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arXiv:quant-ph/0604030

Non-Markovian thermalization of entangled qubits

I. Glendinning, Matthias Jakob, Michael Noelle

Published Apr 5, 2006• 0 citations
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Abstract

We study the decoherence properties of an entangled bipartite qubit system, represented by two two-level atoms that are individually coupled to non-Markovian reservoirs. This coupling ensures that the dynamical equations of the atoms can be treated independently. The non-Markovian reservoirs are described by a model which leads to an exact non-Markovian master equation of the Nakajima-Zwanzig form [J. Salo, S. M. Barnett, and S. Stenholm, Optics Commun. 259, 772 (2006)]. We consider the evolution of the entanglement of a two-atom state that is initially completely entangled, quantified by its concurrence. Collapses and revivals in the concurrence, induced by the memory effects of the reservoir, govern the dynamics of the entangled quantum system. These collapses and revivals in the concurrence are a strong manifestation of the non-Markovian reservoir.

DOI
10.48550/arxiv.quant-ph/0604030

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We study the decoherence properties of an entangled bipartite qubit system, represented by two two-level atoms that are individually coupled to non-Markovian reservoirs. This coupling ensures that the dynamical equations of the atoms can be treated independently. The non-Markovian reservoirs are described by a model which leads to an exact non-Markovian master equation of the Nakajima-Zwanzig form [J. Salo, S. M. Barnett, and S. Stenholm, Optics Commun. 259, 772 (2006)]. We consider the evolution of the entanglement of a two-atom state that is initially completely entangled, quantified by its concurrence. Collapses and revivals in the concurrence, induced by the memory effects of the reservoir, govern the dynamics of the entangled quantum system. These collapses and revivals in the concurrence are a strong manifestation of the non-Markovian reservoir.
The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubit system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.
In the framework of the dissipative dynamics of coupled qubits interacting with independent reservoirs, a comparison between non-Markovian master equation techniques and an exact solution is presented here. We study various regimes in order to find the limits of validity of the Nakajima–Zwanzig and the time-convolutionless master equations in the description of the entanglement dynamics. A comparison between the performances of the concurrence and the negativity as entanglement measures for the system under study is also presented.
We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.
We provide a thorough analysis of the entanglement dynamics of an interacting two-qubit system in the non-Markovian regime. In such a regime, the time scale on which the reservoir degrees of freedom evolve is either of the same order of magnitude or less than that on which the system evolves. We used an exact numerical method; the Quasi-Adiabatic Path Integral (QUAPI) technique, to describe the corresponding qubit dissipative dynamics in such a non-Markovian regime. We computed the time evolution of the density operator for the quibits, from which we quantified the coherences and population dynamics, as well as the qubit-bath coupling effects. Using negativity as a metric, we calculated the dynamics of non-local quantum correlations (entanglement), and indentified a non-Markovian quantum phenomena in terms of early stage disentanglement, and the collapse and revival of entanglement.
We study the entanglement dynamics of three two-level atoms interacting with a structured reservoir. The atoms are initially prepared in a mixed W state while the reservoir is in the vacuum. We show the dependence of entanglement dynamics on the purity of initial atomic state and on the amount of non-Markovianity. When the initial state of atoms is in a W pure state, the entanglement will decay asymptotically, while it vanishes in a finite time if the initial state is in a mixed W state. In addition, as the memory effect of the environment, entanglement can partially revive after it vanishes, and the revival degree is dependent on the strength of non-Markovian effect. In the end, we consider the entanglement generation and its evolution when the initial state of the atoms system is completely separable.
We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima—Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.