[论文解读] Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems

Orazio Scarlatella, Aashish A. Clerk+2 more|arXiv (Cornell University)|Aug 6, 2020

Cold Atom Physics and Bose-Einstein Condensates被引用 2

一句话总结

该论文将动力学平均场理论（DMFT）扩展至马尔可夫开放量子多体系统，提出一种非微扰求解器，用于处理与非马尔可夫 bath 耦合的玻色子杂质问题。研究揭示了由跃迁诱导的耗散过程，这些过程会抑制局部增益并驱动有限频率的超流相变，从根本上改变了驱动-耗散玻色- Hubbard 系统的相图，使其与平均场理论预测显著不同。

ABSTRACT

Open quantum many body systems describe a number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits to ultracold atoms in optical lattices. Their theoretical understanding is hampered by their large Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work we extend the nonequilibrium bosonic Dynamical Mean Field Theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for finite lattice connectivity corrections beyond Gutzwiller mean-field theory. We develop a non-perturbative approach to solve this bosonic impurity problem, which treats the non-Markovian bath in a non-crossing approximation. As a first application, we address the steady-state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition towards a non-equilibrium superfluid, leading to a strong renormalization of the phase boundary at finite-connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.

研究动机与目标

• 开发一种适用于具有马尔可夫耗散的开放量子多体系统的非微扰框架。
• 将非平衡玻色子 DMFT 扩展至包含超越 Gutzwiller 平均场理论的非马尔可夫 bath 效应。
• 研究具有两体损失和非相干泵浦的驱动-耗散玻色- Hubbard 模型的稳态性质。
• 识别并表征标准平均场方法所遗漏的耗散过程。

提出的方法

• 通过 DMFT 将耗散玻色子晶格映射为杂质问题，其中杂质与自洽平均场及非马尔可夫 bath 耦合。
• 利用非交叉图的非微扰重求和方法求解杂质问题，以考虑非马尔可夫关联。
• 实施一种自洽方案，其中 bath 谱函数通过杂质格林函数迭代更新。
• 使用 Lindblad 主方程描述马尔可夫耗散，跃迁算符用于建模两体损失和非相干泵浦。
• 通过求解杂质与 bath 的自洽方程推导稳态性质。
• 将序参量的有限频率不稳定性与量子 van der Pol 振子阵列中的同步转变联系起来。

实验结果

研究问题

• RQ1 跃迁诱导的耗散过程如何影响驱动-耗散玻色- Hubbard 模型的稳态？
• RQ2 非马尔可夫 bath 关联在开放量子系统中如何改变平均场理论的预测？
• RQ3 DMFT 能否捕捉导致非平衡超流体中振荡序参量的有限频率不稳定性？
• RQ4 引入非马尔可夫效应后，如何改变正常相与超流相之间的相边界？
• RQ5 涌现的序参量动力学与量子 van der Pol 振子阵列中的同步之间存在何种联系？

主要发现

• 在 Gutzwiller 平均场理论中缺失的跃迁诱导耗散过程，显著重新分布了稳态布居，并抑制了局部增益。
• 由于这些过程，正常相被强烈重整化，导致局部增益被抑制，并出现稳定的量子-齐诺效应区域。
• 超流相变表现为有限频率不稳定性，导致时间依赖的振荡序参量。
• 在有限连通性下，相边界被强烈重整化，与平均场预测显著偏离。
• 振荡序参量被识别为量子 van der Pol 振子阵列中多体同步转变的特征。
• 非微扰 DMFT 求解器成功捕捉了超越标准平均场近似的非马尔可夫关联与耗散效应。