Lee-Yang theory of Bose-Einstein condensation
Lee-Yang theory of Bose-Einstein condensation
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DOI：
10.1103/physreva.107.033324
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发表时间：
2023-01
影响因子：
2.9
通讯作者：
F. Brange;T. Pyhäranta;Eppu Heinonen;K. Brandner;C. Flindt
中科院分区：
文献类型：
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作者：
F. Brange;T. Pyhäranta;Eppu Heinonen;K. Brandner;C. Flindt
玻色-爱因斯坦凝聚发生在玻色子气体被冷却到其转变温度以下时，基态在宏观上被占据。相变发生在许多粒子的热力学极限内。然而，最近的实验进展使自下而上组装量子多体系统成为可能，例如，通过一次一个地将单个原子添加到光学晶格中。在这里，我们展示了如何从少量玻色子的能量波动中预测玻色气体的凝聚温度。为此，我们利用李-杨相变理论的最新进展，这使我们能够确定零和极点的配分函数在复杂的平面上的逆温度的能量波动的高累积量。通过增加囚禁势中玻色子的数量，我们可以预测配分函数零点在热力学极限下的收敛点，在那里它们达到真实的轴上的反临界温度。使用少于100个玻色子，我们可以估计二维和三维谐振势中玻色气体的凝聚温度，并且我们还发现在一维中没有相变。
Bose-Einstein condensation happens as a gas of bosons is cooled below its transition temperature, and the ground state becomes macroscopically occupied. The phase transition occurs in the thermodynamic limit of many particles. However, recent experimental progress has made it possible to assemble quantum many-body systems from the bottom up, for example, by adding single atoms to an optical lattice one at a time. Here, we show how one can predict the condensation temperature of a Bose gas from the energy fluctuations of a small number of bosons. To this end, we make use of recent advances in Lee-Yang theories of phase transitions, which allow us to determine the zeros and the poles of the partition function in the complex plane of the inverse temperature from the high cumulants of the energy fluctuations. By increasing the number of bosons in the trapping potential, we can predict the convergence point of the partition function zeros in the thermodynamic limit, where they reach the inverse critical temperature on the real axis. Using less than 100 bosons, we can estimate the condensation temperature for a Bose gas in a harmonic potential in two and three dimensions, and we also find that there is no phase transition in one dimension as one would expect.