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arXiv:2312.08379

Effect of nonzero temperature to condensed fraction of a homogeneous dilute weakly interacting Bose gas

Nguyễn Văn Thụ, Pham Duy Thanh

Published Dec 10, 2023• 0 citations
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Abstract

We investigate the effect of non-zero temperature to the condensate fraction of a homogeneous dilute weakly interacting Bose gas in very low-temperature region. Within inproved Hartree-Fock approximation, the Cornwall-Jackiw-Tomboulis effective action approach shows that the thermal fluctuations make the condensate fraction decrease as a second and fourth-order power law of temperature. The result is compared with experimental data. Indeed, the effect of non-infinite size of the trap is also integrated.

DOI
10.48550/arxiv.2312.08379

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We investigate the effect of non-zero temperature to the condensate fraction of a homogeneous dilute weakly interacting Bose gas in very low-temperature region. Within inproved Hartree-Fock approximation, the Cornwall-Jackiw-Tomboulis effective action approach shows that the thermal fluctuations make the condensate fraction decrease as a second and fourth-order power law of temperature. The result is compared with experimental data. Indeed, the effect of non-infinite size of the trap is also integrated.
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We present a study of the effects of temperature upon the excitation frequencies of a Bose-Einstein condensate formed within a dilute gas with a weak attractive, effective interaction between the atoms. We use the self-consistent Hartree-Fock Bogoliubov treatment within the Popov approximation, and we compare our results to previous zero-temperature and Hartree-Fock calculations. The metastability of the condensate is monitored by means of the l = 0 excitation frequency. As the number of atoms in the condensate is increased, with T held constant, this frequency goes to zero, signalling a phase transition to a dense collapsed state. The critical number for collapse is found to decrease as a function of temperature, the rate of decrease being greater than that obtained in previous Hartree-Fock calculations.
In a manner of Cornwal-Jackiw-Tomboulis effective action approach, the density of condensate of a dilute Bose gas confined between two planar walls is investigated within the framework of improved Hartree-Fock. Thereby, the quantum fluctuations are taken into account with presence of high-order terms in the momentum integrals. Our results show that the quantum fluctuations significantly belittle the density of condensate compared with square of the expectation value of the field operator. The comparison with relating results of Gross-Pitaevskii theory is made.
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Beyond standard approaches in existing literature, we explore the relative shift in the transition temperature of a homogeneous dilute Bose gas using the Cornwall-Jackiw-Tomboulis effective action formalism within the improved Hartree-Fock approximation. The first correction to the enhancement of the transition temperature, as compared to that of the ideal Bose gas, is expressed in a universal form: it is linear with respect to the scattering length. The slope of this linear relationship shows excellent agreement with the exact numerical calculations presented in previous studies. Additionally, we identify non-universal terms contributing to the shift.