标题： 光学晶格中玻色-爱因斯坦凝聚体的异常涨落 显示英文标题

标题： Anomalous fluctuations of Bose-Einstein condensates in optical lattices

摘要： 涨落是物理学中的基本现象，对于理解和表征相变非常重要。 在这种理念下，向玻色-爱因斯坦凝聚态（BEC）的相变具有特殊的重要性。 尽管原子BEC中凝聚态粒子数的涨落已在连续系统中被研究过，但对格点系统的实验和理论研究到目前为止仍然缺失。 在这里，我们通过实验和理论相结合的研究，探讨了光学晶格BEC在相变过程中凝聚态粒子数的涨落。 我们既提供了使用超冷$^{87}$Rb原子的实验数据，也基于一种结合玻利乌布诺夫准粒子框架与主方程分析的混合方法进行了数值模拟。 我们发现存在强烈的异常涨落，其中凝聚态粒子数$\delta N_{\rm BEC}^2$的方差随着总原子数按$N^{1+\gamma}$的形式变化，指数约为$\gamma_{\rm theo}=0.74$和$\gamma_{\rm exp}=0.62$，我们认为这是由于二维/三维交叉几何结构和相互作用造成的。 我们的研究强调了陷阱几何结构对涨落性质以及基本量子力学特性的重要性。 显示英文摘要

摘要： Fluctuations are fundamental in physics and important for understanding and characterizing phase transitions. In this spirit, the phase transition to the Bose-Einstein condensate (BEC) is of specific importance. Whereas fluctuations of the condensate particle number in atomic BECs have been studied in continuous systems, experimental and theoretical studies for lattice systems were so far missing. Here, we explore the condensate particle number fluctuations in an optical lattice BEC across the phase transition in a combined experimental and theoretical study. We present both experimental data using ultracold $^{87}$Rb atoms and numerical simulations based on a hybrid approach combining the Bogoliubov quasiparticle framework with a master equation analysis for modeling the system. We find strongly anomalous fluctuations, where the variance of the condensate number $\delta N_{\rm BEC}^2$ scales with the total atom number as $N^{1+\gamma}$ with an exponent around $\gamma_{\rm theo}=0.74$ and $\gamma_{\rm exp}=0.62$, which we attribute to the 2D/3D crossover geometry and the interactions. Our study highlights the importance of the trap geometry on the character of fluctuations and on fundamental quantum mechanical properties.