Search results for "Harmonic oscillator"

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

2006

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.

Unitary Representations of Quantum Superpositions of two Coherent States and beyond

2013

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.

A Swanson-like Hamiltonian and the inverted harmonic oscillator

2022

We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_\theta$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the eigensystem of the Hamiltonian $H$ of the inverted quantum harmonic oscillator can be deduced from that of $H_\theta$. We show that there is no need to introduce a different scalar product using some ad hoc metric operator, as suggested by other authors. Indeed we prove that a distributional approach is sufficient to deal with the Hamiltonian $H$ of the inverted oscillator.

A tomographic approach to non-Markovian master equations

2010

We propose a procedure based on symplectic tomography for reconstructing the unknown parameters of a convolutionless non-Markovian Gaussian noisy evolution. Whenever the time-dependent master equation coefficients are given as a function of some unknown time-independent parameters, we show that these parameters can be reconstructed by means of a finite number of tomograms. Two different approaches towards reconstruction, integral and differential, are presented and applied to a benchmark model made of a harmonic oscillator coupled to a bosonic bath. For this model the number of tomograms needed to retrieve the unknown parameters is explicitly computed.

A bounded version of bosonic creation and annihilation operators and their related quasi-coherent states

2007

Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a \underline{bounded} operator related to an annihilation-like operator. We use this bounded operator to construct a sort of modified harmonic oscillator and we analyze the dynamics of this oscillator from an algebraic point of view.

Quantizations from reproducing kernel spaces

2012

Abstract The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L 2 ( C , d 2 z / π ) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s . We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s -dependent quantizations is also considered.

Deformed Canonical (anti-)commutation relations and non-self-adjoint hamiltonians

2015

Formulas for the thermodynamic properties of dense nitrogen.

1969

Dynamics of a harmonic oscillator coupled with a Glauber amplifier

2020

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…