发表机构
Indian Institute of Technology Mandi; Ben-Gurion University of the Negev; Indian Institute of Technology Ropar（印度技术学院曼迪分校; 内盖夫本-古里安大学; 印度技术学院罗帕尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究谐振子势阱中相干耦合玻色气体的凝聚与磁相变，推导临界温度解析式，并发现相互作用抑制凝聚温度随耦合的变化。
AI 中文摘要
我们研究了限制在三维谐振子势阱中的相干（拉比）耦合玻色气体的凝聚和有限温度磁相变。对于无相互作用系统，我们利用单粒子谱和态密度的半经典描述，推导了临界温度和凝聚分数的解析表达式。在固定粒子数下，相干耦合相对于无耦合系统提高了临界温度，且这种提高随着粒子数$N$的增加而减小。相比之下，有限尺寸修正降低了转变温度，其效应随$N$增大而减弱。随后，我们在Hartree--Fock--Bogoliubov--Popov框架内纳入排斥相互作用，研究了温度--拉比耦合平面中的有限温度相图。系统经历从铁磁凝聚体到顺磁凝聚体，并在更高温度下转变为热气体的连续相变。由凝聚分数消失得到的转变边界与解析的Hartree-Fock预测表现出极好的一致性。我们发现，相互作用显著抑制了凝聚温度随相干耦合增加的变化。
英文摘要
We investigate condensation and finite-temperature magnetic phase transitions in a coherently (Rabi) coupled Bose gas confined in a three-dimensional harmonic trap. For the noninteracting system, we derive analytical expressions for the critical temperature and condensate fraction using a semiclassical description of the single-particle spectrum and density of states. At fixed particle number, coherent coupling enhances the critical temperature relative to the uncoupled system, and this enhancement decreases with increasing particle number $N$. The finite-size correction, in contrast, lowers the transition temperature, with its effect diminishing for larger $N$. We then incorporate repulsive interactions within the Hartree--Fock--Bogoliubov--Popov framework to investigate the finite-temperature phase diagram in the temperature--Rabi coupling plane. The system undergoes successive transitions from a ferromagnetic to a paramagnetic condensate and, at higher temperature, to a thermal gas. The transition boundaries obtained from the vanishing of the condensate fraction show excellent agreement with the analytical Hartree-Fock predictions. We find that the interactions substantially suppress the variation in the condensation temperature with an increase in the coherent coupling.
Comments17 pages, 5 figures
