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Chinese Physics B

Non-Markovianity of a qubit coupled with an isotropic Lipkin–Meshkov–Glick bath

Li-Jun Tian, Min-Min Ti, Xiang-Dong Zhai

Published Sep 29, 2015• 3 citations
Publisher

Abstract

We study the non-Markovianity of the single qubit system coupled with an isotropic Lipkin–Meshkov–Glick (LMG) model by an effective method proposed by Breuer et al . (Breuer H P and Piilo J 2009 Europhys. Lett. 85 5004). It is discovered that the non-Markovianity is concerned with the quantum phase transitions (QPTs). In the open system, we present that the strong coupling inside the bath and the strong interaction between the system and bath can enhance the degree of non-Markovianity. Moreover, the non-Markovianity is stronger and more sensitive for the bath in the symmetric phase than the symmetry broken phase.

DOI
10.1088/1674-1056/24/10/100305

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We study the non-Markovianity of the single qubit system coupled with an isotropic Lipkin–Meshkov–Glick (LMG) model by an effective method proposed by Breuer et al . (Breuer H P and Piilo J 2009 Europhys. Lett. 85 5004). It is discovered that the non-Markovianity is concerned with the quantum phase transitions (QPTs). In the open system, we present that the strong coupling inside the bath and the strong interaction between the system and bath can enhance the degree of non-Markovianity. Moreover, the non-Markovianity is stronger and more sensitive for the bath in the symmetric phase than the symmetry broken phase.
Based on conditional past-future (CPF) correlations, we study the non-Markovianity of a central spin coupled to an isotropic Lipkin-Meshkov-Glick (LMG) bath. Although the dynamics of a system is always non-Markovian, it is found that some measurement time intervals considering a specific process, with respect to a particular set of CPF measurement operators, can be zero, which means that in this case the non-Markovianity of the system could not be detected. Furthermore, the initial system-bath correlations only slightly influence the non-Markovianity of the system in our model. Significantly, it is also found that the dynamics of the system for LMG baths, initially in the ground states corresponding to the symmetric phase and symmetry broken phase, exhibit different properties, and the maximal value of the CPF at the critical point is the smallest, independent of the measurement operator, which means that the criticality can manifest itself by the CPF. Moreover, the effect of bath temperature on the quantum criticality of the CPF depends on the measurement operator.
We explore a dynamic signature of quantum phase transition (QPT) in an isotropic Lipkin-Meshkov-Glick (LMG) model by studying the time evolution of a central qubit coupled to it. We evaluate exactly the time-dependent purity, which can be used to measure quantum coherence, of the central qubit. It is found that distinctly different behaviors of the purity as a function of the parameter reveal clearly the QPT point in the system. It is also clarified that the present model is equivalent to an anti--Jaynes-Cummings model under certain conditions.
We study the quantum dynamics of a single qubit coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The spin bath is described by the Lipkin-Meshkov-Glick model and the bath spins are subjected to a transverse magnetic field. We investigate the qubit interacting via either an Ising- or an XY-type coupling term to subsets of bath spins of differing size. The large degree of symmetry of the bath allows us to find parameter regimes where the initial qubit state is revived at well-defined times after the qubit preparation. These times may become independent of the bath size for large baths and thus enable faithful qubit storage even in the presence of strong coupling to a bath. We analyze a large range of parameters and identify those which are best suited for quantum memories. In general we find that a small number of links between qubit and bath spins leads to less decoherence and that systems with Ising coupling between qubit and bath spins are preferable.
The information scrambling phenomena in an open quantum system modeled by Ising spin chains coupled to Lipkin-Meshkov-Glick (LMG) baths are observed via an interferometric method for obtaining out-of-time-ordered correlators ($\mathcal{F}\ensuremath{-}\mathrm{OTOC}$). We also use an anisotropic bath connecting to a system of tilted field Ising spin chains in order to confirm that such situations are suitable for the emergence of ballistic spreading of information manifested in the light cones in the $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ profiles. Bipartite OTOC is also calculated for a bipartite open system, and its behavior is compared with that of the $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ of a two-spin open system to get a picture of what these measures reveal about the nature of scrambling in different parameter regimes. Additionally, the presence of distinct phases in the LMG model motivated an independent analysis of its scrambling properties, where $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ diagnostics revealed that quantum chaos emerges exclusively in the symmetry-broken phase.
We study the dynamics of an open quantum system interacting with a non-thermal bath. Here, "non-thermal" means that the bath modes do not need to have the same temperature, but they have an effective temperature distribution. We find that, when a quantum system is interacting with such a non-thermal bath far from thermal equilibrium, it is no longer proper to use any coarse-grained Markovian description for the system, even when their coupling strength is quite weak. Especially, when there is coherent transition with strong interference strength in the quantum system, the Markovian master equation would bring in a serious problem of negative probability. After we consider some proper non-Markovian corrections, the problem can be naturally resolved.