AI 中文总结
本研究通过扩展 Gross-Pitaevskii 方程，探究一维量子液滴的声传播，揭示其声速受密度分布等影响的规律，证实声传播可作为探测有限尺寸效应及交叉转变的灵敏探针，为超冷 $^{39}$K 液滴实验观测提供可行途径。
AI 中文摘要
量子液滴的声传播与常规玻色-爱因斯坦凝聚体（BEC）不同，这是由于其自束缚特性及量子涨落的作用。我们研究由对称玻色-玻色混合物形成的一维量子液滴中的声传播，重点关注有限尺寸效应与囚禁效应。采用扩展的 Gross-Pitaevskii 方程，我们从局域密度扰动的实时传播中提取声速，并将其与低能激发谱进行比较。我们发现，与常规 BEC 不同，有限液滴的声速受其密度分布和量子压强贡献的强烈影响：随着粒子数增加，液滴从类高斯分布演变为平顶分布，声速随之降低，趋近于体相量子液滴的值。相反，外部简谐囚禁会压缩液滴并提高声速，使系统趋近于囚禁 BEC 的声学行为。我们的结果表明，声传播可作为探测有限尺寸效应及自束缚量子液滴与常规玻色气体之间 crossover（ crossover 译为“交叉转变”）的灵敏探针，并为超冷 $^{39}$K 液滴的实验观测提供可行途径。
英文摘要
Sound propagation in quantum droplets differs from that in conventional Bose-Einstein condensates (BECs) because of their self-bound nature and the role of quantum fluctuations. We investigate sound propagation in one-dimensional quantum droplets formed by a symmetric Bose-Bose mixture, focusing on finite-size and confinement effects. Using the extended Gross-Pitaevskii equation, we extract the sound velocity from the real-time propagation of localized density perturbations and compare it with the low-energy excitation spectrum. We find that, unlike in a conventional BEC, the sound velocity of a finite droplet is strongly affected by its density profile and quantum-pressure contribution. It decreases with increasing particle number as the droplet evolves from a Gaussian-like to a flat-top profile, approaching the bulk quantum-droplet value. In contrast, external harmonic confinement compresses the droplet and enhances the sound velocity, driving the system toward the acoustic behavior of a trapped BEC. Our results establish sound propagation as a sensitive probe of finite-size effects and the crossover between self-bound quantum droplets and conventional Bose gases, and suggest a feasible route for experimental observation in ultracold $^{39}$K droplets.
Comments11 pages, 6 figures
