arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2111.04041quant-ph
收藏

量子储层工程中的非对角 Lindblad 主方程

Non-diagonal Lindblad master equations in quantum reservoir engineering

Diego N. Bernal-García, Lujun Huang, Andrey E. Miroshnichenko, Matthew J. Woolley

备注：
20 pages, 4 figures. The title was changed. A new section and an appendix were included. Minor revisions were made to the rest of the manuscript
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文针对由非对角Lindblad主方程描述的线性高斯系统提出了一阶和二阶矩动力学方程，可高效求解稳态解析解，发现Duan纠缠判据同样适用于费米子系统，并应用于光机械系统双模纠缠研究。

摘要：

储层工程已被证明是控制开放量子系统的一种实用方法，通过适当地操纵储层和系统-储层相互作用来保持量子相干性。在这种情况下，对于由不同部分组成的系统，通常通过对系统的其余组件进行绝热消除来描述感兴趣子系统的动力学。这一过程通常会导致子系统的一个有效主方程，它不具备 Gorini-Kossakowski-Lindblad-Sudarshan 主方程的对角形式（这里称为对角 Lindblad 形式）。相反，它具有更一般的结构（这里称为非对角 Lindblad 形式），明确揭示了子系统各组件之间的耗散耦合。在这项工作中，我们提出了一组动力学方程，用于描述由非对角 Lindblad 主方程描述的线性高斯系统（玻色子和费米子）的正则变量的一阶矩和二阶矩。我们的方法高效，并允许获得稳态的解析解。我们补充了对协方差矩阵方法的回顾，重点关注与纠缠测量相关的方法。值得注意的是，我们的探索产生了一个令人惊讶的副产品：通常应用于玻色子系统以验证纠缠的 Duan 判据，被发现同样适用于费米子系统。我们以一个实际例子作为结论，在该例子中我们重新审视了光机械装置中的双模机械纠缠。我们的方法对受含时哈密顿量支配的系统采用绝热消除，为检验以前未曾探索的物理机制打开了大门。

英文摘要：

Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised of different parts, it is common to describe the dynamics of a subsystem of interest by performing an adiabatic elimination of the remaining components of the system. This procedure often leads to an effective master equation for the subsystem that is not in the diagonal form of the Gorini-Kossakowski-Lindblad-Sudarshan master equation (here called diagonal Lindblad form). Instead, it has a more general structure (here called non-diagonal Lindblad form), which explicitly reveals the dissipative coupling between the various components of the subsystem. In this work, we present a set of dynamical equations for the first and second moments of the canonical variables for linear Gaussian systems, bosonic and fermionic, described by non-diagonal Lindblad master equations. Our method is efficient and allows one to obtain analytical solutions for the steady state. We supplement our findings with a review of covariance matrix methods, focusing on those related to the measurement of entanglement. Notably, our exploration yields a surprising byproduct: the Duan criterion, commonly applied to bosonic systems for verification of entanglement, is found to be equally valid for fermionic systems. We conclude with a practical example, where we revisit two-mode mechanical entanglement in an optomechanical setup. Our approach, which employs adiabatic elimination for systems governed by time-dependent Hamiltonians, opens the door to examine physical regimes that have not been explored before.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑