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arXiv:2210.10866 · Physical Review A

Berezinskii-Kosterlitz-Thouless phase transition with Rabi-coupled bosons

Koichiro Furutani, Andrea Perali, Luca Salasnich

Published Apr 19, 2023• 8 citations
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Abstract

The authors perform a renormalization-group analysis of the superfluid--normal-state Berezinskii-Kosterlitz-Thouless transition in a binary Bose mixture with an intercomponent and a Rabi coupling, which involves half-integer vortices and the formation of vortex molecule-antimolecule pairs. It reveals that the Rabi coupling enhances the Berezinskii-Kosterlitz-Thouless transition temperature while it exhibits nonmonotonic dependence on the intercomponent coupling.

DOI
10.1103/physreva.107.l041302

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The authors perform a renormalization-group analysis of the superfluid--normal-state Berezinskii-Kosterlitz-Thouless transition in a binary Bose mixture with an intercomponent and a Rabi coupling, which involves half-integer vortices and the formation of vortex molecule-antimolecule pairs. It reveals that the Rabi coupling enhances the Berezinskii-Kosterlitz-Thouless transition temperature while it exhibits nonmonotonic dependence on the intercomponent coupling.
We study the Berezinskii-Kosterlitz-Thouless (BKT) transition of two-component Bose mixtures in two spatial dimensions. When phases of both components are decoupled, half-quantized vortex-antivortex pairs of each component induce two-step BKT transitions. On the other hand, when phases of both components are synchronized through the intercomponent Josephson coupling, two species of vortices of each component are bound to form a molecule, and, in this case, we find that there is only one BKT transition by molecule-antimolecule pairs. Our results can be tested by two weakly connected Bose systems such as two-component ultracold diluted Bose mixtures with the Rabi oscillation, and multiband superconductors.
We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group Z\mathbb{Z}Z, and Z2\mathbb{Z}_2Z2​ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.
Motivated by the physics of coherently coupled, ultracold atom-molecule mixtures, we investigate a classical model possessing the same symmetry, namely a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry, associated with the mass conservation in the mixture [U(1) symmetry], times the Z2{\mathbb{Z}}_{2}Z2​ symmetry in the phase relationship between atoms and molecules. In two spatial dimensions the latter symmetry can lead to a finite-temperature Ising transition, associated with (quasi) phase locking between the atoms and the molecules. On the other hand, the U(1) symmetry has an associated Berezinskii-Kosterlitz-Thouless (BKT) transition towards quasicondensation of atoms or molecules. The existence of the two transitions is found to depend crucially on the population imbalance (or detuning) between atoms and molecules: When the molecules are the majority in the system, their BKT quasicondensation transition occurs at a higher temperature than that of the atoms; the latter has the unconventional nature of an Ising (quasi) phase-locking transition, lacking a finite local order parameter below the critical temperature. When the balance is gradually biased towards the atoms, the two transitions merge together to leave out a unique BKT transition, at which both atoms and molecules acquire quasi-long-range correlations, but only atoms exhibit conventional BKT criticality, with binding of vortex-antivortex pairs into short-range dipoles. The molecular vortex-antivortex excitations bind as well, but undergo a marked crossover from a high-temperature regime in which they are weakly bound, to a low-temperature regime of strong binding, reminiscent of their transition in the absence of atom-molecule coupling.
Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition and show that superfluidity is even more sensitive to imbalance than for three-dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations. This allows to identify a phase-separation region and tricritical points due to imbalance. In contrast to superfluidity in the three-dimensional case, the effect of imbalance is also pronounced in the strong-coupling regime.