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arXiv:2008.00640

Non-Markovian qubit dynamics in nonequilibrium environments

Xiang-Ji Cai

Published Aug 3, 2020• 0 citations
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Abstract

We theoretically study the non-Markovian dynamics of qubit systems coupled to nonequilibrium environments with nonstationary and non-Markovian statistical properties. The reduced density matrix of the single qubit system satisfies a closed third-order differential equation with all the higher-order environmental correlations taken into account and the reduced density matrix of the two qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for a given evolution time when the two qubit system is initially prepared in the composite Bell states and the extended Werner states, respectively. It is shown that the environmental nonstationary feature can suppress the decoherence and disentanglement dynamics and can reduce the coherence and entanglement revivals in non-Markovian dynamics regime. In addition, it is shown that the environmental non-Markovian feature can enhance the coherence revivals in the single decoherence dynamics and the entanglement revivals in the two qubit disentanglement dynamics, respectively. Furthermore, the environmental nonstationary and non-Markovian features can enhance the nonlocality of the two qubit system.

DOI
10.48550/arxiv.2008.00640

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We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.
We theoretically investigate the non-Markovian dynamical decoherence of a quantum system coupled to nonequilibrium environments with nonstationary statistical properties. We show the time evolution of the decoherence factor in real-imaginary space to study the environment-induced energy renormalization and backaction of coherence which are associated with the unitary and nonunitary parts of the quantum master equation, respectively. It is also shown that the nonequilibrium decoherence dynamics displays a transition between Markovian and non-Markovian and the transition boundary depends on the environmental parameters. The results are helpful for further understanding non-Markovian dynamics and coherence backaction on an open quantum system from environments.
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 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 investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.