[论文解读] Universality in driven open quantum matter

Lukas M. Sieberer, Michael Buchhold+2 more|arXiv (Cornell University)|Dec 5, 2023

Advanced Thermodynamics and Statistical Mechanics被引用 7

一句话总结

本文通过 Lindblad-Keldysh 场论，为驱动开放量子物质中的普遍性建立了一个统一的理论框架，揭示了对称性、态的纯度和标度律如何支配非平衡稳态。该研究在不同量子平台（包括里德堡原子、冷原子和超导量子比特）中识别出普遍行为，展示了非平衡普遍性的新实现形式，包括 KPZ 标度、自组织临界性以及量子临界性，这些现象在平衡系统中均无对应物。

ABSTRACT

Universality is a powerful concept, which enables making qualitative and quantitative predictions in systems with extensively many degrees of freedom. It finds realizations in almost all branches of physics, including in the realm of nonequilibrium systems. Our focus here is on its manifestations within a specific class of nonequilibrium stationary states: driven open quantum matter. Progress in this field is fueled by a number of uprising platforms ranging from light-driven quantum materials over synthetic quantum systems like cold atomic gases to the functional devices of the noisy intermediate scale quantum era. These systems share in common that, on the microscopic scale, they obey the laws of quantum mechanics, while detailed balance underlying thermodynamic equilibrium is broken due to the simultaneous presence of Hamiltonian unitary dynamics and nonunitary drive and dissipation. The challenge is then to connect this microscopic physics to macroscopic observables, and to identify universal collective phenomena that uniquely witness the breaking of equilibrium conditions, thus having no equilibrium counterparts. In the framework of a Lindblad-Keldysh field theory, we discuss on the one hand the principles delimiting thermodynamic equilibrium from driven open stationary states, and on the other hand show how unifying concepts such as symmetries, the purity of states, and scaling arguments are implemented. We then present instances of universal behavior structured into three classes: new realizations of paradigmatic nonequilibrium phenomena, including a survey of first experimental realizations; novel instances of nonequilibrium universality found in these systems made of quantum ingredients; and genuinely quantum phenomena out of equilibrium, including in fermionic systems. We also discuss perspectives for future research on driven open quantum matter.

研究动机与目标

• 为驱动开放量子系统在热平衡之外的普遍性建立统一的理论框架。
• 识别驱动开放量子物质中缺乏平衡对应物的普遍集体现象，例如 KPZ 普遍性和量子临界性。
• 通过对称性、标度和格林函数，将微观 Lindblad 动力学与宏观可观测量联系起来。
• 探索在里德堡原子阵列和冷原子气体等平台中非平衡普遍性的实验实现。
• 将临界性和对称性自发破缺的概念扩展至具有非幺正动力学和耗散的开放量子系统。

提出的方法

• 为驱动开放量子系统构建 Lindblad-Keldysh 场论，将动力学映射到具有经典场和量子场的 Keldysh 作用量。
• 应用 Keldysh 旋转以推导出滞后、先进和 Keldysh 格林函数，从而能够描述非平衡关联函数。
• 使用规范功率计数和重整化群（RG）技术，分析确定性和半经典极限下的标度行为。
• 通过对称性分析识别普遍性类，包括经典对称性的自发破缺和耗散性戈尔登斯通定理。
• 分析具体模型，如紧致 KPZ 方程、定向渗流和暗态双稳态，以提取普遍标度指数。
• 将该框架应用于费米子系统、拓扑相变和耗散性杂质，揭示新的量子普遍性类。

Figure 1: Top: Illustration of the sandpile model. Sand is piling up on a plate via slow deposition ( $=$ drive). The sandpile reaches a critical slope at which friction and gravitation balance each other. Further deposition triggers scale invariant avalanches, which deplete at the boundaries ( $=$

实验结果

研究问题

• RQ1 Keldysh 作用量中的对称性和守恒律如何支配驱动开放量子系统中的普遍行为？
• RQ2 驱动开放凝聚体中的普遍标度律和临界指数是什么？它们与平衡对应物有何不同？
• RQ3 KPZ 普遍性是否可能在二维驱动开放玻色-爱因斯坦凝聚体中出现？在空间各向异性下，其稳定性机制是什么？
• RQ4 暗态在实现普遍非平衡动力学中起到什么作用，特别是在量子 Zeno 效应和纯化过程中的作用？
• RQ5 量子临界性在驱动开放系统中如何表现？它与噪声驱动的 Luttinger 液体有何区别？

主要发现

• 本文确立了驱动开放量子物质中的普遍性源于 Keldysh 作用量中的对称性和标度，即使在缺乏细致平衡的情况下亦成立。
• KPZ 普遍性在一二维驱动开放凝聚体中得以实现，强空间各向异性下由非对称 KPZ 方程支配二维临界行为。
• 噪声激活的涡旋解绑机制稳定了二维驱动开放凝聚体中的有序相，使 KPZ 标度可观测。
• 在一维系统中，噪声激活的时空涡旋破坏了 KPZ 标度，标志向湍流的相变。
• 本文在驱动开放玻色气体中识别出一类新的量子临界固定点，其标度行为与平衡量子临界性显著不同。
• 驱动系统中暗态双稳态导致一阶相变，具有普遍标度行为，可在里德堡原子和超导量子比特平台中实现。

Figure 2: Self-organized criticality in a gas of ultracold Rydberg atoms. (a) Driving an inhomogeneously trapped gas with an off-resonant laser induces the facilitated spreading of excitations (blue dots). (b) Evolution of the density of atoms $n$ ( $\equiv n(t,\mathbf{x})$ ) and the excitation dens