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arXiv:0710.2220 · Physical Review A

Quantum phases of mixtures of atoms and molecules on optical lattices

V. G. Rousseau, P. J. H. Denteneer

Published Jan 14, 2008• 23 citations
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Abstract

We investigate the phase diagram of a two-species Bose-Hubbard model including a conversion term, by which two particles from the first species can be converted into one particle of the second species, and vice versa. The model can be related to ultracold atom experiments in which a Feshbach resonance produces long-lived bound states viewed as diatomic molecules. The model is solved exactly by means of quantum Monte Carlo simulations. We show that an ``inversion of population'' occurs, depending on the parameters, where the second species becomes more numerous than the first species. The model also exhibits an exotic incompressible ``super-Mott'' phase where the particles from both species can flow with signs of superfluidity, but without global supercurrent. We present two phase diagrams, one in the chemical potential, conversion plane, the other in the chemical potential, detuning plane.

DOI
10.1103/physreva.77.013609

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We investigate the phase diagram of a two-species Bose-Hubbard model including a conversion term, by which two particles from the first species can be converted into one particle of the second species, and vice versa. The model can be related to ultracold atom experiments in which a Feshbach resonance produces long-lived bound states viewed as diatomic molecules. The model is solved exactly by means of quantum Monte Carlo simulations. We show that an inversion of population'' occurs, depending on the parameters, where the second species becomes more numerous than the first species. The model also exhibits an exotic incompressible super-Mott'' phase where the particles from both species can flow with signs of superfluidity, but without global supercurrent. We present two phase diagrams, one in the chemical potential, conversion plane, the other in the chemical potential, detuning plane.
We study the ground state and the thermal phase diagram of a two-species Bose-Hubbard model, with $\text{U}(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry, describing atoms and molecules on a two-dimensional optical lattice interacting via a Feshbach resonance. Using quantum Monte Carlo simulations and mean-field theory, we show that the conversion between the two species, coherently coupling the atomic and molecular states, has a crucial impact on the Mott-superfluid transition and stabilizes an insulating phase with a gap controlled by the conversion term---the Feshbach insulator---instead of a standard Mott-insulating phase. Depending on the detuning between atoms and molecules, this model exhibits three phases: the Feshbach insulator, a molecular condensate coexisting with noncondensed atoms, and a mixed atomic-molecular condensate. Employing finite-size scaling analysis, we observe three-dimensional (3D) XYXYXY (3D Ising) transition when U(1)\text{U}(1)U(1) (Z2{\mathbb{Z}}_{2}Z2​) symmetry is broken, whereas the transition is first order when both U(1)\text{U}(1)U(1) and Z2{\mathbb{Z}}_{2}Z2​ symmetries are spontaneously broken. The finite-temperature phase diagram is also discussed. The thermal disappearance of the molecular superfluid leads to a Berezinskii-Kosterlitz-Thouless transition with unusual universal jump in the superfluid density. The loss of the quasi-long-range coherence of the mixed atomic and molecular superfluid is more subtle since only atoms exhibit conventional Berezinskii-Kosterlitz-Thouless criticality. We also observe a signal compatible with a classical first-order transition between the mixed superfluid and the normal Bose liquid at low temperature.
Our work concerns the effects of strong correlations of ultracold atoms in optical lattices in three different scenarios. First we analyze the influence of dissipative processes on the superfluid-Mott insulator transition in the Bose-Hubbard model, observing a shift of the well-known phase transition. In a second setup atoms are trapped in state-dependent lattices; we show that any asymmetry in the contact interaction produces a form of correlated hopping, which results in a pair superfluid phase, with interesting correlation properties that differentiate it from an ordinary atomic Bose-Einstein condensate. Finally we investigate a two-species Bose-Hubbard model including a conversion term, which can be implemented experimentally through a Feshbach resonance producing long-lived bound states. We are particularly interested in the exotic incompressible, yet superfluid “super-Mott” phase.
We investigate the phase diagram of a two-species Bose-Hubbard model describing atoms and molecules on a lattice, interacting via a Feshbach resonance. We identify a region where the system exhibits an exotic super-Mott phase and regions with phases characterized by atomic and/or molecular condensates. Our approach is based on a recently developed exact quantum Monte Carlo algorithm: the stochastic Green function algorithm with tunable directionality. We confirm some of the results predicted by mean-field studies, but we also find disagreement with these studies. In particular, we find a phase with an atomic but no molecular condensate, which is missing in all mean-field phase diagrams.
Ultracold atomic gases may be the ultimate quantum simulator.These isolated systems have the lowest temperatures in the observable universe, and their properties and interactions can be precisely and accurately tuned across a full spectrum of behaviors, from few-body physics to highly-correlated many-body effects.The ability to impose potentials on and tune interactions within ultracold gases to mimic complex systems mean they could become a theorist's playground.One of their great strengths, however, is also one of the largest obstacles to this dream: isolation.This thesis touches on both of these themes.First, methods to characterize phases and quantum critical points, and to construct finite temperature phase diagrams using experimentally accessible observables in the Bose Hubbard model are discussed.Then, the transition from a weakly to a strongly interacting Bose-Fermi mixture in the continuum is analyzed using zero temperature numerical techniques.Real materials can be emulated by ultracold atomic gases loaded into optical lattice potentials.We discuss the characteristics of a single boson species trapped in an optical lattice (described by the Bose Hubbard model) and the hallmarks of the quantum critical region that separates the superfluid and the Mott insulator ground states.We propose a method to map the quantum critical region using the single, experimentally accessible, local quantity R, the ratio of compressibility to local number fluctuations.The procedure to map a phase diagram with R is easily generalized to inhomogeneous systems and generic many-body Hamiltonians.We illustrate it here using quantum Monte Carlo simulations of the 2D Bose Hubbard model.Secondly, we investigate the transition from a degenerate Fermi gas weakly coupled List of Tables Table Page 2.1 Techniques to Probe Atoms in Optical Lattices . . . . . .
We consider the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength in the grand canonical ensemble with a common chemical potential. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram in the vicinity of odd filling Mott states. We find that the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.
We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations. In addition to the usual contact repulsive interactions between the particles, the Hamiltonian has an interconversion term which allows the transformation of two particles from one species to the other. The phases are characterized by their solid or superfluid properties and by their polarization, i.e., the difference in the populations. When interspecies interactions are smaller than the intraspecies ones, the system is unpolarized, whereas in the opposite case the system is unpolarized in even Mott insulator lobes and polarized in odd Mott lobes and also in the superfluid phase. We show that in the latter case the transition between the Mott insulator of total density 2 and the superfluid can be of either second or first order depending on the relative values of the interactions, whereas the transitions are continuous in all other cases.