Search results for "Continuous"
showing 10 items of 899 documents
Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
2012
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory …
Density-potential mappings in quantum dynamics
2012
In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case as it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an ex…
A Perturbative Approach to Continuous-Time Quantum Error Correction
2014
We present a novel discussion of the continuous-time quantum error correction introduced by Paz and Zurek in 1998 [Paz and Zurek, Proc. R. Soc. A 454, 355 (1998)]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the 3-qubit and the 5-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame featur…
Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing struc…
2008
We investigate the structural aspects of genuine multipartite entanglement in Gaussian states of continuous variable systems. Generalizing the results of [Adesso & Illuminati, Phys. Rev. Lett. 99, 150501 (2007)], we analyze whether the entanglement shared by blocks of modes distributes according to a strong monogamy law. This property, once established, allows to quantify genuine N-partite entanglement in terms of the "residual contangle" not encoded into 2,...,K,...,(N-1)-partite quantum correlations. The explicit expression of this entanglement measure is derived, by a recursive formula, for a subclass of Gaussian states. These are fully symmetric (permutation-invariant) states multi-…
Distillation by repeated measurements: Continuous spectrum case
2010
Repeated measurements on a part of a bipartite system strongly affect the other part not measured, whose dynamics is regulated by an effective contracted evolution operator. When the spectrum of this operator is discrete, the latter system is driven into a pure state irrespective of the initial state, provided the spectrum satisfies certain conditions. We here show that even in the case of continuous spectrum an effective distillation can occur under rather general conditions. We confirm it by applying our formalism to a simple model.
Microscopic biasing of discrete-time quantum trajectories
2021
We develop a microscopic theory for biasing the quantum trajectories of an open quantum system, which renders rare trajectories typical. To this end we consider a discrete-time quantum dynamics, where the open system collides sequentially with qubit probes which are then measured. A theoretical framework is built in terms of thermodynamic functionals in order to characterize its quantum trajectories (each embodied by a sequence of measurement outcomes). We show that the desired biasing is achieved by suitably modifying the Kraus operators describing the discrete open dynamics. From a microscopical viewpoint and for short collision times, this corresponds to adding extra collisions which enf…
Demonstration of a fully tuneable entangling gate for continuous-variable one-way quantum computation
2015
We introduce a fully tuneable entangling gate for continuous-variable one-way quantum computation. We present a proof-of-principle demonstration by propagating two independent optical inputs through a three-mode linear cluster state and applying the gate in various regimes. The genuine quantum nature of the gate is confirmed by verifying the entanglement strength in the output state. Our protocol can be readily incorporated into efficient multi-mode interaction operations in the context of large-scale one-way quantum computation, as our tuning process is the generalisation of cluster state shaping.
Scattering of Particles by Potentials
2013
The three prototypes of spectra of self-adjoint operators, the discrete spectrum, with or without degeneracy, the continuous spectrum, and the mixed spectrum, as well as the corresponding wave functions, contain important information about the physical systems that they describe
Geometry and time scale of the rotational dynamics in supercooled toluene
1998
Multidimensional deuteron NMR provides powerful tools for studying molecular reorientation in supercooled liquids. We present results on selectively deuterated toluene-${d}_{5},$ which may be one of the molecularly most simple van der Waals glass formers. From two-time correlation functions the time scale of reorientation was obtained slightly above the calorimetric glass transition temperature. The applied stimulated echo method provides a geometry parameter that, in analogy to $q$-dependent scattering experiments, allows one to investigate the geometry of the elementary rotational process. Continuous time random walk computer simulations were used for the interpretation of the data. It is…
Properties of Scattering Matrices in a Vicinity of Thresholds
2021
Chapter 3 is devoted to various properties of a waveguide scattering matrix, which is a matrix function on the waveguide continuous spectrum. There is a sequence of threshold values of the spectral parameter where the scattering matrix changes its size; the thresholds accumulate at infinity. In particular, both two-sided limits of the scattering matrix are calculated at every threshold.