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Acta Physica Sinica

Finite-Temperature Effects in Ultracold Atomic Gases

HOU Licong, HE Liangjun, Biao Dong, ZHANG Yongchang

Published Sep 4, 2026• 0 citations
Publisher

Abstract

自玻色–爱因斯坦凝聚体实验实现以来，超冷原子体系已成为研究量子多体物理的理想平台之一。尽管零温平均场理论取得了巨大成功，但实际系统温度不可能降至绝对零度，必然面临有限温效应。热涨落不仅会导致非凝聚成分增加，也可能引起其他反常物理效应，例如偶极冷原子系统中温度驱动的超固态相变。本文总结了处理冷原子气体有限温效应的三大主要理论框架：温度依赖的扩展Gross-Pitaevskii方程（TeGPE）、连续空间经典场方法（PGPE/SPGPE）以及量子蒙特卡罗方法（QMC），梳理了上述方法在处理有限温基态相图、非平衡耗散动力学以及强关联涨落等物理问题中的理论优势与适用条件；最后展望了能够实时自洽追踪热原子气体反馈效应的量子动力学方法。

DOI
10.7498/aps.76.20260786

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自玻色–爱因斯坦凝聚体实验实现以来，超冷原子体系已成为研究量子多体物理的理想平台之一。尽管零温平均场理论取得了巨大成功，但实际系统温度不可能降至绝对零度，必然面临有限温效应。热涨落不仅会导致非凝聚成分增加，也可能引起其他反常物理效应，例如偶极冷原子系统中温度驱动的超固态相变。本文总结了处理冷原子气体有限温效应的三大主要理论框架：温度依赖的扩展Gross-Pitaevskii方程（TeGPE）、连续空间经典场方法（PGPE/SPGPE）以及量子蒙特卡罗方法（QMC），梳理了上述方法在处理有限温基态相图、非平衡耗散动力学以及强关联涨落等物理问题中的理论优势与适用条件；最后展望了能够实时自洽追踪热原子气体反馈效应的量子动力学方法。
从白天一它的发现， c 超导性是异常还普遍的 pseudogap 现象，一致还有待于在物理社区以内为被到达，在超过 27 年集中的研究努力以后。在这篇文章，我们将以理论理解和试验性的观察在原子费密气体在 pseudogap 现象的学习考察进步。我们证明为在强烈交往的费密气体的 pseudogap 的存在有充分、不含糊的证据。在这上下文，我们将介绍它是的 pseudogap 物理和表演的一个配对的变化理论确实为高 T 的一个强壮的候选人理论 c 超导性。
We review c-field methods for simulating the non-equilibrium dynamics of degenerate Bose gases beyond the mean-field Gross-Pitaevskii approximation. We describe three separate approaches that utilise similar numerical methods, but have distinct regimes of validity. Systems at finite temperature can be treated with either the closed-system projected Gross-Pitaevskii equation (PGPE), or the open-system stochastic projected Gross-Pitaevskii equation (SPGPE). These are both applicable in quantum degenerate regimes in which thermal fluctuations are significant. At low or zero temperature, the truncated Wigner projected Gross-Pitaevskii equation (TWPGPE) allows for the simulation of systems in which spontaneous collision processes seeded by quantum fluctuations are important. We describe the regimes of validity of each of these methods, and discuss their relationships to one another, and to other simulation techniques for the dynamics of Bose gases. The utility of the SPGPE formalism in modelling non-equilibrium Bose gases is illustrated by its application to the dynamics of spontaneous vortex formation in the growth of a Bose-Einstein condensate.
在 ultracold Rydberg 气体的学习的最近的开发要求试验性的精深，高原子、光的密度必须与外部领域和敏感 Rydberg 原子察觉的优秀控制在被相结合的先进水平。我们描述过去常生产并且学习从稠密的 ultracold 激动的交往 Rydberg 原子的一个定制的试验性的系统原子气体。实验用高流动寒冷原子来源和三根横梁为快责任周期被优化了光偶极子陷井。后者启用在几个数量级上原子密度和温度调节，一路上到 Bose 爱因斯坦冷凝作用转变。包围原子的电极结构允许对电场和 Rydberg 原子的单个粒子的敏感领域电离察觉的精确控制。我们考察在不同许多身体系统上加亮强壮的 Rydberg-Rydberg 相互作用的影响的二个实验。首先， Rydberg 封锁效果习惯于预先组织在它进 ultracold 血浆的自发的进化以前的原子气体。第二，称为黑暗状态的电磁声子的光子和原子的混合状态被学习。由看 Rydberg 激动的原子的统计分发，我们揭示在黑暗状态的电磁声子之间的关联。这些实验将最终在强烈交往的政体提供许多身体现象的更深的理解，包括在在量水平的原子和灯之间的强烈联合的血浆和接口的学习。
Quantum many-body systems offer rich physics, their theoretical description, however, faces challenges. An experimentally controllable and well-characterised system is provided by Bose-Einstein condensates (BECs) motivating a complete open {quantum} system treatment of dissipative mechanisms. The stochastic projected Gross-Pitaevskii equation (SPGPE) offers such a treatment at finite temperature, capturing several relaxation mechanisms. This thesis completes the SPGPE under its usual assumptions, so that all possible two-body collisions are finally considered. The respective relevance of the distinct processes are established. The SPGPE models ultracold Bose gases by dividing them into a low-energy coherent region containing the condensate and low-energy excitations and a high-energy incoherent region acting as a reservoir. In its framework, a coupling between coherent and incoherent region has been derived via two distinct mechanisms: number damping, stemming from scattering events between incoherent region particles in which one of them loses enough energy to enter the coherent region. And energy damping, stemming form number conserving scattering events between a particle in the coherent and incoherent region each. However, in practical applications of the SPGPE, often only the first mechanism, number damping, is accounted for, despite evidence that other damping channels can play a dominant role in dynamical relaxation. In this thesis, we develop an SPGPE theory of the remaining two-body reservoir interaction. It describes scattering events between two coherent region particles leading to one gaining enough energy to leave the coherent and enter the incoherent region. I demonstrate that, despite its previous neglect, this evaporative damping is comparable in strength to number damping. Evaporative damping completes the SPGPE description of ultracold Bose gases, giving a first-principle picture containing all possible two-body collisions in their evolution at finite temperature I further perform an analysis of the linearised SPGPE, valid at sufficiently high phase space density. It allows the identification of an ideal energy cut off, dividing the coherent and incoherent region. It moreover demonstrates the importance of energy damping. The analysis shows that with rising phase space density it increasingly dominates over both, number and evaporative damping. Studying the Jones-Roberts soliton (JRS) extends the proven dominance of energy damping at high phase-space density to the decay of nonlinear structures. Energy damping is revealed to determine the decay for slow JRSs, corresponding to vortex dipoles, as well as fast JRSs, forming rarefaction pulses. The predicted decay behaviour enables an experimentally feasible quantitative test of the SPGPE reservoir theory. The results of this thesis highlight the importance of damping mechanisms in the SPGPE that have so far gained little attention. The demonstrated dominance of energy damping at high phase-space density establishes the need of including this process in any study of dynamics in the high phase-space density regime. At higher temperatures closer to the transition, the inclusion of evaporative damping is also found to become crucial in obtaining an appropriate first-principle picture of the dynamics of ultracold Bose gases. These findings have implications for finite-temperature dynamical properties such as decay rates, excitation linewidths and equilibration times.