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arXiv:0910.0050 · Physica Scripta

Two-qubit entanglement dynamics for two different non-Markovian environments

Bruno Bellomo, Rosario Lo Franco, Sabrina Maniscalco, Giuseppe Compagno

Published Sep 1, 2010• 48 citations
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Abstract

We study the time behaviour of entanglement between two noninteracting qubits, each immersed in its own environment for two different non-Markovian conditions: a high- Q cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band gap (PBG). We find that revivals and retardation of entanglement loss may occur by adjusting the cavity–qubit detuning, in the first case, while partial entanglement trapping occurs in a nonideal PBG.

DOI
10.1088/0031-8949/2010/t140/014014

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We study the time behaviour of entanglement between two noninteracting qubits, each immersed in its own environment for two different non-Markovian conditions: a high- Q cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band gap (PBG). We find that revivals and retardation of entanglement loss may occur by adjusting the cavity–qubit detuning, in the first case, while partial entanglement trapping occurs in a nonideal PBG.
We study how the environment of photonic band gap (PBG) materials affects entanglement dynamics of qubits. Entanglement between the single qubit and the PBG environment is investigated through the von Neumann entropy while that for two initially entangled qubits in this PBG reservoir is through concurrence. Dynamics of these measurements are solved in use of the fractional calculus which has been shown appropriate for the systems with non-Markovian dynamics. Entropy dynamics of the single qubit system reveals that the coupling with the PBG reservoir prevents decoherence of the qubit through the steady entropy with non-zero value. The effect of PBG reservoir on the concurrence of the two-qubit system leads to the long-time entanglement preservation. The concurrence dynamics shows that unphysical entanglement trapping does not exist in the system with the qubit frequency lying outside the PBG region. Long-time memory effect of the PBG reservoir occurs only for the qubit frequency in the PBG region. Entanglement mechanisms resulting from this long-time memory effect are discussed.
Abstract We investigate the time evolution of a general two-qubit pure entangled state in different structured environments. A general expression is obtained to evaluate the entanglement dynamics of two-qubit systems for two different dissipative environments in the non-Markovian regime. In one case it is single Lorentzian and is detuned from the system while in the other case two Lorentzians form a photonic band gap and is resonant with the system. In the first case, we show that entanglement can be generated from the initial separable state in the non-Markovian regime. Compared to our earlier work under Markov approximation (Tahira et al 2008 J. Phys. B: At. Mol. Opt. Phys . 41 205501), we show that disentanglement rates as well as sudden death times are modified in structured environments. Therefore, we can retain the entanglement for a longer time by controlling the system–environment coupling parameters.
The models of two qubits separately trapped in two independent Markovian or non-Markovian environments have been investigated. The distinction of the two-qubit entanglement dynamics in different environments has also been discussed in detail. The results show that, in non-Markovian environments, the possible usage time of entanglement can be extended due to its memory effect. On the other hand, we note that, compared to Markovian environments, the two-qubit entanglement could be protected better in non-Markovian environments by modulating the detuning between qubits and cavities. Finally, an intuitive physical interpretation for these results is given.
We examine the impact of the non-Markovian environment on the dynamical behavior of the quantum coherence and entropy squeezing considering a two-level atomic system (qubit) immersed in a reservoir with zero-temperature for two types of non-Markovian environments. We consider a cavity little off-resonance with the transition frequency of the qubit and the case of a non-perfect photonic band gap (PBG). We show that the amount of coherence is dependent on the structure of the environment and influenced through the memory effects. We obtain that the delay and revival of the coherence loss might take place by controlling the detuning of the cavity-qubit system. Whereas, a partial coherence trapping occurs in non-ideal PBG and the decrease of the gap width will destroy the coherence. On the other hand, we show the situation for which the squeezing is occurring and enhanced with respect to the main parameters for the system. Finally, we display the monotonic dependence of the quantum coherence and squeezing on the main model parameters.
The quantum discord dynamics of two non-coupled two-level atoms independently interacting with their reservoir is studied under two kinds of non-Markovian conditions, namely, an off-resonant case with atomic transition frequency and a photonic band gap. In the first case, the phenomenon of the quantum discord loss and the oscillatory behavior of the quantum discord can occur by changing the detuning quantity and reducing the spectral coupling width for any initial Bell state. Under the second condition, the trapping phenomenon of the quantum discord can be presented by adjusting the width of gap, that is, the quantum discord of two atoms keep a nonzero constant for a long time.
We investigate the roles of different qubit—environment decoherence models on the entanglement trapping of two qubits. By considering three environmental models (the single photonic band gap model, the common photonic band gap model, and the two independent photonic band gaps model), we note that the final values of entanglement trapping are determined by these different models. We also give the conditions of obtaining the larger entanglement trapping by comparing two-qubit entanglement dynamics in different decoherence models. Moreover, the comparison of entanglement trapping between two Bell-like states in the same decoherence model are also carried out.