Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
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局部耦合到一维自旋链的两个量子位之间并发的生成
DOI：
10.1103/physreva.94.022316
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Dutta
中科院分区：
文献类型：
--
作者：
T. Nag;A. Dutta
我们考虑一个广义的中心自旋模型，由两个中心量子位和一个环境自旋链（具有周期性边界条件）组成，这些中心量子位在同一位置或在相隔距离 $d$ 的两个不同位置局部弱连接。我们的目的是研究当量子位最初处于非纠缠状态时，纠缠的后续时间生成，通过并发进行量化。在均衡情况下，我们表明，当环境自旋链至关重要时，并发会在较大的 $d$ 值下生存。重要的是，在平衡和非平衡情况下观察到的一个共同特征是，两个量子位在临界淬灭时变得最大程度地纠缠，而后者是由环境横向场的突然但全局的变化造成的。随着自旋链的非平衡演化，我们对 $d\neq 0$ 的研究表明存在一个阈值时间，高于该阈值时间并发达到有限值。此外，我们表明独立的退相干通道（DC）的数量由 $d$ 以及控制时间演化的两个基础哈密顿量的横向场的局部差异决定。如本文所述，通过分析这些通道的非平衡演化来表征临界和非临界淬火同时出现的性质相似的行为。当退相干因子或与最快 DC 相关的回波衰减到零时，并发性最大；相反，并发消失的条件是由中间 DC 之一的相关衰减决定的。通过分析单个量子位的密度降低，我们还解释了相移速率总是慢于解缠结速率的观察结果。
We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance $d$. Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of $d$ when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the non-equilibrium situations while the latter is created by a sudden but global change of the environmental transverse field, is that the two qubits become maximally entangled for the critical quenching. Following a non-equilibrium evolution of the spin chain, our study for $d\neq 0$, indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by $d$ as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the non-equilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined non-trivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate.