倾斜玻色-爱因斯坦凝聚体中局域化的动力学特征与基布尔-祖雷克标度
Dynamical Signatures and Kibble-Zurek Scaling of Localization in Tilted Bose-Einstein Condensates
AI总结：
该研究以加载于浅光晶格的一维玻色-爱因斯坦凝聚体为对象，通过淬火和有限速率斜坡分析，确立了淬火响应与有限速率标度作为局域化的互补动力学探针，揭示了倾斜诱导局域化的动力学特征及基布尔-祖雷克标度规律。
AI中文摘要：
我们研究加载在浅光晶格中的一维玻色-爱因斯坦凝聚体中由倾斜诱导的局域化的非平衡特征。倾斜强度是局域化-退局域化转变的控制参数，我们还考虑了排斥相互作用的影响，这种作用倾向于使凝聚体退局域化。我们首先通过相互作用强度和外倾斜的突然淬火来表征局域化和退局域化区域，利用存活概率及其功率谱密度分析所得动力学。局域化的凝聚体表现出强记忆保持、显著的 revival（ revival 指量子态的复苏）、规则动力学以及窄谱响应，而退局域化的凝聚体则表现出被抑制的 recurrence（ recurrence 指量子态的复现）、不规则动力学以及在多个频率上更宽的谱权重分布。随后，我们研究倾斜强度跨越局域化阈值的有限速率斜坡，利用局域化长度和玻戈留波夫激发能隙提取相关临界指数，并对驱动动力学进行基布尔-祖雷克标度分析。我们的结果确立了淬火响应和有限速率标度作为相互作用玻色气体中局域化的互补动力学探针，与倾斜光晶格中的冷原子实验直接相关。
英文摘要：
We study nonequilibrium signatures of tilt-induced localization in a one-dimensional Bose-Einstein condensate loaded in a shallow optical lattice. The tilt strength acts as a control parameter for the localization-delocalization crossover. We also consider the effects of repulsive interactions, which tend to delocalize the condensate. We first characterize localized and delocalized regimes through sudden quenches of the interaction strength and the external tilt. The resulting dynamics is analyzed using the survival probability and its power spectral density. Localized condensates exhibit strong memory retention, pronounced revivals, regular dynamics and a narrow spectral response, whereas delocalized condensates show suppressed recurrences, irregular dynamics and a broader distribution of spectral weight over many frequencies. We then investigate finite-rate ramps of the tilt strength across the localization threshold. Using the localization length and the Bogoliubov excitation gap, we extract the relevant critical exponents and perform Kibble-Zurek scaling analysis in the driven dynamics. Our results establish quench response and finite-rate scaling as complementary dynamical probes of localization in interacting Bose gases, with direct relevance to cold-atom experiments in tilted optical lattices.
