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 $U(1)\times {\mathbb{Z}}_2$ 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.

18 pages, 16 figures

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• Magnetic quasi-long-range ordering in nematics due to competition between higher-order couplings
• Multiple phase transitions in the $XY$ model with nematic-like couplings
• Quantum and Thermal Phase Transitions in a Bosonic Atom-Molecule Mixture in a Two-dimensional Optical Lattice
• Phase Diagrams of Antiferromagnetic Spin-1 Bosons on Square Optical Lattice with the Quadratic Zeeman Effect
• Quantum Triticality of Bosonic Atomic-Molecular Mixtures with Feshbach Coupling
• Two-stage melting of an inter-component Potts long-range order in two dimensions