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Chinese Physics B

Pairing transitions in a binary Bose gas

Zesheng 泽盛 Shen 沈, Lan Yin

Published Jun 4, 2025• 3 citations
Publisher

Abstract

Abstract The stable Bardeen–Schrieffer–Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we propose that a stable BCS state of bosons can be realized in a binary Bose gas with s-wave intra-species repulsion and an inter-species attraction in the mean-field-stable region. We find that above the Bose–Einstein condensation (BEC) transition temperature, there is a phase transition from the normal state to a BCS state driven by inter-species pairing. When the temperature decreases, another phase transition from the BCS state to a mixed state featuring both atomic BEC and inter-species pairing occurs. As the temperature is further lowered, the mixed state is eventually taken over by the pure BEC state. We present the phase diagram of this system and discuss its experimental implications.

DOI
10.1088/1674-1056/ade075

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Abstract The stable Bardeen–Schrieffer–Cooper (BCS) pairing state of a bosonic system has long been sought theoretically and experimentally. Here we propose that a stable BCS state of bosons can be realized in a binary Bose gas with s-wave intra-species repulsion and an inter-species attraction in the mean-field-stable region. We find that above the Bose–Einstein condensation (BEC) transition temperature, there is a phase transition from the normal state to a BCS state driven by inter-species pairing. When the temperature decreases, another phase transition from the BCS state to a mixed state featuring both atomic BEC and inter-species pairing occurs. As the temperature is further lowered, the mixed state is eventually taken over by the pure BEC state. We present the phase diagram of this system and discuss its experimental implications.
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 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 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.
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.
This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) \nto Bose-Einstein condensation (BEC) evolution in ultracold superfluid \nFermi gases when the interaction between atoms is varied. The tuning of \nattractive interactions permits the ground state of the system to evolve from a weak \nfermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs \nto a strong fermion attraction limit of tightly bound small bosonic molecules \nwhich undergo BEC. \nThis evolution is accompanied by anomalous behavior of many superfluid \nproperties, and reveals several quantum phase transitions. \nThis thesis has two parts: \nIn the first part, I analyze zero and nonzero orbital angular momentum \npairing effects, and show that a quantum phase transition occurs for \nnonzero angular momentum pairing, unlike the sss-wave case where the BCS \nto BEC evolution is just a crossover. \nIn the second part, I analyze two-species fermion mixtures with mass and \npopulation imbalance in continuum, trap and lattice models. In contrast with \nthe crossover physics found in the mass and population balanced mixtures, \nI demonstrate the existence of phase transitions between normal and \nsuperfluid phases, as well as phase separation between superfluid (paired) \nand normal (excess) fermions in imbalanced mixtures as a function of scattering \nparameter and mass and population imbalance.
We study the formation of quantum droplets in the mixture of a single-component Bose–Einstein condensate (BEC), and a two-species Fermi superfluid across a wide Feshbach resonance. With repulsive boson-boson and attractive boson-fermion interactions, we show that quantum droplets can be stabilized by attractive fermion-fermion interactions on the Bardeen–Cooper–Schrieffer (BCS) side of the resonance, and can also exist in the deep BEC regime under weak boson-fermion interactions. We map out the phase diagram for stable droplets with respect to the boson-boson and boson-fermion interactions, and discuss the role of different types of quantum fluctuations in the relevant regions of the BCS-BEC crossover. Our work reveals the impact of fermion pairing on the formation of quantum droplets in Bose–Fermi mixtures, and provides a useful guide for future experiments.