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Communications in Theoretical Physics

Dynamics of Nonclassicality of Time- and Conductivity-Dependent Squeezed States and Excited Even/Odd Coherent States

Roohollah Daneshmand, Mohammad Kazem Tavassoly

Published Mar 1, 2017• 5 citations
Publisher

Abstract

Abstract Recently, the quantum description of electromagnetic waves in conducting media has been performed. It has been demonstrated that in particular case, the Hamiltonian of the corresponding field can be expressed by Caldirola–Kanai Hamiltonian. In this paper, using the associated annihilation and creation operators of the above-mentioned quantized field, the time- and conductivity-dependent squeezed vacuum and one-photon squeezed states as well as their superpositions, and also the time- and conductivity-dependent excited even and odd coherent states are produced. Also, using a few well-known nonclassicality criteria, the time evolution of nonclassicality features of the above classes of obtained states, in addition to the influence of medium conductivity on them are demonstrated, numerically. It has been shown that the nonclassicality indicators may be adjusted by tuning the conductivity of media.

DOI
10.1088/0253-6102/67/4/365

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Abstract Recently, the quantum description of electromagnetic waves in conducting media has been performed. It has been demonstrated that in particular case, the Hamiltonian of the corresponding field can be expressed by Caldirola–Kanai Hamiltonian. In this paper, using the associated annihilation and creation operators of the above-mentioned quantized field, the time- and conductivity-dependent squeezed vacuum and one-photon squeezed states as well as their superpositions, and also the time- and conductivity-dependent excited even and odd coherent states are produced. Also, using a few well-known nonclassicality criteria, the time evolution of nonclassicality features of the above classes of obtained states, in addition to the influence of medium conductivity on them are demonstrated, numerically. It has been shown that the nonclassicality indicators may be adjusted by tuning the conductivity of media.
Recently the quantum description of electromagnetic waves in conducting media has been performed. It has been deduced that, in particular situations the Hamiltonian of corresponding field can be expressed by the well‐known Caldirola‐Kanai Hamiltonian. In this paper, using the associated annihilation and creation operators of the above‐mentioned real physical system, a few schemes for the generation of some classes of time‐dependent multipartite entangled coherent squeezed states are proposed. To achieve the purpose, the interaction of a narrow bunch of two‐level atoms with such a quantized field in a conducting cavity and in the presence of a strong‐driving classical field is taken into account. The influence of the conductivity parameter on the degree of entanglement and atomic population inversion is studied, numerically. As will be clarified, the related physical quantities can be controlled by the conductivity parameter. In detail, it is shown that the entanglement reaches to its maximum value with smaller delay in the presence of larger values of conductivity. Also, it is observed that by increasing the conductivity, the time for occurring collapse‐revival in the atomic inversion is decreased. image
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type Hamiltonian. Eigenstates of quadratic and linear invariants are constructed, the solutions being expressed in terms of a complex parametric function that obeys classical oscillator equation with time-varying frequency. The time evolutions of initial Glauber coherent states and Fock states are considered. The medium conductivity and the time-dependent electric permeability are shown to generate squeezing and non-vanishing covariances. In the time-evolved coherent and squeezed states all the second statistical moments of the electric and magnetic field components are calculated and shown to mminimize the Robertson-Schrödinger uncertainty relation.
Recently, two-mode entangled squeezed states have been produced using even and odd squeezed states. Based on such entangled states, we introduce two new classes of quantum states, namely single-mode excited (depleted) entangled squeezed states which are obtained via the iterated action of the creation (annihilation) operator on the first mode of the two-mode entangled squeezed states. In continuation, we study the amount of entanglement of the introduced states by calculating the 'concurrence' and 'linear entropy'. In addition, we investigate several nonclassicality features such as the sub-Poissonian statistics, second-order correlation function between the two modes and quadrature squeezing. Finally, in order to establish the physical realization of the introduced states, a theoretical scheme for their generation based on the interaction of a two-level atom with a quantized cavity field is proposed.
In this paper, we introduce two new classes of nonlinear squeezed states that we name as f-deformed squeezed vacuum state |ξ, f〉 even and f-deformed squeezed first excited state |ξ, f〉 odd , which according to their production processes, essentially include only even and odd bases of Fock space, respectively. In the continuation, we introduce the superposition of these two distinct nonlinear squeezed states with a respective phase φ. Then, some of the criteria which imply the nonclassicality of the states, such as Mandel parameter, second-order correlation function, quadrature squeezing, amplitude-squared squeezing, Husimi and Wigner–Weyl quasi-distribution functions, are numerically examined. At last, by considering a well-known nonlinearity function associated with a nonlinear physical system, we present our results which outcome from the numerical calculations. It is shown that, the introduced f-deformed states can reveal high nonclassical features.
We present a quantum description of electromagnetic waves propagating through time-dependent homogeneous nondispersive conducting and nonconducting linear media without charge sources. Based on the Coulomb gauge and the quantum invariant method, we find the exact wave functions for this problem. In addition, we construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinate and momentum space as well as the uncertainty product for each mode of the electromagnetic field.
In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f -deformed creation operator A = f ( n ) a † on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f -deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.