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International Journal of Modern Physics B

Influence of the counter-rotating terms on the quantum dynamics of the damped harmonic oscillator in a deformed bath

Mohsen Daeimohammad

Published May 17, 2019• 1 citation
Publisher

Abstract

The aim of the present study is to investigate the effect of the counter-rotating terms on the quantum dynamics of a harmonic oscillator in the presence of a deformed bath. We first obtain the Langevin equation of motion for damped oscillator with and without the rotating-wave approximation (RWA). Then, we study the effect of the counter-rotating terms on the diffusion coefficients. Then, we obtain the equation of motion for the harmonic oscillator correlation function with and without the RWA. Finally, we investigate the influence of the counter-rotating terms on the oscillator correlation function.

DOI
10.1142/s0217979219501261

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The aim of the present study is to investigate the effect of the counter-rotating terms on the quantum dynamics of a harmonic oscillator in the presence of a deformed bath. We first obtain the Langevin equation of motion for damped oscillator with and without the rotating-wave approximation (RWA). Then, we study the effect of the counter-rotating terms on the diffusion coefficients. Then, we obtain the equation of motion for the harmonic oscillator correlation function with and without the RWA. Finally, we investigate the influence of the counter-rotating terms on the oscillator correlation function.
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Abstract We analyze the steady-state characteristics of a damped harmonic oscillator (system) in the presence of a non-Markovian bath characterized by Lorentzian spectral density. Although Markovian baths presume memoryless dynamics, the introduction of complex temporal connections by a non-Markovian environment radically modifies the dynamics of the system and its steady-state behaviour. We obtain the steady-state Green’s function and correlation functions of the system using the Schwinger–Keldysh formalism. In both rotating and non-rotating wave approximation, we analyzed various emergent properties like effective temperature and distribution function. We also explore the impact of dissipation and non-Markovian bath on the quantum Zeno and anti-Zeno effects. We show that a transition between Zeno to anti-Zeno effect can be tuned by bath spectral width and the strength of dissipation.
The aim of this study is to investigate dynamical properties of a two-mode f-deformed cavity- field ‎coupled to an effective two-level atom with and without the rotating wave approximation. The first ‎section discusses the theoretical model of the interaction between a two-mode cavity-field and an ‎effective two-level atom within the framework of an f-DJCM without the rotating wave ‎approximation. After that, we obtain the reduced density matrix of the cavity-field with and without ‎the rotating-wave approximation. Then, we have investigated the effect of the counter-rotating ‎terms on temporal evolution of various non-classical properties of the cavity-field, i.e., photon-‎counting statistics, the cross correlation between the modes of the field, and the quantum ‎fluctuations of the quadrature components. Particularly, we compare the numerical result for three ‎different values of the deformation parameter q (q=1, q=1.1, q=0.9) with and without applying the rotating ‎wave approximation. By using of the numerical method, we concluded that even under the ‎condition in which the RWA is considered to be valid, there are the significant effects of virtual-‎photon field on the photon-counting statistics, the cross correlation between the modes of the ‎field, and the quantum fluctuations of the quadrature components‎.
We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic or a fermionic environment with a detuned Lorentz spectrum at zero temperature is analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity whether the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.
Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed.