Multiple transitions of coupled atom-molecule bosonic mixtures in two dimensions

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)×Z2 symmetry, associated with the mass conservation in the mixture (U (1) symmetry), times the Z2 symmetry in the phase relationship between atoms and molecules. In two spatial dimensions the latter symmetry can lead to a finitetemperature 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.

Competing nematic interactions in a generalizedXYmodel in two and three dimensions

“…[71]). Trying to disentangle the roles of the two terms in the Hamiltonian, by introducing two variables per site and an onsite coupling between them [17,32,38,40,41], may also be helpful to better understand the new phases for q > 4. These questions, together with a better description of the geometry of topological defects are left for a future work.…”

“…(1) and, as a consequence, which type of vortices, integer or semi-integer (see below) is going to be relatively suppressed. This class of models, with ferromagnetic and/or antiferromagnetic interactions, was used to model the interlayer interactions of stacked bent-core molecules in liquid crystals [11], DNA packing [12], structural phases of cyanide polymers [13,14], quasicondensation in atom-molecule, bosonic mixtures [15][16][17], and out-of-equilibrium self-propelled polar particles [18], with a similar, albeit dynamical, phase diagram in the latter case.…”

“…A closely related class of models consists on a double XY model with an extra term coupling the two variables that in the limit of strong coupling recovers the Hamiltonian Eq. (1) [17,32,33]. The models with q > 2 have been recently investigated as well [34,35] (higher harmonics have been also considered in Ref.…”