[论文解读] Pattern formation in driven condensates

Kiryang Kwon, J. H. Choi|arXiv (Cornell University)|Jan 9, 2026

Cold Atom Physics and Bose-Einstein Condensates被引用 0

一句话总结

简要：对驱动量子气体中模式形成的实验与理论进展的综述，涵盖费拉底波在玻色子和费米子系统中的表现、二维模式形成、表面模态、时间晶体，以及来自反流不稳定性的涌现图案。

ABSTRACT

Spontaneous pattern formation out of homogeneous media is one of the well-understood examples of hydrodynamic instabilities in classical systems, which naturally leads to the question of its manifestation in quantum fluids. Bose-Einstein condensates (BECs) of atomic gases have been an ideal platform for studying many-body quantum phenomena, such as superfluidity, and simultaneously providing an opportunity to broaden our understanding of classical hydrodynamics into quantum systems. In this review, we introduce a range of experimental studies on the pattern formation in quantum fluids of atomic gases under external driving, including Faraday waves in one and two dimensions, surface patterns, and counterflow instabilities in a mixture of superfluids. The pattern formation in the quantum system can be understood through the parametric amplification process, where an unstable dynamical mode can be exponentially amplified, similar to classical systems. Remarkably, the governing equations for surface excitations of trapped BECs can be mathematically equivalent to those of shallow water, indicating a universal description of the hydrodynamic instability across classical and quantum domains. However, the condensates, as superfluids, also possess fundamental quantum characteristics, such as quantized vorticity and a distinct dissipation channel. These unique features showcase many-body fragmentation under strong modulation and the generation of vortices in the nonlinear regime, which could offer a pathway to the study of quantum turbulence. Furthermore, the coexistence of long-range phase coherence and density modulation in driven condensates could provide unexplored features, such as those seen in supersolid-like sound modes, within nonequilibrium settings.

研究动机与目标

• 总结量子气体中非平衡模式形成的实验进展。
• 解释经典不稳定性概念如何转化到量子流体及其独特特征。
• 在玻色与费米系统以及二维几何中展示费拉底波现象。
• 讨论量子流体中来自反流不稳定性的涌现图案。

提出的方法

• 综合在各种驱动方案下对BECs和费米气体中费拉底图样的实验观测。
• 通过参量共振与非线性模耦合的理论解释进行突出。
• 呈现实验观测到的二维模式形成与表面多边模态，并结合对称性分析。
• 将实验发现与亚谐频响应及相干动力学的时间晶体概念联系起来。
• 在均场描述失效时，讨论从头算多体方法（如 MCTDHB）等。

Figure 1: Various patterns in classical systems. (a) Polygonal structure observed in Sputnik Planum, Pluto. Adapted with permission from ref McKinnon2016 , Springer Nature Limited. (b) Various Chladni patterns in oscillating square-shaped metal plate. Adapted from ref Tuan2018 under a Creative Commo

实验结果

研究问题

• RQ1 驱动的量子气体在不同维度和相互作用体系中如何表现费拉底图样？
• RQ2 在周期驱动下，量子流体的模式形成被哪些机制稳定或不稳定？
• RQ3 观测到的图案是否可在 Floquet 设置中被解释为时间晶体或其他非平衡相？
• RQ4 表面与反流不稳定在量子流体中如何表现，与经典对应物相比有何不同？
• RQ5 在超出均场描述的情况下，多体相关性在模式形成中扮演何种角色？

主要发现

• 在BEC中，费拉底图样可通过陷阱频率、相互作用调制或定制势驱动来实现，观测到密度调制，有时也出现共振波。
• 在二维中，物质波喷射和规则晶格图样（方形、三角、六边形）由于非线性模耦合和参量放大而出现。
• 通过吸收样边界在有限系统中实现稳定的二维费拉底图样，从而通过非线性模竞争形成方格晶格，近似无限系统。
• 驱动凝聚态的表面模态可表现为多边形图样（D2–D7），其共振频率与自然表面模态频率的两倍相关，部分模态显示动力学不稳定。
• 时钟型行为（在驱动频率的一半处的亚谐响应）在时空图样中被观测到，表明长期相位相干性与非线性饱和。
• 费米气体中的实验在BEC一侧看到费拉底波，相位传播速度与超流中的音速一致；在 BCS 侧由于凝聚分量减少，仍存在挑战。

Figure 2: Faraday pattern in Bose-Einstein condensates. Absorption images of trapped quasi one-dimensional BEC after modulating the radial trap frequency. Labels in each image represent the driving frequencies. Adapted with permission from Engels2007 , APS.