Multiple Transitions of Coupled Atom-Molecule Bosonic Mixtures in Two Dimensions

TL;DR

This paper studies phase transitions in a 2D classical model of coupled atom-molecule mixtures, revealing how population imbalance influences the sequence and nature of BKT and Ising transitions.

Contribution

It introduces a detailed analysis of coupled atom-molecule systems with $U(1) imes bZ_2$ symmetry, highlighting the effects of population imbalance on phase transition behavior.

Findings

Majority molecules lead to a higher-temperature BKT transition for molecules than atoms.

Balanced populations cause the two transitions to merge into a single BKT transition.

Molecular vortex-antivortex pairs exhibit a crossover from weak to strong binding with temperature.

Abstract

Motivated by the physics of coherently coupled, ultracold atom-molecule mixtures, we investigate a classical model possessing the same symmetry -- namely a $U(1)\times \mathbb{Z}_2$ symmetry, associated with the mass conservation in the mixture ($U(1)$ symmetry), times the $\mathbb{Z}_2$ 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 quasi-condensation 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 majority in the system, their BKT quasi-condensation 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.