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

Motivated by the physics of coherently coupled, ultracold atom-molecule mixtures, we investigate a classical model possessing the same symmetry, namely a U(1) x Z(2) symmetry, associated with the mass conservation in the mixture [U(1) symmetry], times the 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 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.