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Chinese Physics B

BCS pairing state in an asymmetric binary Bose gas

Zesheng 泽盛 Shen 沈, Lan Yin

Published Sep 2, 2025• 0 citations
Publisher

Abstract

Abstract The BCS pairing state has been predicted to be stable in a symmetric binary Bose gas with the intraspecies repulsion and interspecies attraction. In experiments, the binary Bose gases are generally asymmetric. In this work, we study the pairing state in a dilute asymmetric binary Bose system with the intraspecies repulsions and interspecies attraction and show that it is stable in a certain region of the phase space. We find that there always exists a best density ratio for given total density and coupling constants, where the temperature width of the BCS region is maximized. At the best density ratio, both components have the almost same ideal BEC temperature. We also found that there are two critical density ratios where the BCS phase vanishes. The stability of the BCS state against pairing fluctuations is shown by expanding the Helmholtz free energy of BCS state near the normal state and proving that it is a local minimum point.

DOI
10.1088/1674-1056/ae0160

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We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the BCS-pairing state of bosons can be formed with weakly attractive interspecies and repulsive intraspecies interactions. The quasiparticle excitation energies are anisotropic due to spin-orbit coupling. This BCS-pairing state is energetically favored over Bose-Einstein condensation (BEC) of atoms at low densities. As the density increases, there is a first-order transition from the BCS to BEC states.
The stable Bardeen-Schrieffer-Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we study the BCS state of a binary Bose gas with sss-wave intra-species repulsions and an inter-species attraction in the mean-field-stable region. We find that above the Bose-Einstein-Condensation (BEC) transtion temperature, there is a phase transtion from the normal state to the BCS state due to inter-species pairing. When the temperature decreases, another phase transtion from the BCS state to the mixture state with both atomic BEC and inter-species pairs occurs. As the temperature is further lowered, the mixuture state is taken over by the BEC state. The phase diagram of this system is presented and experimental implications are discussed.
We study the Bardeen–Cooper–Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin–orbit coupling (SOC). In the dilute limit at low temperature, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose–Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density.
We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the Bardeen-Cooper-Shrieffer (BCS) pairing state of bosons can be formed with weakly-attractive inter-species and repulsive intra-species interactions. The quasiparticle excitation energies are anisotropic due to spin-orbit coupling. This BCS paring state is energetically favored over Bose-Einstein condensation (BEC) of atoms at low densities. As the density increases, there is a first-order transition from the BCS to BEC states.
We study the pairing instability and mechanical collapse of a dilute homogeneous Bose gas with an attractive interaction. The pairing phase is found to be a saddle point and is unstable against pairing fluctuations. This pairing saddle point exists above a critical temperature. Below this critical temperature, the system is totally unstable in the pairing channel. Thus the system could collapse in the pairing channel in addition to mechanical collapse. The critical temperatures of pairing instability and mechanical collapse are higher than the Bose-Einstein condensation (BEC) temperature of an ideal Bose gas with the same density. When fluctuations are taken into account, we find that the critical temperature of mechanical collapse is even higher. The difference between the collapse temperature and the BEC temperature is proportional to (n∣as∣3)2/9,(n|{a}_{s}{|}^{3}{)}^{2/9},(n∣as​∣3)2/9, where n is the density and as{a}_{s}as​ is the scattering length.