Decoherence dynamics of a charged particle within a non-demolition type interaction in non-commutative phase-space

Abstract

This paper studies decoherence without dissipation of charged magneto-oscillator in the framework of quantum non-demolition type interaction in non-commutative phase-space. The master equation is derived considering the non-commutativity effects of a bath of harmonic oscillators to study the dynamics of such a system, and its possible exact solution is presented. By analyzing this solution, it turns out that the process involving decoherence without energy dissipation can be observed explicitly. In addition, the decoherence factor and the measure of coherence via linear entropy dynamic are deduced for two types of reservoir, namely the ohmic and super-ohmic reservoirs at low and high temperature limits. Numerical results obtained show that the coherence is better preserved in the system when non-commutativity effects are taken into account at low temperature, while the inverse phenomenon is observed at high temperature. Moreover, by kindly adjusting the non-commutative parameters, it is possible to improve the coherence time scale of the system. Another interesting result can be observed from the system’s coherence time scale, which is very sensitive to the magnetic field and thus adding to non-commutative parameters, it may be useful to control decoherence in the system.

Intrinsic decoherence for the displaced harmonic oscillator

“…We have studied the decaying dynamics of a displaced harmonic oscillator for initially coherent and squeezed states. (15). The parameters are α = 4, ω = 4, γ = 10, λ = 0.7, r = 0.3, where we choose to maintain the real part r of the squeeze coefficient and variate their complex phase θ.…”

“…some time ago, Mandal [14], shows a way to calculate the quasidistribution of photons in the squeezed states of light when the parameters are taken as purely real. Germain et al [15] explicitly shows the effects of a non-commutative bath of oscillators on a magneto-oscillator, they gives the solution for decoherence without dissipation using the master's equation formulation. Recently, Lu [16], reported the evolution of orthogonal coherent states given the solution of the master's equation, showing how the decoherence affects the negativity of the associate Wigner's function.…”

“…Figure 4: Expectation value of â † â given by(15). The parameters are α = 4, ω = 4, γ = 10, λ = 0.7, r = 0.3, where we choose to maintain the real part r of the squeeze coefficient and variate their complex phase θ.…”

Decoherence and the ultraviolet cutoff: non-Markovian dynamics of a charged particle in a magnetic field

“…In the corresponding study linear entropy has been considered as the measure of the purity of the states in non-commutative space [34]. The density operator and the Wigner function for an an-harmonic oscillator were computed in a 2D non-commutative phase space and the effects of magnetic field on the decoherence rate were highlighted, using time-independent coefficients, featuring the Markovian heat bath dynamics [35][36][37]. Later, the master equation was derived for the momentum coupling scenario in the framework of non-Markovian dynamics [38].…”

Intrinsic decoherence dynamics in the three-coupled harmonic oscillators interaction

“…al [3] showed that in a ring arrangement of coupled harmonic oscillators. Decoherence without dissipation of a charged magneto-oscillator by using quantum non-demolition interactions in non-commutative phase-space has also been recently studied [2].…”