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arXiv:1701.01624 · Physical review. B./Physical review. B

Phase diagram of bosons in a two-dimensional optical lattice with infinite-range cavity-mediated interactions

Thibaut Flottat, Laurent de Forges de Parny, F. Hébert, V. G. Rousseau, G. G. Batrouni

Published Apr 3, 2017• 57 citations
arXivHTMLPDF

Abstract

A high-finesse optical cavity allows the establishment of long-range interactions between bosons in an optical lattice when most cold-atom experiments are restricted to short-range interactions. Supersolid phases have recently been experimentally observed in such systems. Using both exact quantum Monte Carlo simulations and the Gutzwiller approximation, we study the ground-state phase diagrams of a two-dimensional Bose-Hubbard model with infinite-range interactions which describes such experiments. In addition to superfluid and insulating Mott phases, the infinite-range checkerboard interactions introduce charge-density waves and supersolid phases. We study here the system at various particle densities, elucidate the nature of the phases and quantum phase transitions, and discuss the stability of the phases with respect to phase separation. In particular we confirm the existence and stability of a supersolid phase detected experimentally.

DOI
10.1103/physrevb.95.144501

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A high-finesse optical cavity allows the establishment of long-range interactions between bosons in an optical lattice when most cold-atom experiments are restricted to short-range interactions. Supersolid phases have recently been experimentally observed in such systems. Using both exact quantum Monte Carlo simulations and the Gutzwiller approximation, we study the ground-state phase diagrams of a two-dimensional Bose-Hubbard model with infinite-range interactions which describes such experiments. In addition to superfluid and insulating Mott phases, the infinite-range checkerboard interactions introduce charge-density waves and supersolid phases. We study here the system at various particle densities, elucidate the nature of the phases and quantum phase transitions, and discuss the stability of the phases with respect to phase separation. In particular we confirm the existence and stability of a supersolid phase detected experimentally.
We numerically simulate strongly correlated ultracold bosons coupled to a high-finesse cavity field, pumped by a laser beam in the transverse direction. Assuming a weak classical\mathit{classical}classical optical lattice added in the cavity direction, we model this system by a generalized Bose-Hubbard model, which is solved by means of bosonic dynamical mean-field theory. The complete phase diagram is established, which contains two novel self-organized quantum phases, lattice supersolid and checkerboard solid, in addition to conventional phases such as superfluid and Mott insulator. At finite but low temperature, thermal fluctuations are found to enhance the buildup of the self-organized phases. We demonstrate that cavity-mediated long-range interactions can give rise to stable lattice supersolid and checkerboard solid phases even in the regime of strong sss-wave scattering. In the presence of a harmonic trap, we discuss coexistence of these self-organized phases, as relevant to experiments.
Motivated by experiments performed by Landig et al. [Nature (London) 532, 476 (2016)], we consider a two-dimensional Bose gas in an optical lattice, trapped inside a single mode superradiant Fabry-Perot cavity. The cavity mediates infinite-range checkerboard interactions between the atoms, which produces competition between Mott insulator, charge-density wave, superfluid, and supersolid phases. We calculate the phase diagram of this Bose gas in a homogeneous system and in the presence of a harmonic trap.
Abstract Recent experiments with ultracold atoms in an optical lattice have realized cavity-mediated long-range interaction and observed the emergence of a supersolid phase and a density wave phase in addition to Mott insulator and superfluid phases. Here we consider theoretically the effect of uncorrelated disorder on the phase diagram of this system and study the two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated diagonal disorder. We also study the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions in the presence of uncorrelated diagonal disorder. The extended Bose-Hubbard model with nearest-neighbor interactions has been realized in the experiment using dipolar interaction recently. With the help of quantum Monte Carlo simulations using the worm algorithm, we determine the phase diagram of those two models. We compare the phase diagrams of cavity-mediated long-range interactions with nearest-neighbor interactions. We show that two kinds of Bose glass phases exist: one with and one without density wave order. We also find that weak disorder enhances the supersolid phase. Graphical abstract
Two types of long-range interactions, dipolar interaction and cavity-mediated interaction, lead to exotic quantum phases. Both interactions were realized and observed in optical lattice setups. Here, we study quantum phases of dipolar bosons trapped in optical lattices and coupled to a high-finesse cavity where both dipolar interaction and cavity-mediated interaction coexist. We perform quantum Monte Carlo simulations and find that the checkerboard solid is enhanced and the checkerboard supersolid phase can exist in a wide range of densities (e.g., $0.27\ensuremath{\lesssim}n\ensuremath{\lesssim}0.73$). Our unbiased numerical results suggest that both solid and supersolid phases can be achieved experimentally with magnetic atoms coupled to a cavity.
In this paper, we consider a two-component atomic Bose lattice gas inside an optical cavity to explore a competition between the short-range collisional and cavity-mediated long-range interactions. Utilizing a self-consistent mean-field approach, we map out the ground-state phase diagrams showing the superfluid, lattice supersolid, Mott insulator, and spin-density wave phases. Unlike its single-component analog, this lattice supersolid is here characterized by the coexistence of the superfluid and the spin-density wave. Moreover, for the relatively small long-range interaction, the phase diagrams exhibit a correspondence between the parity of the lattice filling number and the spin imbalance. Finally, we propose how to detect the different quantum phases under current experimental setups.
We study a system with competing short- and global-range interactions in the framework of the Bose-Hubbard model. Using a mean-field approximation we obtain the phase diagram of the system and observe four different phases: a superfluid, a supersolid, a Mott insulator, and a charge-density wave, where the transitions between the various phases can be either of first or second order. We qualitatively support these results using Monte Carlo simulations. An analysis of the low-energy excitations shows that the second-order phase transition from the charge-density wave to the supersolid is associated with the softening of particle- and holelike excitations which give rise to a gapless mode and an amplitude Higgs mode in the supersolid phase. This amplitude Higgs mode is further transformed into a roton mode which softens at the supersolid to superfluid phase transition.