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Journal of the Optical Society of America B

Effect of feedback control on the dynamics of quantum discord with and without the rotating-wave approximation

Jun-Qing Cheng, Wei Wu, Jing‐Bo Xu

Published Mar 1, 2017• 2 citations
Publisher

Abstract

We investigate the effect of quantum-jump-based feedback on the dynamics of quantum discord for two noninteracting two-level atoms coupled to a single mode of the cavity field with and without the rotating-wave approximation. It is found that the counterrotating terms can be helpful for generating steady states, and the value of steady-state quantum discord can be increased to approach 1 in the long-time limit by feedback controls. Furthermore, we also explore the influence of the time evolutions of mean excitation number in total systems and atomic subsystems on the quantum correlations and show that the enhancement of mean excitation number in atomic subsystems by feedback controls leads to the high value of steady-state quantum discord.

DOI
10.1364/josab.34.000701

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We investigate the effect of quantum-jump-based feedback on the dynamics of quantum discord for two noninteracting two-level atoms coupled to a single mode of the cavity field with and without the rotating-wave approximation. It is found that the counterrotating terms can be helpful for generating steady states, and the value of steady-state quantum discord can be increased to approach 1 in the long-time limit by feedback controls. Furthermore, we also explore the influence of the time evolutions of mean excitation number in total systems and atomic subsystems on the quantum correlations and show that the enhancement of mean excitation number in atomic subsystems by feedback controls leads to the high value of steady-state quantum discord.
The dynamics of two identical atoms is studied, which is resonantly coupled to a single-mode cavity under two different quantum feedback controls, i.e., the symmetric feedback control and the nonsymmetric feedback control. Correspondingly, the quantum discord of the system is induced to reach steady values under these two kinds of feedback controls. Furthermore, in some cases, the steady value of quantum discord of the system under symmetric feedback control is much larger than the steady value under nonsymmetric feedback control. The situation is just the opposite when the initial state is |eg〉. It is also found that the feedback is not good for getting a high discord when the initial state is in the form of Werner-like state (d = 0).
The entanglement dynamics of two identical atoms coupled to a single-mode cavity is considered. Based on the reduced non-perturbative quantum master equation method, the entanglement evolution of the two atoms with spontaneous emission under the quantum-jump-based feedback control is investigated beyond the conventional rotating-wave approximation (RWA). The research of entanglement evolution beyond RWA is a significant problem because of its importance to the field of strong coupling. The result of numerical simulations shows that an appropriate feedback control can prolong the entanglement time and increase the entanglement amplitude. The effect of synchronous control on two atoms is superior to that of one control.
We investigate the quantum discord dynamics of two noninteracting two-level atoms, each trapped in a single-mode optical cavity which is filled with a nonlinear Kerr-like medium. It is found that quantum discord vanishes only asymptotically although entanglement disappears suddenly during the time evolution. Furthermore, we explore the influence of the nonlinear Kerr-like medium on the dynamics of quantum discord, quantum mutual information, and classical correlation of two atoms. It is shown that the amount of quantum discord, quantum mutual information, and classical correlation of two atoms can be improved by adjusting the value of the Kerr medium. Finally, we also study the effect of phase dissipation on this system by making use of the Monte Carlo wavefunction method.
The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using a recently derived Lindblad type quantum optical master equation [F. Beaudoin, J. M. Gambetta, and A. Blais, Phys. Rev. A 84, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.
Dynamics of the quantum entanglement and quantum discord of two qubits in two independent baths and a common bath with the Lorentzian spectrum are studied exactly in the numerical sense within the hierarchy approach. The effects of the counter-rotating-wave terms from the system–bath coherence on these quantum correlations are systematically discussed and comparisons with previous ones under the rotating-wave approximation are also performed. For two independent baths, beyond the weak system–bath coupling, the counter-rotating-wave terms essentially change evolutions of both the entanglement and quantum discord. With increase of the coupling, revival of the entanglement after a period of complete disentanglement is suppressed dramatically and finally disappears, and the quantum discord becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the counter-rotating-wave terms, but the quantum discord shows quite different behaviors if initiated from spin-correlated states. In the non-Markovian regime, the quantum discord is almost not influenced by the counter-rotating-wave terms and is generally finite in the long-time evolution at arbitrary coupling while in the Markovian regime, it is significantly enhanced with the strong coupling.
This paper studies quantum discord of two qutrits coupled to their own environments independently and coupled to the same environment simultaneously under quantum-jump-based feedback control. Our results show that spontaneous emission, quantum feedback parameters, classical driving, initial state, and detection efficiency all affect the evolution of quantum discord in a two-qutrit system. We find that under the condition of designing proper quantum-jump-based feedback parameters, quantum discord can be protected and prepared. In the case where two qutrits are independently coupled to their own environments, classical driving, spontaneous emission, and low detection efficiency have negative effect on the protection of quantum discord. For different initial states, it is found that the evolution of quantum discord under the control of appropriate parameters is similar. In the case where two qutrits are simultaneously coupled to the same environment, the classical driving plays a positive role in the generation of quantum discord, but spontaneous emission and low detection efficiency have negative impact on the generation of quantum discord. Most importantly, we find that the steady discord depends on feedback parameters, classical driving, and detection efficiency, but not on the initial state.