Lee-Yang theory of Bose-Einstein condensation

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2023-03

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en

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10
1-10

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Physical Review A, Volume 107, issue 3

Abstract

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 fewer 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.

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Funding Information: This work was supported by the Academy of Finland through the Finnish Centre of Excellence in Quantum Technology (Projects No. 312057 and No. 312299) and Grants No. 318937 and No. 331737. The work was also supported by the Medical Research Council (Grant No. MR/S034714/1) and the Engineering and Physical Sciences Research Council (Grant No. EP/V031201/1). T.P. acknowledges support from the Nokia Industrial Doctoral School in Quantum Technology. K.B. acknowledges support from the University of Nottingham through a Nottingham Research Fellowship. Publisher Copyright: © 2023 American Physical Society.

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Citation

Brange, F, Pyhäranta, T, Heinonen, E, Brandner, K & Flindt, C 2023, ' Lee-Yang theory of Bose-Einstein condensation ', Physical Review A, vol. 107, no. 3, 033324, pp. 1-10 . https://doi.org/10.1103/PhysRevA.107.033324