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Chinese Physics Letters

Entanglement Dynamics of Two Qubits Coupled Independently to Cavities in the Ultrastrong Coupling Regime: Analytical Results

Wei-Ting Zhu, Qing-Bao Ren, Liwei Duan, Qing‐Hu Chen

Published May 1, 2016• 14 citations
Publisher

Abstract

Dynamics of quantum entanglement of two qubits in two identical quantum Rabi models is studied analytically in the framework of corrections to the rotating-wave approximations. A closed-form expression for the entanglement dynamics initiated from the well-known Bell states is derived, which is very close to the numerical exact results up to the ultrastrong coupling regime. It is found that the vanishing entanglement can be purely induced by the counter-rotating terms, and can be enhanced with the atom–cavity coupling.

DOI
10.1088/0256-307x/33/5/050302

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Dynamics of quantum entanglement of two qubits in two identical quantum Rabi models is studied analytically in the framework of corrections to the rotating-wave approximations. A closed-form expression for the entanglement dynamics initiated from the well-known Bell states is derived, which is very close to the numerical exact results up to the ultrastrong coupling regime. It is found that the vanishing entanglement can be purely induced by the counter-rotating terms, and can be enhanced with the atom–cavity coupling.
We revisit the analytic solution of the two-qubit quantum Rabi model with inhomogeneous coupling and transition frequencies using a displaced oscillator basis. This approach enables us to apply the same truncation rules and techniques adopted in the Rabi model to the two qubits system. The derived analytical spectra match perfectly with the numerical solutions in the parameter regime where the qubits’ transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultrastrong coupling regime. We further explore the dynamical behavior of the two qubits as well as the evolution of entanglement. The analytical methods provide unexpectedly accurate results in describing the dynamics of the two qubits in the present experimentally accessible coupling regime. The time evolutions of the probability for the qubits show that the collapse-revival phenomena emerge, survive and finally disappear when one coupling strength increases from weak to strong coupling regimes and the other coupling strength is well into the ultrastrong coupling regime. The inhomogeneous coupling system exhibits new dynamics, which are different from the homogeneous coupling 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.
We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.
We analyze the dynamics of the quantum Rabi model for two qubits interacting through a common bosonic field (resonator), focusing on the generation and detection of maximally entangled states. We obtain analytical results for the unitary dynamics of this system in the slow-qubit (or degenerate) regime, considering ultra-strong coupling between qubits and resonator mode, for which the rotating wave approximation (RWA) is no longer applicable. We also numerically investigate the dynamics beyond the slow-qubit condition in order to study the validity of the model in the presence of less strict conditions.
The decoherence of two initially entangled qubits in non-Markovian reservoirs has been investigated exactly without Born-Markovian approximation or rotating-wave approximation (RWA). The nonperturbative quantum master equation is derived and its exact solution is obtained. The decoherence behavior of two qubits, initially entangled in Bell states, has been investigated in the weak coupling regime and strong coupling regime. The results show that the counter-rotating wave terms have obvious influence on the decoherence behavior in the non-Markovian regime.