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arXiv:1212.4071 · Physical Review A

Dissipative dynamics of quantum correlations in the strong-coupling regime

Ferdi Altintas, Resul Eryiğit

Published Feb 27, 2013• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.022124

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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.
The dynamics of atom–field entanglement for a system composed of two atoms resonantly coupled to a single mode leaky cavity field has been investigated beyond rotating wave approximation (RWA). By using a monogamic relation for the entanglement of formation (EOF) as well as the lower bound of the EOF for bipartite mixed states in higher dimensions, contrary to the RWA case, the atom–field system in the steady states is found to be entangled in the strong-coupling regime and the entanglement can grow as a function of atom–field coupling strength.
We have studied the dynamics of quantum correlations such as entanglement, Bell nonlocality and quantum discord between identical and unidentical atoms interacting with a single-mode cavity field and subject to cavity decay. The effect of single-atom detuning, cavity decay rate and initial preparation of the atoms on the corresponding correlation measures have been investigated. It is found that even under strong dissipation, time evolution can create high quantum discord while entanglement and Bell nonlocality stay zero for an initially separable state. Quantum discord increases while entanglement decreases in a certain time period under dissipation for the initial state that both atoms are in the excited state if the qubits are identical. For some types of initial states, cavity decay is shown to drive the system to a stationary state with high entanglement and quantum discord.
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.
We consider a model of two qubits, which interact through a Rotating Wave Approximation (RWA) potential; while the first qubit is incoherently pumped to its excited state, the second qubit loses its excitations by contact to a zero-temperature bath. We show that purely dissipative effects (and the help of the qubit-qubit interaction) can produce entangled stationary states. The steady state entanglement is significant when the interaction constant, and the pumping and dissipation rates are of the same order of magnitude. In this toy model, the entanglement of the system exists only when the two thermal baths are on and the qubits are coupled; if we turn off either the pumping or the dissipation these correlations disappear. We calculate and compare two quantifiers of non-classical correlations: the quantum discord [3] and the entanglement of formation, in the steady state. We find an analytical form for the conditions for which the steady-state qubit-qubit entanglement attains its maximum value Css..
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.
Entanglement evolution of two independent Jaynes-Cummings atoms without the rotating-wave approximation (RWA) is studied by a numerically exact approach. Previous results based on the RWA are essentially modified in the strong-coupling regime ($g\ensuremath{\geqslant}0.1$), which has been reached in the recent experiments on the flux qubit coupled to the LC\mathit{LC}LC resonator. For the initial Bell state with anticorrelated spins, entanglement sudden death (ESD) is absent in the RWA but does appear in the present numerical calculation without the RWA. Aperiodic entanglement evolution in the strong-coupling regime is observed. The strong atom-cavity coupling facilitates the ESD. The sign of the detuning plays an essential role in the entanglement evolution for strong coupling, which is irrelevant in the RWA. Analytical results based on an unitary transformation are also given, which could not modify the RWA picture essentially. It is suggested that the activation of the photons may be the origin of ESD in this system.