside the cavity, and can be controlled by the phase difference of the two laser beams. © 2005 The American Physical Society

Competition between inter- and intra- molecular energy exchanges in a simple quantum model of a dimer

Abstract We propose a fully quantum model to describe the dynamics of a possible radiationless energy transfer process between identical and nearly localized molecules or monomers coupled through a dipole–dipole term. The system is studied as an environmentally isolated dimeric pair and we find that its dynamics exhibits a competition between the process ruling out the transfer of energy among different degrees of freedom of a given monomer and the one steering the intermolecular passage of excitations from a monomer to the other one. Such a competition is quantitatively characterized investigating on the temporal behaviour of quantum covariances of some couples of appropriate observables h…

Exact dynamics of XX central spin models

The dynamical behavior of a star network of spins, wherein each of N decoupled spins interact with a central spin through non uniform Heisenberg XX interaction is exactly studied. The time-dependent Schrodinger equation of the spin system model is solved starting from an arbitrary initial state. The resulting solution is analyzed and briefly discussed.

Dissipative effects on a generation scheme of a W state in an array of coupled Josephson junctions

The dynamics of an open quantum system, consisting of three superconducting qubits interacting with independent reservoirs, is investigated to elucidate the effects of the environment on a unitary generation scheme of W states (Migliore R et al 2006 Phys. Rev. B 74 104503). To this end a microscopic master equation is constructed and its exact resolution predicts the generation of a Werner-like state instead of the W state. A comparison between our model and a more intuitive phenomenological model is also considered, in order to find the limits of the latter approach in the case of structured reservoirs.

Interaction-free evolution in the presence of time-dependent Hamiltonians

The generalization of the concept of interaction-free evolutions (IFE) [A. Napoli, {\it et al.}, Phys. Rev. A {\bf 89}, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows for much more rich structures of interaction-free states and interaction-free subspaces. The general condition for the occurrence of IFE is found and exploited to analyze specific situations. Several examples are presented, each one associated to a class of Hamiltonians with specific features.

Cavity QED with a trapped ion in a leaky cavity

The dynamics of the interaction of a quantized cavity field and the vibronic degrees of freedom of a trapped ion is studied under realistic conditions by including cavity losses, spontaneous electronic transitions, and atomic nonlinearities. As long as spontaneous electronic transitions are negligible, analytical results are derived for describing the interaction of the trapped ion and the damped cavity field in the secular approximation. Under more general conditions, when the secular approximation breaks down and spontaneous emission effects become important, the dynamics of the system is studied by quantum-trajectory methods. As an example we demonstrate that, by exploiting the nonlinear…

Single-shot generation and detection of a two-photon generalized binomial state in a cavity

A "quasi-deterministic" scheme to generate a two-photon generalized binomial state in a single-mode high-Q cavity is proposed. We also suggest a single-shot scheme to measure the generated state based on a probe two-level atom that "reads" the cavity field. The possibility of implementing the schemes is discussed.

Freezing the dynamics of a rf SQUID qubit via its strong coupling to a quantized microwave field

In this paper we show the results concerning the study of the dynamics of a rf SQUID qubit exposed to a quantized monochromatic microwave source in the strong coupling limit. We bring out more details of the possibility both of controlling and hindering the oscillations between the two qubit flux states when we consider opportunely prepared initial field states. The importance of conceiving of such kinds of theoretical schemes in view of possible applications in the context of quantum computing is briefly discussed.

Dissipative effects on a scheme of generation of a W state in an array of coupled Josephson junctions

The dynamics of an open quantum system, consisting of three superconducting qubits interacting with independent reservoirs, is investigated to elucidate the effects of the environment on a unitary generation scheme of W states (Migliore R et al 2006 Phys. Rev. B 74 104503). To this end a microscopic master equation is constructed and its exact resolution predicts the generation of a Werner-like state instead of the W state. A comparison between our model and a more intuitive phenomenological model is also considered, in order to find the limits of the latter approach in the case of structured reservoirs.

Fluctuation theorems for non-Markovian quantum processes

Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical-like non-Markovian stochastic unravelling, which is demonstrated to lead to a correction of the standard entropic fluctuation theorem. This correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system: Due to memory e…

Interaction free and decoherence free states

An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical co…

On new ways of group methods for reduction of evolution-type equations

AbstractNew exact solutions of the evolution-type equations are constructed by means of a non-point (contact) symmetries. Also we analyzed the discrete symmetries of Maxwell equations in vacuum and decoupled ones to the four independent equations that can be solved independently.

Bell's inequality violation for entangled generalized Bernoulli states in two spatially separate cavities

We consider the entanglement of orthogonal generalized Bernoulli states in two separate single-mode high-$Q$ cavities. The expectation values and the correlations of the electric field in the cavities are obtained. We then define, in each cavity, a dichotomic operator expressible in terms of the field states which can be, in principle, experimentally measured by a probe atom that ``reads'' the field. Using the quantum correlations of couples of these operators, we construct a Bell's inequality which is shown to be violated for a wide range of the degree of entanglement and which can be tested in a simple way. Thus the cavity fields directly show quantum non-local properties. A scheme is als…

Elementary symmetric functions of two solvents of a quadratic matrix equations

Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.

Revealing non-classical behaviours in the oscillatory motion of a trapped ion

The possibility of revealing non-classical behaviours in the dynamics of a trapped ion via measurements of the mean value of suitable operators is reported. In particular we focus on the manifestation known as `` Parity Effect\rq\rq which may be observed \emph{directly measuring} the expectation value of an appropriate correlation operator. The experimental feasibility of our proposal is discussed.

Reconstruction of Hamiltonians from given time evolutions

In this paper we propose a systematic method to solve the inverse dynamical problem for a quantum system governed by the von Neumann equation: to find a class of Hamiltonians reproducing a prescribed time evolution of a pure or mixed state of the system. Our approach exploits the equivalence between an action of the group of evolution operators over the state space and an adjoint action of the unitary group over Hermitian matrices. The method is illustrated by two examples involving a pure and a mixed state.

Time Evolution of two distant SQUID rings irradiated with entangled electromagnetic field

Two distant mesoscopic SQUID rings are irradiated with two mode microwaves produced by the same source. The time evolution of the system is studied. The two microwave modes are correlated. It is shown that the currents tunnelling through the Josephson junctions in the distant rings, are also correlated.

Steering Distillation Processes through Zeno dynamics

A quantum system in interaction with a repeatedly measured one undergoes a nonunitary time evolution and is pushed into a subspace substantially determined by the two-system coupling. The possibility of suitably modifying such an evolution through quantum Zeno dynamics (i.e., the generalized quantum Zeno effect) addressing the system toward an a priori decided target subspace is illustrated. Applications and their possible realizations in the context of trapped ions are also discussed.

Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields

The quantum dynamics of a $\hat{\mathbf{J}}^2=(\hat{\mathbf{j}}_1+\hat{\mathbf{j}}_2)^2$-conserving Hamiltonian model describing two coupled spins $\hat{\mathbf{j}}_1$ and $\hat{\mathbf{j}}_2$ under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of $\hat{\mathbf{J}}^2$ is dynamically invariant and the Hamiltonian of the total system restricted to any one of such $(j_1+j_2)-|j_1-j_2|+1$ eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical…

Nonclassical effects in the dynamics of a two-mode cavity coupled to a two-level atom in the presence of damping

Cooling of Many-Body Systems via Selective Interactions

We propose a model describing $N$ spin-1/2 systems coupled through $N$-order homogeneous interaction terms, in presence of local time-dependent magnetic fields. This model can be experimentally implemented with current technologies in trapped ions and superconducting circuits. By introducing a chain of unitary transformations, we succeed in exactly converting the quantum dynamics of this system into that of $2^{N-1}$ fictitious spin-1/2 dynamical problems. We bring to light the possibility of controlling the unitary evolution of the $N$ spins generating GHZ states under specific time-dependent scenarios. Moreover, we show that by appropriately engineering the time-dependence of the coupling…

Entanglement dynamics in a spin star system

The implementation of more and more efficient nanodevices exploitable in applicative contexts like for example quantum computers often requires a highly challenging miniaturizing process aimed at packing a huge number of point-like basic elements whose dynamics mimics indeed that of a qubit. Stimulated by such a requirement, over the last few years theoretical schemes using the language of the spin ½ system models have been investigated. The main reason is that besides the simple dynamical behaviour of each elementary constituent these Hamiltonian models do indeed capture basic ingredients of several physical situations differing one another mainly for the numerical values of some relevant …

A microscopic monomeric mechanism for interpreting intrinsic optical bistability observed in Yb3+-doped bromide materials

We present a mechanism able to show intrinsic bistable behaviour involving single Yb3+ ions embedded into bromide lattices, in which intrinsic optical bistability (IOB) has been observed. The mechanism is based on the experimentally found coupling between the Yb3+ ion and the totally symmetric local mode of vibration of the [YbBr6]3- coordination unit. The model reproduces the IOB observed in CsCdBr3:1% Yb3+ and allows to understand the experimentally found presence of the phenomenon in the other bromides, but its absence in Cs3Lu2Cl9:Yb3+.

Zeno dynamics and high-temperature master equations beyond secular approximation

Complete positivity of a class of maps generated by master equations derived beyond the secular approximation is discussed. The connection between such class of evolutions and physical properties of the system is analyzed in depth. It is also shown that under suitable hypotheses a Zeno dynamics can be induced because of the high temperature of the bath.

Solution of the Lindblad equation in Kraus representation

The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix elements. The solution is then naturally given in an operator form, known as the Kraus representation. Following a few simple examples, the general applicability of the method is clarified.

Exactly solvable time-dependent pseudo-Hermitian su(1,1) Hamiltonian models

An exact analytical treatment of the dynamical problem for time-dependent 2x2 pseudo-hermitian su(1,1) Hamiltonians is reported. A class of exactly solvable and physically transparent new scenarios are identified within both classical and quantum contexts. Such a class is spanned by a positive parameter $\nu$ that allows to distinguish two different dynamical regimes. Our results are usefully employed for exactly solving a classical propagation problem in a guided wave optics scenario. The usefulness of our procedure in a quantum context is illustrated by defining and investigating the su(1,1) "Rabi" scenario bringing to light analogies and differences with the standard su(2) Rabi model. Ou…

Macroscopic jumps of the axial angular momentum variance of a bidimensionally trapped ion

Abstract The time evolution of the axial angular momentum [Lcirc] z of an ion confined in a bidimensional trap is investigated. We find that, under suitable initial conditions, the interaction of the ion with two properly configured classical laser beams induces a peculiar dynamical behaviour of the axial angular momentum fluctuations. We show, in fact, that there exists an instant of time at which the variance of [Lcirc] z undergoes variations proportional to N 2 further to a change of one quantum only in the initial total number N ≫ 1 of vibrational quanta. The non-classical origin of these macroscopic jumps is brought to the light and carefully discussed.

Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths

The dynamics of two interacting spins coupled to separate bosonic baths is studied. An analytical solution in Born approximation for arbitrary spectral density functions of the bosonic environments is found. It is shown that in the non-Markovian cases concurrence "lives" longer or reaches greater values.

Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation

A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. {\em et al.} 2007 Phys. Rev. A {\bf 75}, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation.

Stimulated Raman adiabatic passage in a $\Lambda$-system in the presence of quantum noise

We exploit a microscopically derived master equation for the study of STIRAP in the presence of decay from the auxiliary level toward the initial and final state, and compare our results with the predictions obtained from a phenomenological model previously used [P. A. Ivanov, N. V. Vitanov, and K. Bergmann, Phys. Rev. A 72, 053412 (2005)]. It is shown that our approach predicts a much higher efficiency. The effects of temperature are also taken into account, proving that in b-STIRAP thermal pumping can increase the efficiency of the population transfer.

New approach to describe two coupled spins in a variable magnetic field

We propose a method to describe the evolution of two spins coupled by hyperfine i nteraction in an external time- dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved exactly in a constant, appropriately oriented magnetic field. In order to t reat t he n onstationary d ynamical p roblem, we modify the time-dependent Schrödinger equation through a change of representation that, by exploiting an instantaneous (adiabatic) basis makes the time-dependent Hamiltonian diagonal at any time instant. The solution of the transformed time-dependent Schrödinger FRVBUJPO in the form of chronologically ordered exponents with transpar…

Coherent Control of Stimulated Emission inside one dimensional Photonic Crystals:Strong Coupling regime

The present paper discusses the stimulated emission, in strong coupling regime, of an atom embedded inside a one dimensional (1D) Photonic Band Gap (PBG) cavity which is pumped by two counter-propagating laser beams. Quantum electrodynamics is applied to model the atom-field interaction, by considering the atom as a two level system, the e.m. field as a superposition of normal modes, the coupling in dipole approximation, and the equations of motion in Wigner-Weisskopf and rotating wave approximations. In addition, the Quasi Normal Mode (QNM) approach for an open cavity is adopted, interpreting the local density of states (LDOS) as the local density of probability to excite one QNM of the ca…

Generation of Schrödinger Cats in Trapped Ions

A quantum system in interaction with a repeatedly measured one is subjected to a non-unitary time evolution provoking the decay of some states in favor of the remaining ones. Under appropriate hypotheses the system may be addressed exactly toward a quantum state or pushed into a pre-selected finite-dimensional subspace. On the basis of such a general strategy, we propose to exploit suitable vibronic couplings in order to ‘extract’ trapped ion center of mass states of motion characterized by well defined absolute value of an angular momentum projection. In particular, since it implies the simultaneous presence of opposite angular momentum projections, we show the realizability of Schrödinger…

Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits

In this paper we investigate the quantum dynamics of two spin-1 systems, $\vec{\textbf{S}}_1$ and $\vec{\textbf{S}}_2$, adopting a generalized $(\vec{\textbf{S}}_1+\vec{\textbf{S}}_2)^2$-nonconserving Heisenberg model. We show that, due to its symmetry property, the nine-dimensional dynamics of the two qutrits exactly decouples into the direct sum of two sub-dynamics living in two orthogonal four- and five-dimensional subspaces. Such a reduction is further strengthened by our central result consisting in the fact that in the four-dimensional dynamically invariant subspace, the two qutrits quantum dynamics, with no approximations, is equivalent to that of two non interacting spin 1/2's. The …

Reconstructing the vibrational state of a trapped ion

A new approach for reconstructing the vibrational quantum state of a trapped ion is proposed. The method rests upon the current ability of manipulating the trapped ion state and on the possibility of effectively measuring the scalar product of the two vibrational cofactors of a vibronic entangled state. The experimental feasibility of the method is briefly discussed.

Maximally entangled states of two flux qubits in a microwave cavity

Exact decoupling of two dipole-dipole interacting dimers

It is today possible to test many quantum mechanical predictions, even the most puzzling ones, setting up sophisticated experiments on exemplary "textbook" physical systems like a single atom or molecule or a single material quantum harmonic oscillator. It is therefore conceptually highly exciting to conceive simple but not trivial physical situations representable by exactly solvable hamiltonian models, in the grasp of the experimentalists. In this paper we study a physical system consisting of two coupled identical dimers. Each molecule possesses both fermionic and bosonic degrees of freedom and its internal non adiabatic dynamics is governed by a bilinear term conserving the total excita…

Sulla durata del ciclo vitale di Orobanche variegata e O. Rapum-genistae (Orobanchaceae)

Spin‐Chain‐Star Systems: Entangling Multiple Chains of Spin Qubits

We consider spin-chain-star systems characterized by N-wise many-body interactions between the spins in each chain and the central one. We show that such systems can be exactly mapped into standard spin-star systems through unitary transformations. Such an approach allows the solution of the dynamic problem of an XX$X X$ spin-chain-star model and transparently shows the emergence of quantum correlations in the system, based on the idea of entanglement between chains.

Quantum counter-propagation in open optical cavities via the quasi-normal-mode approach

By using the quasi-normal-mode (QNM) formalism in a second quantization scheme, the problem of the counter-propagation of electromagnetic fields inside optical cavities is studied. The links between QNM operators and canonical destruction and creation operators describing the external free field, as well as the field correlation functions, are found and discussed. An application of the theory is performed for open cavities whose refractive index satisfies symmetric properties.

Stimulated Raman adiabatic passage in an open quantum system: Master equation approach

A master equation approach to the study of environmental effects in the adiabatic population transfer in three-state systems is presented. A systematic comparison with the non-Hermitian Hamiltonian approach [N. V. Vitanov and S. Stenholm, Phys. Rev. A {\bf 56}, 1463 (1997)] shows that in the weak coupling limit the two treatments lead to essentially the same results. Instead, in the strong damping limit the predictions are quite different: in particular the counterintuitive sequences in the STIRAP scheme turn out to be much more efficient than expected before. This point is explained in terms of quantum Zeno dynamics.

Raccolta, conservazione e caratterizzazione agrobotanica delle antiche cultivar di Phaseolus vulgaris L. (Fabaceae) nel comprensorio dei Nebrodi (Sicilia)

Development of Sicilian bean core collection using morphological descriptors

Different species and varieties of bean, spread in Sicily, are representative of local agricultural practices, as result of a careful exploration. Many landraces have become obsolete due to the spread of commercial varieties, but are still cultivated in small areas of Nebrodi Mountains (ME-Italy) and are endangered. The Sicilian bean landraces are often poorly known but represent a genetic heritage to be preserve and to enhance. The ex situ conservation of Sicilian bean landraces was carried out in “Living Plants Germplasm Bank” of Ucria (ME-Italy), founded by the Nebrodi Regional Park, and in “Sicilian Plant Germplasm Repository” of STEBICEF Department - University of Palermo. Within ex si…

Quantum Computation with Generalized Binomial States in Cavity Quantum Electrodynamics

We study universal quantum computation in the cavity quantum electrodynamics (CQED) framework exploiting two orthonormal two-photon generalized binomial states as qubit and dispersive interactions of Rydberg atoms with high-$Q$ cavities. We show that an arbitrary qubit state may be generated and that controlled-NOT and 1-qubit rotation gates can be realized via standard atom-cavity interactions.

Anisotropy-Induced Effects in the Dynamics of an Ion Confined in a Two-Dimensional Paul Trap

We investigate the role of anisotropy in the dynamics of a single trapped ion interacting with two orthogonal laser beams, considering how it modifies a scheme for the generation of Schrödinger cat states and the so called parity effect in two-dimensional isotropic Paul traps. We find that anisotropy gives rise to a richer class for the generated states and to a larger number of observables sensitive to the parity of the number of excitation of the vibrational motion of the ion.

Coherent control of stimulated emission process inside one-dimensional photonic crystals

The control of the stimulated emission processes in a 1D PC is discussed. A non-canonical quantization is adopted (QNM). The decay rate of the stimulated emission depends on the cavity and phase-difference of the pumps.

Progress towards innovative and energy efficient logic circuits

Abstract The integration of superconductive nanowire logic memories and energy efficient computing Josephson logic is explored. Nanowire memories are based on the integration of switchable superconducting nanowires with a suitable magnetic material. These memories exploit the electro-thermal operation of the nanowires to efficiently store and read a magnetic state. In order to achieve proper memory operation a careful design of the nanowire assembly is necessary, as well as a proper choice of the magnetic material to be employed. At present several new superconducting logic families have been proposed, all tending to minimize the effect of losses in the digital Josephson circuits replacing …

Unitary Transfer of Entanglement in Multipartite Two-Level Systems

The dynamics of a system composed by two pairs of dipolarly coupled two-level atoms is exactly studied. We show that the initial entanglement stored in a couple of atoms not directly interacting is fully transferred to the other pair in a periodic way. The observability of this phenomenon in laboratory is briefly discussed both in terms of its temporal scale and of its stability against uncertainties in the geometrical parameters defining the physical system.

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic", case (same shape of the box through all the process) and the case with deformation.

Nondissipative Decoherence and Entanglement in the Dynamics of a Trapped Ion

We study the robustness of the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion with respect to the presence of non-dissipative sources of decoherence.

Preparation of macroscopically distinguishable superpositions of circular or linear oscillatory states of a bidimensionally trapped ion

A simple scheme for the generation of two different classes of bidimensional vibrational Schrodinger cat-like states of an isotropically trapped ion is presented. We show that by appropriately adjusting an easily controllable parameter having a clear physical meaning, the states prepared by our procedure are quantum superpositions of either vibrational axial angular momentum eigenstates or Fock states along two orthogonal directions.

Radon transform as a set of probability distributions

It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.

Diffusion and transfer of entanglement in an array of inductively coupled flux qubits

A theoretical scheme to generate multipartite entangled states in a Josephson planar-designed architecture is reported. This scheme improves the one published in [Phys. Rev. B 74, 104503 (2006)] since it speeds up the generation of W entangled states in an MxN array of inductively coupled Josephson flux qubits by reducing the number of necessary steps. In addition, the same protocol is shown to be able to transfer the W state from one row to the other.

An algebraic approach to the study of multipartite entanglement

A simple algebraic approach to the study of multipartite entanglement for pure states is introduced together with a class of suitable functionals able to detect entanglement. On this basis, some known results are reproduced. Indeed, by investigating the properties of the introduced functionals, it is shown that a subset of such class is strictly connected to the purity. Moreover, a direct and basic solution to the problem of the simultaneous maximization of three appropriate functionals for three-qubit states is provided, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of GHZ-states.

One-dimensional quantum-spin—phonon solitons

The quantum dynamics of a compressible harmonic chain of $N$ two-level atoms strongly interacting with the phonons of the lattice is investigated. Two types of mixed excitations are discussed which propagate through the lattice exhibiting solitonic properties. The first type of solitonlike excitation describes the motion of the wall separating two magnetoelastic domains. This transports less energy than the second type of solitonlike excitation which describes the motion of a single spin reversal in the chain. An explicit expression is obtained for the speed of these excitations as a function of an appropriate shape parameter $h$. These results are obtained by approximate self-consistent in…

Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED

A high-fidelity scheme to generate N-photon generalized binomial states (NGBSs) in a single-mode high-Q cavity is proposed. A method to construct superpositions of exact orthogonal NGBSs is also provided. It is then shown that these states, for any value of N, may be used for a realization of a controlled-NOT gate, based on the dispersive interaction between the cavity field and a control two-level atom. The possible implementation of the schemes is finally discussed.

Stimulated emission control in Photonic Crystals: Strong coupling regime in QNM approach

Stimulated emission, in strong coupling regime, in a one dimensional photonic crystals is described by considering two counter-propagating pumps. Quasi normal mode approach is used and coherent control of the Rabi splitting is discussed.

Analytically solvable 2×2 PT -symmetry dynamics from su(1,1)-symmetry problems

A protocol for explicitly constructing the exact time-evolution operators generated by $2\ifmmode\times\else\texttimes\fi{}2$ time-dependent $PT$-symmetry Hamiltonians is reported. Its mathematical applicability is illustrated with the help of appropriate examples. The physical relevance of the proposed approach within gain-loss system scenarios, like two coupled waveguides, is discussed in detail.

Entanglement and heat capacity in a two-atom Bose–Hubbard model

Abstract We show that a two-atom Bose–Hubbard model exhibits three different phases in the behavior of thermal entanglement in its parameter space. These phases are demonstrated to be traceable back to the existence of level crossings in the ground state of the same system. Significant similarities between the behaviors of thermal entanglement and heat capacity in the parameter space are brought to light thus allowing to interpret the occurrence and the meaning of all these three phases.

Generation of Glauber coherent state Superpositions via Unitary Transformations

Dynamical stabilization of spin systems in time-dependent magnetic fields

The quantum dynamics of a spin system subjected to a Rabi magnetic field configuration modified by a weak oscillating field along the Z-axis is investigated. We show that when the Rabi frequency is appropriately matched with the frequency of the perturbative field, the spin system exhibits a dynamical stabilization phenomenon defined as the tendency to occupy a fixed quantum superposition during a finite period of time.

Analytically solvable Hamiltonians for quantum two-level systems and their dynamics

A simple systematic way of obtaining analytically solvable Hamiltonians for quantum two-level systems is presented. In this method, a time-dependent Hamiltonian and the resulting unitary evolution operator are connected through an arbitrary function of time, furnishing us with new analytically solvable cases. The method is surprisingly simple, direct, and transparent and is applicable to a wide class of two-level Hamiltonians with no involved constraint on the input function. A few examples illustrate how the method leads to simple solvable Hamiltonians and dynamics.

Dynamics of a harmonic oscillator coupled with a Glauber amplifier

A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional subspaces. Resorting to the Jordan-Schwinger map, the dynamical problem within each invariant subspace may be traced back to an effective SU(2) Hamiltonian model expressed in terms of spin variables only. This circumstance allows to analytically solve the dynamical problem and thus to study the exact dynamics of the oscillator-amplifier system under specific time-dependent scenarios. Peculiar physical effects are brought to light by comparing the dynamics…

Quantum Nondemolition Measurement and Quantum State Manipulation in Two Dimensional Trapped Ion

An extension of QNDmeasuremen t of the vibrational energy of the trapped ion from one dimensional case to the bidimensional one is presented. Our approach exploits the fixed phase difference existing between the two orthogonal and appropriately configured classical laser beams determining the vibronic coupling. We in fact show that this phase difference may play the role of an adjustable external parameter which allows to optimize the measurement scheme itself in terms of both precision and sensitivity. Our proposal provides a cooling method for the trapped ion from the vibrational thermal state. Due to the coherent superposition of two sub Rabi oscillations, the Rabi frequency degeneration…

Thermal localizable entanglement in a simple multipartite system

The quantum correlations present in a system of three coupled spins 12 in a thermal state are investigated. Localizable entanglement, as well as concurrence function, is exactly evaluated. The results obtained show the existence of a temperature range corresponding to which it is impossible to localize entanglement.

NON-MARKOVIAN DYNAMICS OF CAVITY LOSSES

We provide a microscopic derivation for the non-Markovian master equation for an atom-cavity system with cavity losses and show that they can induce population trapping in the atomic excited state, when the environment outside the cavity has a non-flat spectrum. Our results apply to hybrid solid state systems and can turn out to be helpful to find the most appropriate description of leakage in the recent developments of cavity quantum electrodynamics.

Loss induced collective subradiant Dicke behaviour in a multiatom sample

The exact dynamics of $N$ two-level atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity is reported. Stationary radiation trapping effects are found and very transparently interpreted in the context of our approach. We prove that initially injecting one excitation only in the $N$ atoms-cavity system, loss mechanisms asymptotically drive the matter sample toward a long-lived collective subradiant Dicke state. The role played by the closeness of the $N$ atoms with respect to such a cooperative behavior is brought to light and carefully discussed.

Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla

In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system&ndash

A single atom-based generation of Bell states of two cavities

A new conditional scheme for generating Bell states of two spatially separated high-Q cavities is reported. Our method is based on the passage of one atom only through the two cavities. A distinctive feature of our treatment is that it incorporates from the very beginning the unavoidable presence of fluctuations in the atom-cavity interaction times. The possibility of successfully implementing our proposal against cavity losses and atomic spontaneous decay is carefully discussed.

Resetting of a planar superconducting quantum memory

We consider and analyze a scheme for the reset of a M × N planar array of inductively coupled Josephson flux qubits. We prove that it is possible to minimize the resetting time of an arbitrary chosen row of qubits by properly switching on and off the coupling between pairs of qubits belonging to the same column. In addition, the analysis of the time evolution of the array allows us to single out the class of generalized W states which can be successfully reset.

An application of the arithmetic euler function to the construction of nonclassical states of a quantum harmonic oscillator

Abstract All quantum superpositions of two equal intensity coherent states exhibiting infinitely many zeros in their Fock distributions are explicitly constructed and studied. Our approach is based on results from number theory and, in particular, on the properties of arithmetic Euler function. The nonclassical nature of these states is briefly pointed out. Some interesting properties are brought to light.

A quantum particle in a box with moving walls

We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.

Three-mode two-boson Jaynes–Cummings model in trapped ions

In this paper, we analyse a two-boson three-mode Jaynes–Cummings model which can be implemented in the context of trapped ions. The symmetries of the Hamiltonian are brought to light and analysed in detail in order to solve the eigenvalue problem. The calculation of the time evolution operator shows the possibility of realizing interesting applications, such as the generation of nonclassical states.

Governing survival probabiity to distill quantum states

Dynamical behaviour of an XX central spin model through Bethe ansatz techniques

Following the Bethe ansazt procedure the exact dynamics of an XX central spin model is revealed. Particular initial conditions are analyzed and the consequent time evolution is compared with the exact solution obtained by solving the time-dependent Schrudinger equation. The interest towards spin systems and in particular central spin systems, is motivated by the recent developments in more applicative contexts.

Dynamics of a single trapped ion in an optical underdamped cavity

The dynamics of a single trapped ion placed inside a high Q optical cavity is studied in presence of cavity losses and far from the Lamb-Dicke regime. In the underdamped cavity limit, analytical results for describing the dynamics of the system are derived making use of the secular approximation. Our method allows to obtain analytical expressions for the time evolution of the joint vibration-photon number distribution and for the occupation probability of the upper electronic state of the ion.

Quantum signatures in the dynamics of two dipole-dipole interacting soft dimers

The quantum covariances of physically transparent pairs of observables relative to two dimers hosted in a solid matrix are exactly investigated in the temporal domain. Both dimers possess fermionic and bosonic degrees of freedom and are dipolarly coupled. We find out and describe clear signatures traceable back to the presence and persistence of quantum coherence in the time evolution of the system. Manifestations of a competition between intramolecular and intermolecular energy migration mechanisms are brought to light. The experimental relevance of our results is briefly commented.

Nonlocal properties of entangled two-photon generalized binomial states in two separate cavities

We consider entangled two-photon generalized binomial states of the electromagnetic field in two separate cavities. The nonlocal properties of this entangled field state are analyzed by studying the electric field correlations between the two cavities. A Bell's inequality violation is obtained using an appropriate dichotomic cavity operator, that is in principle measurable.

Classes of Exactly Solvable Generalized Semi-Classical Rabi Systems

The exact quantum dynamics of a single spin-1/2 in a generic time-dependent classical magnetic field is investigated and compared with the quantum motion of a spin-1/2 studied by Rabi and Schwinger. The possibility of regarding the scenario studied in this paper as a generalization of that considered by Rabi and Schwinger is discussed and a notion of time-dependent resonance condition is introduced and carefully legitimated and analysed. Several examples help to disclose analogies and departures of the quantum motion induced in a generalized Rabi system with respect to that exhibited by the spin-1/2 in a magnetic field precessing around the $z$-axis. We find that, under generalized resonanc…

Quantum plasmonics with multi-emitters: application to stimulated Raman adiabatic passage

We construct a mode-selective effective model describing the interaction of the localised surface plasmon polaritons (LSPs) supported by a spherical metal nanoparticle (MNP) with N quantum emitters (QEs) in an arbitrary geometric arrangement. Simplifying previously presented procedures, we develop a formulation in which the field response in the presence of the MNP can be decomposed into orthogonal modes, expanding the Green tensor of the system in the spherical vector harmonics basis and using the generalized global Löwdin orthogonalization algorithm. We investigate the possibility of using the LSPs as mediators of an efficient control of population transfer between two QEs. We show that a…

Parity effects with single trapped ions

Selective reset of a chain of interacting superconducting qubits

We propose and analyze a scheme for the selective reset of a chain of inductively coupled Josephson flux qubits initially prepared in a multipartite entangled state. The possibility of controlling at will the coupling between two prefixed qubits is exploited to drive a "generalized W state" to a factorized state with only one qubit in the excited state and all the other qubits in their own ground states.

New Quantum Effects in the Dynamics of a Two-mode Field Coupled to a Two-level Atom

Abstract The dynamics of a degenerate two-mode electromagnetic field coupled to a single two-level atom is investigated both analytically and numerically. New quantum effects are discussed concerning the time dependence of the photon number and of its fluctuations, assuming that at t = 0 one of the modes is coherent and the other is empty. The field dynamics are dominated by oscillatory net exchanges of a large number of photons between the two modes, displaying amplitude decay. Over a longer time scale, revivals and collapses in the field populations take place. The time scales of these phenomena are much larger than those of the atomic Rabi oscillations decay. Moreover, the system attains…

Quantized electromagnetic fields as control tools for flux qubits

Oscillations of the purity in the repeated-measurement-based generation of quantum states

Repeated observations of a quantum system interacting with another one can drive the latter toward a particular quantum state, irrespectively of its initial condition, because of an {\em effective non-unitary evolution}. If the target state is a pure one, the degree of purity of the system approaches unity, even when the initial condition of the system is a mixed state. In this paper we study the behavior of the purity from the initial value to the final one, that is unity. Depending on the parameters, after a finite number of measurements, the purity exhibits oscillations, that brings about a lower purity than that of the initial state, which is a point to be taken care of in concrete appl…

Robust stationary entanglement of two coupled qubits in independent environments

The dissipative dynamics of two interacting qubits coupled to independent reservoirs at nonzero temperatures is investigated, paying special attention to the entanglement evolution. The counter-rotating terms in the qubit-qubit interaction give rise to stationary entanglement, traceable back to the ground state structure. The robustness of this entanglement against thermal noise is thoroughly analyzed, establishing that it can be detected at reasonable experimental temperatures. Some effects linked to a possible reservoir asymmetry are brought to light.

Bounds on bipartite entanglement from fixed marginals

We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of candidates for maximally entangled mixed states with respect to fixed marginals for two qudits. Interestingly, it turns out such states are always quasidistillable. Moreover, they are extremal in the convex set of two qudit states with fixed marginals. Our observations are supported by numerical analysis.

Generation of multipartite entangled states in Josephson architectures

We propose and analyze a scheme for the generation of multipartite entangled states in a system of inductively coupled Josephson flux qubits. The qubits have fixed eigenfrequencies during the whole process in order to minimize decoherence effects and their inductive coupling can be turned on and off at will by tuning an external control flux. Within this framework, we will show that a W state in a system of three or more qubits can be generated by exploiting the sequential one by one coupling of the qubits with one of them playing the role of an entanglement mediator.

Realization of a space reversal operator

In this paper we propose the realization of a bosonic-fermionic interaction in the context of trapped ions whose effect upon the ion center of mass degrees of freedom is properly speaking a spatial inversion. The physical system and its features are accurately described and some applications are briefly discussed.

Interaction-free evolving states of a bipartite system

We show that two interacting physical systems may admit entangled pure or non separable mixed states evolving in time as if the mutual interaction hamiltonian were absent. In this paper we define these states Interaction Free Evolving (IFE) states and characterize their existence for a generic binary system described by a time independent Hamiltonian. A comparison between IFE subspace and the decoherence free subspace is reported. The set of all pure IFE states is explicitly constructed for a non homogeneous spin star system model.

Proposal of a Computational Approach for Simulating Thermal Bosonic Fields in Phase Space

When a quantum field is in contact with a thermal bath, the vacuum state of the field may be generalized to a thermal vacuum state, which takes into account the thermal noise. In thermo field dynamics, this is realized by doubling the dimensionality of the Fock space of the system. Interestingly, the representation of thermal noise by means of an augmented space is also found in a distinctly different approach based on the Wigner transform of both the field operators and density matrix, which we pursue here. Specifically, the thermal noise is introduced by augmenting the classical-like Wigner phase space by means of Nos&eacute

Riccati equation-based generalization of Dawson's integral function

A new generalization of Dawson's integral function based on the link between a Riccati nonlinear differential equation and a second-order ordinary differential equation is reported. The MacLaurin expansion of this generalized function is built up and to this end an explicit formula for a generic cofactor of a triangular matrix is deduced.

Governing Survival Probability to Distill Quantum States

A quantum system interacting with a repeatedly measured one undergoes a nonunitary time evolution pushing it into some specific subspaces. We deeply investigate the origin of the relevant selection rule, bringing to the light its connection with the survival probability related with the two-system interaction. The possibility of inducing an effective dynamics in the distilled subspace just during the distillation process is demonstrated.

A continued fraction based approach for the Two-photon Quantum Rabi Model

We study the Two Photon Quantum Rabi Model by way of its spectral functions and survival probabilities. This approach allows numerical precision with large truncation numbers, and thus exploration of the spectral collapse. We provide independent checks and calibration of the numerical results by studying an exactly solvable case and comparing the essential qualitative structure of the spectral functions. We stress that the large time limit of the survival probability provides us with an indicator of spectral collapse, and propose a technique for the detection of this signal in the current and upcoming quantum simulations of the model. E.L. acknowledges fruitful discussions with D. Braak. I.…

Effective Landau-Zener transitions in circuit dynamical Casimir effect with time-varying modulation frequency

We consider the dissipative single-qubit circuit QED architecture in which the atomic transition frequency undergoes a weak external time-modulation. For sinusoidal modulation with linearly varying frequency we derive effective Hamiltonians that resemble the Landau-Zener problem of finite duration associated to a two- or multi-level systems. The corresponding off-diagonal coupling coefficients originate either from the rotating or the counter-rotating terms in the Rabi Hamiltonian, depending on the values of the modulation frequency. It is demonstrated that in the dissipation less case one can accomplish almost complete transitions between the eigenstates of the bare Rabi Hamiltonian even f…

Maximally entangled states of N spatially separated cavities

Entangling two uncoupled flux qubits via their sequential interaction with a quantized electromagnetic field

A theoretical scheme for the generation of maximally entangled states of two superconducting flux qubits via their sequential interaction with a monochromatic quantum field is presented. The coupling of the qubits with the quantized field can be tuned on and off resonance by modulating the effective Josephson energy of each qubit via an externally applied magnetic flux. The system operates in such a way as to transfer the entanglement from a bipartite field-qubit subsystem to the two qubits. This scheme is attractive in view of the implementation of practical quantum processing systems.

The physical origin of a photon-number parity effect in cavity quantum electrodynamics

Abstract The rapidly increasing capability to modulate the physicochemical properties of atomic groups and molecules by means of their coupling to radiation, as well as the revolutionary potential of quantum computing for materials simulation and prediction, fuel the interest for non-classical phenomena produced by atom-radiation interaction in confined space. One of such phenomena is a “parity effect” that arises in the dynamics of an atom coupled to two degenerate cavity field modes by two-photon processes and manifests itself as a strong dependence of the field dynamics on the parity of the initial number of photons. Here we identify the physical origin of this effect in the quantum corr…

Influence of dissipation on the extraction of quantum states via repeated measurements

A quantum system put in interaction with another one that is repeatedly measured is subject to a non-unitary dynamics, through which it is possible to extract subspaces. This key idea has been exploited to propose schemes aimed at the generation of pure quantum states (purification). All such schemes have so far been considered in the ideal situations of isolated systems. In this paper, we analyze the influence of non-negligible interactions with environment during the extraction process, with the scope of investigating the possibility of purifying the state of a system in spite of the sources of dissipation. A general framework is presented and a paradigmatic example consisting of two inte…

Dynamics of quantum discord of two coupled spin-1/2’s subjected to time-dependent magnetic fields

Abstract We describe the dynamics of quantum discord of two interacting spin-1/2’s subjected to controllable time-dependent magnetic fields. The exact time evolution of discord is given for various input mixed states consisting of classical mixtures of two Bell states. The quantum discord manifests a complex oscillatory behaviour in time and is compared with that of quantum entanglement, measured by concurrence. The interplay of the action of the time-dependent magnetic fields and the spin-coupling mechanism in the occurrence and evolution of quantum correlations is examined in detail.

Symmetries and Supersymmetries in Trapped Ion Hamiltonian Models

Dissipative dynamics of two coupled qubits: a short review of some recent results

In this paper, we review some results concerning the dissipative dynamics of two coupled qubits interacting with independent reservoirs. In particular, we focus on the role of counter-rotating terms in the qubit-qubit coupling, showing that their presence is the origin of stationary entanglement, which also turns out to be robust with respect to temperature. We also discuss the performances of different non-Markovian approaches in the description of the qubit-qubit dynamics, by considering a simplified exactly solvable Hamiltonian model.

Nonclassical correlations in superconducting circuits

A key step on the road map to solid-state quantum information processing (and to a deeper understanding of many counterintuitive aspects of quantum mechanics) is the generation and manipulation of nonclassical correlations between different quantum systems. Within this framework, we analyze the possibility of generating maximally entangled states in a system of two superconducting flux qubits, as well as the effect of their own environments on the entanglement dynamics. The analysis reported here confirms that the phenomena of sudden birth and sudden death of the entanglement do not depend on the particular measure of the entanglement adopted.

Intraenvironmental correlations in the ground state of a nonisolated two-state particle

The existence of entanglement in the ground state of a two-level particle coupled to a bosonic environment is proved. The quantum covariances of pairs of simple dynamical variables relative to different subsystems are explicitly shown to be bounded. Physically interpretable conditions for the occurrence of weak intraenvironmental correlations are reported and discussed. The potentialities of our treatment are briefly put into evidence.

Primi dati sulla coltivazione del fagiolo azuki (Vigna angularis) e del fagiolo indiano (V. radiata) nell'Orto botanico di Palermo

Entanglement sudden death and sudden birth in two uncoupled spins

We investigate the entanglement evolution of two qubits interacting with a common environment trough an Heisenberg XX mechanism. We reveal the possibility of realizing the phenomenon of entanglement sudden death as well as the entanglement sudden birth acting on the environment. Such analysis is of maximal interest at the light of the large applications that spin systems have in quantum information theory.

Scaling of non-Markovian Monte Carlo wave-function methods

We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values of arbitrary operators of interest can be calculated, all the quantities in the equation being easily obtainable from the scaled Monte Carlo simulations. In the optimal case, the scaling method can be used, within the weak coupling approximation, to reduce the size of the generated Monte Carlo ensemble by several orders of magnitude. Thus, the developed method allows faster simulations and makes it possible to solve the dynamics of the certain class of no…

Exact treatment of linear difference equations with noncommutative coefficients

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.

Revealing Anisotropy in a Paul Trap Through Berry Phase

When an ion confined in an anisotropic bidimensional Paul trap is subjected to a laser beam oriented along an arbitrary direction, the interaction between its electronic and vibrational degrees of freedom is described by a time-dependent Hamiltonian model as a consequence of the lack of symmetry. Appropriately choosing the laser frequency, the Hamiltonian model turns out to be sinusoidally oscillating at the difference between the proper frequencies of the center of mass of the ion. Thus, if the anisotropy of the trap is sufficiently small, the evolution of the system can be considered as adiabatic. In the context of this physical situation we have calculated the Berry phase acquired in a c…

Detuning effects in STIRAP processes in the presence of quantum noise

The Stimulated Raman adiabatic passage (STIRAP) in three-state systems in the presence of quantum noise is considered. A comparison is made between different models, one based on a phenomenological introduction of decays, one traceable back to a microscopic description of the system-environment interaction. Effects related, to off-resonance in the coupling between the involved states are considered.

Quantum theory of heating of a single trapped ion

The heating of trapped ions due to the interaction with a {\it quantized environment} is studied {\it without performing the Born-Markov approximation}. A generalized master equation local in time is derived and a novel theoretical approach to solve it analytically is proposed. Our master equation is in the Lindblad form with time dependent coefficients, thus allowing the simulation of the dynamics by means of the Monte Carlo Wave Function (MCWF) method.

Unitary Representations of Quantum Superpositions of two Coherent States and beyond

The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results are briefly outlined.

An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.

Zeno-like phenomena in STIRAP processes

The presence of a continuous measurement quantum Zeno effect in a stimulated Raman adiabatic passage is studied, exploring in detail a sort of self-competition of the damping, which drives the system toward a loss of population and, at the same time, realizes the conditions for optimizing the adiabatic passage.

Effective hamiltonian approach to the non-Markovian dynamics in a spin-bath

We investigate the dynamics of a central spin that is coupled to a bath of spins through a non-uniform distribution of coupling constants. Simple analytical arguments based on master equation techniques as well as numerical simulations of the full von Neumann equation of the total system show that the short-time damping and decoherence behaviour of the central spin can be modelled accurately through an effective Hamiltonian involving a single effective coupling constant. The reduced short-time dynamics of the central spin is thus reproduced by an analytically solvable effective Hamiltonian model.

Nonunitary generation of nonclassical states of a bidimensional harmonic oscillator

A scheme for generating quantum superpositions of macroscopically distinguishable states of the vibrational motion of a bidimensionally trapped ion is reported. We show that these states possess highly nonclassical properties controllable by an adjustable parameter simply related to the initial condition of the confined system

Nonclassical correlations in superconducting circuits

A key step on the road map to solid-state quantum information processing (and to a deeper understanding of many counterintuitive aspects of quantum mechanics) is the generation and manipulation of nonclassical correlations between different quantum systems. Within this framework, we analyze the possibility of generating maximally entangled states in a system of two superconducting flux qubits, as well as the effect of their own environments on the entanglement dynamics. The analysis reported here confirms that the phenomena of sudden birth and sudden death of the entanglement do not depend on the particular measure of the entanglement adopted.

Generalized Interaction-Free Evolutions

A thorough analysis of the evolutions of bipartite systems characterized by the \lq effective absence\rq\, of interaction between the two subsystems is reported. First, the connection between the concepts underlying Interaction-Free Evolutions (IFE) and Decoherence-Free Subspaces (DFS) is explored, showing intricate relations between these concepts. Second, starting from this analysis and inspired by a generalization of DFS already known in the literature, we introduce the notion of generalized IFE (GIFE), also providing a useful characterization that allows to develop a general scheme for finding GIFE states.

BUILDING AN ENTANGLEMENT MEASURE ON PHYSICAL GROUND

We introduce on physical grounds a new measure of multipartite entanglement for pure states. The function we define is discriminant and monotone under LOCC and moreover can be expressed in terms of observables of the system.

Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator

We use the exact solution for the damped harmonic oscillator to discuss some relevant aspects of its open dynamics often mislead or misunderstood. We compare two different approximations both referred to as Rotating Wave Approximation. Using a specific example, we clarify some issues related to non--Markovian dynamics, non--Lindblad type dynamics, and positivity of the density matrix.

Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature

This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling…

Analytical and numerical analysis of the atom–field dynamics in non-stationary cavity QED

We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field–atom coupling on the photon generation from vacuum via the dynamical Casimir effect.

JOSEPHSON MESOJUNCTIONS AS DETECTORS OF LOW-INTENSITY QUANTIZED COHERENT FAR-INFRARED FIELDS

We show that the quantum nature of a mesoscopic Josephson junction may be exploited for detecting low-intensity electromagnetic quantized fields. In particular we prove that intensity and phase of single-mode quantized coherent field may be reconstructed measuring amplitude and quantum noise of the first quantum Shapiro step occurring in the I-V characteristic of the ultrasmall Josephson junction.

W-like states of N uncoupled spins 1/2

The exact dynamics of a disordered spin star system, describing a central spin coupled to N distinguishable and non interacting spins 1/2, is reported. Exploiting their interaction with the central single spin system, we present possible conditional schemes for the generation of W-like states, as well as of well-defined angular momentum states, of the N uncoupled spins. We provide in addition a way to estimate the coupling intensity between each of the N spins and the central one. Finally the feasibility of our procedure is briefly discussed.

Quantum Zeno subspaces induced by temperature

We discuss the partitioning of the Hilbert space of a quantum system induced by the interaction with another system at thermal equilibrium, showing that the higher the temperature the more effective is the formation of Zeno subspaces. We show that our analysis keeps its validity even in the case of interaction with a bosonic reservoir, provided appropriate limitations of the relevant bandwidth.

A new monomeric interpretation of intrinsic optical bistability observed in Yb3+-doped bromide materials

We present a mechanism able to show intrinsic bistable behaviour involving single Yb3+ ions embedded into bromide lattices, in which intrinsic optical bistability (IOB) has been observed. The mechanism is based on the experimentally found coupling between the Yb3+ ion and the totally symmetric local mode of vibration of the [YbBr6]3- coordination unit. The model reproduces the IOB observed in CsCdBr3:1% Yb3+ and allows to understand the experimentally found presence of the phenomenon in the other bromides, but its absence in Cs3Lu2Cl9:Yb3+.

Second quantization and Atomic Spontaneous Emission inside 1D Photonic Crystals via Quasi Normal Modes approach

Generation of Pair Coherent States in Two-dimensional Trapped Ion

We consider a two-dimensional (2D) trapped ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level of the ion. Due to the coherent superposition of two sub-Rabi oscillations involved in the bimodal vibrations, the Rabi frequency degeneration and offset may occur in this model. This provides the possibility of generating the pair coherent state in the 2D trapped ion.

A CASE OF BIPARTITE PATELLA IN A PALEOCHRISTIAN NECROPOLIS IN MARSALA (ITALY)

Dissipation-induced stationary entanglement in dipole-dipole interacting atomic samples

The dynamics of two two-level dipole-dipole interacting atoms coupled to a common electro-magnetic bath and closely located inside a lossy cavity, is reported. Initially injecting only one excitation in the two-atom cavity system, loss mechanisms asymptotically drive the matter sample toward a stationary maximally entangled state. The role played by the closeness of the two atoms, with respect to such a cooperative behavior, is carefully discussed. Stationary radiation trapping effects are found and transparently interpreted.

Unitary decoupling treatment of a quadratic bimodal cavity quantum electrodynamics model

We consider a two-photon quantum model of radiation–matter interaction between a single two-level atom and a degenerate bimodal high-Q cavity field. Within this tripartite system, the explicit construction of two collective radiation modes, one of which is freely evolving and the other one quadratically coupled to the matter subsystem, is reported. The meaning and advantages of such a decoupling treatment are carefully discussed.

Quasi-Normal Frequencies in Open Cavities: An Application to Photonic Crystals

The electromagnetic field in an optical open cavity is analyzed in the framework of the Quasi-Normal Modes theory. The role of the complex quasi-normal frequencies in the transmission coefficient and their link with the density of quasi-modes function is clarified. An application to a quarter-wave symmetric one-dimensional photonic crystals is discussed to illustrate the usefulness and the meaning of our results.

Non-Markovian Wave Function Simulations of Quantum Brownian Motion

The non-Markovian wave function method (NMWF) using the stochastic unravelling of the master equation in the doubled Hilbert space is implemented for quantum Brownian motion. A comparison between the simulation and the analytical results shows that the method can be conveniently used to study the non-Markovian dynamics of the system.

A new mathematical tool for an exact treatment of open quantum system dynamics

A new method to obtain an operatorial exact solution of a wide class of Markovian master equations is presented. Its key point is the existence of a constant of motion partitioning the Hilbert space into finite-dimensional subspaces. The consequent possibility of representing the reduced density operator as a block diagonal matrix is shown. Each “block operator” evolves under the action of a non-unitary operator explicitly derived. Our mathematical approach is illustrated applying it to simple physical systems.

Collective behavior ofMbosonic modes interacting with a single two-level atom

The Hamiltonian describing, without the rotating-wave approximation (RWA), the linear interaction between M bosonic modes with an Einstein spectrum and a single two-level atom is exactly and canonically transformed introducing M suitable collective independent field modes, in such a way that only one among them is coupled to the atom. Some physical consequences of this fact are analyzed and, in particular, the existence of radiation-trapping phenomena together with the possibility of atomic absorption suppression is established. The applicability of the RWA to this system is discussed and the importance of the effective-field statistics for the time evolution of the system is pointed out.

Tripartite thermal correlations in an inhomogeneous spin-star system

We exploit the tripartite negativity to study the thermal correlations in a tripartite system, that is the three outer spins interacting with the central one in a spin-star system. We analyze the dependence of such correlations on the homogeneity of the interactions, starting from the case where central-outer spin interactions are identical and then focusing on the case where the three coupling constants are different. We single out some important differences between the negativity and the concurrence.

Interpreting concurrence in terms of covariances in a generalized spin star system

The quantum dynamics of M pairwise coupled spin 1/2 is analyzed and the time evolution of the entanglement get established within a prefixed couple of spins is studied. A conceptual and quantitative link between the concurrence function and measurable quantities is brought to light providing a physical interpretation for the concurrence itself as well as a way to measure it. A generalized spin star system is exactly investigated showing that the entanglement accompanying its rich dynamics is traceable back to the covariance of appropriate commuting observables of the two spins.

Steering distillation processes through quantum Zeno dynamics

A quantum system in interaction with a repeatedly measured one undergoes a nonunitary time evolution and is pushed into a subspace substantially determined by the two-system coupling. The possibility of suitably modifying such an evolution through quantum Zeno dynamics (i.e., the generalized quantum Zeno effect) addressing the system toward an a priori decided target subspace is illustrated. Applications and their possible realizations in the context of trapped ions are also discussed.

Coherent and squeezed vibrations for discrete variable harmonic oscillators

In this work we study different types of coherent and squeezed states for the Charlier, Kravchuk and Meixner oscillators. We calculate the average values of different observables corresponding to the coherent states. We found that the coherent and squeezed states of the Kravchuk oscillator are unstable. There are also coherent and squeezed states that are similar to the coherent and squeezed states of the harmonic oscillator. We have introduced a discrete variable model for the biophoton coherent radiation, and the coherent thermal and squeezed thermal states. © 2009 Taylor & Francis.

Exactly solvable time-dependent models of two interacting two-level systems

Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics. Each of the sub-dynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.

Supplementary material 1 from: Galasso G, Domina G, Angiolini C, Azzaro D, Bacchetta G, Banfi E, Barberis D, Barone G, Bartolucci F, Bertolli A, Bolpagni R, Bonari G, Bracchetti L, Calvia G, Campus G, Cancellieri L, Cavallaro V, Conti F, Cuena-Lombraña A, D'Alessandro E, Dal Corso G, Dalla Vecchia A, De Natale A, Del Guacchio E, Di Gregorio G, Di Gristina E, Di Stefano M, Fanfarillo E, Federici A, Federici G, Ferretti G, Festi F, Fiaschi T, Filibeck G, Fois M, Gariboldi L, Gestri G, Gubellini L, Guiggi A, Hofmann N, Laface VLA, Lallai A, Lazzeri V, Lecis AP, Lonati M, Lucchese F, Lupoletti J, Maestri S, Mainetti A, Mantino F, Mascia F, Masin RR, Mei G, Merli M, Messina A, Musarella CM, Nota G, Olivieri N, Paura B, Pellegrini R, Pica A, Pittarello M, Podda L, Praleskouskaya S, Prosser F, Ratini G, Ravetto Enri S, Roma-Marzio F, Salerno G, Selvaggi A, Soldano A, Spampinato G, Stinca A, Tardella FM, Tavilla G, Tomaselli V, Tomasi G, Tosetto L, Venanzoni R, Lastrucci L (2022) Notulae to the Italian alien vascular flora: 13. Italian Botanist 13: 27-44. https://doi.org/10.3897/italianbotanist.13.85863

Supplementary data

A perturbative treatment of the evolution operator associated with Raman couplings

Distilling Angular Momentum Schrödinger Cats in Trapped Ions

Flux qubits in interaction with a quantized electromagnetic field of a lossy cavity

Maximally entangled states of two flux qubits in a microwave cavity

Entanglement and quantum computing with circuit QED-like systems

Time evolution of two distant SUID rings irradiated with entangled electromagnetic fields

Entanglement of distant SQUID rings

CONTROLLING THE QUANTUM DYNAMICS OF MULTIPARTITE JOSEPHSON CIRCUITS

CONTROLLING THE QUANTUM DYNAMICS OF MULTIPARTITE JOSEPHSON CIRCUITS

Distillation of Schrödinger Cats in Trapped Ions

Riccati equation-based generalization of Dawson’s integral function

A new mathematical tool for an exact treatment of the dynamics of open quantum systems