Lai G-Y, Hsueh C-H, Wu W C
Department of Physics, National Taiwan Normal University, Taipei, 11677, Taiwan.
Department of Optoelectric Physics, Chinese Culture University, Taipei, 11114, Taiwan.
Sci Rep. 2025 Sep 26;15(1):33079. doi: 10.1038/s41598-025-16729-4.
Quantum droplets-arising from the delicate balance between repulsive and attractive interactions-continue to be of significant interest in the study of ultracold atomic systems. In this work, we revisit the ground-state properties and collective dynamics of one-dimensional quantum droplets. We identify a critical effective particle number, [Formula: see text], at which the superfluid fraction [Formula: see text] exhibits a distinct inflection point, indicating a structural transition in the ground state. For [Formula: see text], the density profile is sharply peaked, whereas for [Formula: see text], it flattens into a plateau-like shape well-approximated by the Thomas-Fermi model. Additionally, we show that super-Gaussian functions provide excellent fits to the ground-state density profiles, offering a simple and accurate modeling approach. To study the system's dynamical behavior, we develop an analytical framework for quantum droplets subjected to a periodic lattice potential. In the weak-lattice limit ([Formula: see text]), the excitation spectrum reveals a Goldstone gapless phonon mode, characteristic of superfluidity. However, at low densities, the inclusion of Lee-Huang-Yang corrections leads to phonon instabilities, consistent with the transition from a peak- to a plateau-like ground state. In the strong-lattice regime (large [Formula: see text]), a gap opens in the lowest excitation modes, suggesting a crossover from a superfluid to a Mott-insulating phase. Our findings should shed light on key aspects of a low-dimensional quantum droplet.
量子液滴源于排斥相互作用和吸引相互作用之间的微妙平衡，在超冷原子系统的研究中一直备受关注。在这项工作中，我们重新审视了一维量子液滴的基态性质和集体动力学。我们确定了一个临界有效粒子数，[公式：见原文]，在该数处超流分数[公式：见原文]呈现出一个明显的拐点，这表明基态存在结构转变。对于[公式：见原文]，密度分布急剧峰值化，而对于[公式：见原文]，它变平为类似托马斯 - 费米模型很好近似的平台状形状。此外，我们表明超高斯函数能很好地拟合基态密度分布，提供了一种简单而准确的建模方法。为了研究系统的动力学行为，我们为受周期晶格势作用的量子液滴开发了一个分析框架。在弱晶格极限（[公式：见原文]）下，激发谱揭示了一个戈德斯通无隙声子模式，这是超流性的特征。然而，在低密度下，包含李 - 黄 - 杨修正会导致声子不稳定性，这与从峰值状到平台状基态的转变一致。在强晶格 regime（大[公式：见原文]）中，最低激发模式出现能隙，表明从超流相到莫特绝缘相的转变。我们的发现应该能阐明低维量子液滴的关键方面。
