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Laser Physics

Spin squeezing and pairwise entanglement under non-Markovian environments with dynamical decoupling pulses

Jun‐Qi Li, Lei Du, J-Q Liang

Published Jul 3, 2018• 2 citations
Publisher

Abstract

Abstract We study the effect of non-Markovian environments on spin squeezing and pairwise entanglement of a qubit ensemble in the presence of dynamical decoupling pulses. Each qubit of the ensemble interacts with its own environment, and the environments are independent and identical. It is shown that spin squeezing and entanglement may display sudden death, asymptotic vanishing and revival behaviors. Moreover, it is indicated that spin squeezing and entanglement can be protected effectively by employing appropriate pulse separate time and pulse number as well as non-Markovian properties.

DOI
10.1088/1555-6611/aac7e5

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Abstract We study the effect of non-Markovian environments on spin squeezing and pairwise entanglement of a qubit ensemble in the presence of dynamical decoupling pulses. Each qubit of the ensemble interacts with its own environment, and the environments are independent and identical. It is shown that spin squeezing and entanglement may display sudden death, asymptotic vanishing and revival behaviors. Moreover, it is indicated that spin squeezing and entanglement can be protected effectively by employing appropriate pulse separate time and pulse number as well as non-Markovian properties.
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We study the decoherence of spin squeezing under non-Markovian channels and consider an ensemble of NNN independent spin-1/21/21/2 particles with exchange symmetry. Each spin interacts with its own bath, and the baths are independent and identical. For this kind of open system, the spin squeezing under decoherence can be investigated from the dynamics of the local expectations. The reduced dynamics is obtained by the exact hierarchy equation method. The numerical results show that the spin squeezing may display both sudden and asymptotic vanishing; however, the revival phenomenon does not happen. In contrast, the concurrence shows multiple sudden vanishing and revival phenomena.
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.
In order to witness multipartite correlations beyond pairwise entanglement, spin-squeezing parameters are analytically calculated for a spin ensemble in a collective initial state under three different decoherence channels. It is shown that, in analogy to pairwise entanglement, the spin squeezing described by different parameters can suddenly become zero at different vanishing times. This finding shows the general occurrence of sudden vanishing phenomena of quantum correlations in many-body systems, which here is referred to as spin-squeezing sudden death (SSSD). It is shown that the SSSD usually occurs due to decoherence and that SSSD never occurs for some initial states in the amplitude-damping channel. We also analytically obtain the vanishing times of spin squeezing.
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 study the dynamical behavior of two initially entangled qubits, each locally coupled to an environment embodied by an interacting spin chain. We consider energy-exchange qubit–environment couplings resulting in rich and highly non-trivial entanglement dynamics. We obtain exact results for the time evolution of the concurrence between the two qubits and find that, by tuning the interaction parameters, one can freeze the dynamics of entanglement, therefore inhibiting their relaxation into the spin environments, as well as activate a sudden-death phenomenon. We also discuss the effects of an environmental quantum phase transition on the features of the two-qubit entanglement dynamics.