线性引力类约束下谐波捕获的一维量子液滴的集体动力学
Collective dynamics of harmonically trapped 1D quantum droplets under linear gravitational-like confinement
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中文总结 AI 辅助
研究一维二元玻色 - 爱因斯坦凝聚体中谐波约束量子液滴在类引力势下的动力学，通过分析质心等动力学及量子态表征得出相关特性，数值模拟验证，展示了线性势对集体激发等性质的影响。
中文摘要 AI 辅助
我们在一维扩展的格罗斯-皮塔耶夫斯基框架内，研究了二元玻色-爱因斯坦凝聚体中谐波约束量子液滴在恒定线性（类引力）势下的动力学，包括LHY修正。通过分析质心（COM）和宽度动力学，我们表明单极（呼吸）模式仍受谐波约束支配，其频率对线性扰动渐近不敏感，证明了内部集体激发对均匀外部强迫的鲁棒性。相比之下，COM表现出与相互作用相关的输运，弱约束产生大的敏感性和快速位移，而强约束即使在大强迫下也抑制输运。COM响应随陷阱频率增加而单调降低。我们还通过量子费舍尔信息和维格纳准概率分布进一步表征了演化的量子态，表明线性势能够在有限时间内可控地产生具有增强计量灵敏度的态，而更强的约束将高灵敏度 regime 的起始点转移到更大的强迫强度。基于分步傅里叶方法的数值模拟证实了所得解的动力学稳定性。这些结果说明了线性引力类陷阱对一维超稀量子流体的集体激发、输运和量子计量性质的影响。
英文摘要
We investigate the dynamics of harmonically confined quantum droplets in a binary Bose Einstein condensate within the one dimensional extended Gross Pitaevskii framework, including LHY corrections, under a constant linear (gravitational like) potential. By analyzing the COM and width dynamics, we show that the monopole (breathing) mode remains governed by the harmonic confinement, with a frequency asymptotically insensitive to the linear perturbation, demonstrating the robustness of internal collective excitations against uniform external forcing. In contrast, the COM exhibits interaction-dependent transport, with weak confinement producing large susceptibility and rapid displacement, whereas strong confinement suppresses transport even under large forcing. The COM response decreases monotonically with increasing trap frequency. We further characterize the evolving quantum state through the quantum Fisher information and Wigner quasi-probability distributions, showing that the linear potential enables controlled generation of states with enhanced metrological sensitivity over finite times, while stronger confinement shifts the onset of the high-sensitivity regime to larger forcing strengths. Numerical simulations based on the split-step Fourier method confirm the dynamical stability of the obtained solutions. These results illustrate the impact of linear gravitational like trap on the collective excitations, transport, and quantum metrological properties of 1D ultradilute quantum fluids.
