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arXiv:1007.3792 · Physical Review A

Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir

Md. Manirul Ali, Po‐Wen Chen, Hsi‐Sheng Goan

Published Aug 11, 2010• 37 citations
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Abstract

We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see a remarkable difference between the non-Markovian entanglement dynamics and its Markovian counterpart. We show that a non-Markovian decoherence-free state is also decoherence free in the Markovian regime, but all the Markovian decoherence-free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from a squeezed vacuum bath to a squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.

DOI
10.1103/physreva.82.022103

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We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see a remarkable difference between the non-Markovian entanglement dynamics and its Markovian counterpart. We show that a non-Markovian decoherence-free state is also decoherence free in the Markovian regime, but all the Markovian decoherence-free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from a squeezed vacuum bath to a squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.
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The decoherence of two initially entangled qubits in a squeezed vacuum cavity has been investigated exactly. The results show that, first, in principle, the disentanglement time decreases with the increasing of squeeze parameter r, due to the augmenting of average photon number of every mode in squeezed vacuum cavity. Second, there are entanglement revivals after complete disentanglement for the case of even parity initial Bell state, while there are entanglement decrease and revival before complete disentanglement for the case of odd parity initial Bell state. The results are quite different from that of the case for qubits in a vacuum cavity.
Entanglement in continuous-variable Gaussian systems is a key resource, and common reservoirs can both suppress and generate correlations. Existing work focused on pre-entangled states or Markovian baths, leaving open whether separable squeezed inputs entangle in structured environments or under modulation. We study two bosonic modes coupled to a common reservoir, each initialized in a separable squeezed vacuum. Dynamics are analyzed utilizing Gaussian covariance methods, evolved under approximate Non-Markovian quantum state diffusion (QSD), finite-temperature pseudomode embeddings, and Bures-based non-Markovian diagnostics. We identify three mechanisms absent in Markovian dynamics: (1) A detuning condition that freezes entanglement trajectories across reservoir correlation times; (2) birth, death, and revival of entanglement from orthogonal inputs; and (3) integer-locked beating with square-wave oscillations produced by periodic detuning. All mechanisms persist at finite temperature, with deviations bounded within 5% in cryogenic regimes and 20% at moderate occupations. These deviation bounds align with cryogenic cavity, phononic, and optomechanical platforms, where structured spectral densities and detuning modulation are already accessible. Structured reservoirs are shown to emerge as tunable entanglement resources for continuous-variable quantum technologies.
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 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.