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.
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 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
s-wave scattering. In the presence of a harmonic trap, we discuss coexistence of these self-organized phases, as relevant to experiments.
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.
The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional square optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid (SF) at all tilt angles θ provided that the strength of dipolar interaction is below a critical value . Upon increasing the interaction strength while keeping θ fixed, the SF phase is destabilized in favor of a checkerboard or a stripe solid (SS) depending on the tilt angle. We explore the nature of the phase transition between the two solid phases, identifying a region of metastable emulsion states intervening between the two solid lobes. Additionally, we study the stability of these quantum phases against thermal fluctuations and find that the SS is the most robust, making it the best candidate for experimental observation.
Recent advances in realizing nearly degenerate dipolar gases in optical lattices have enabled the study of quantum systems with long-range anisotropic interactions. Here, we investigate hard-core dipolar bosons on a two-dimensional square lattice described by an extended Bose--Hubbard model. Using path-integral quantum Monte Carlo simulations at fixed azimuthal angle
φ=45∘, we investigate density instabilities arising from first-order phase transitions. We start by mapping the ground-state phase diagram at half filling as a function of dipolar interaction strength and polar angle
θ. For weak interactions, the system remains superfluid for all
θ. Above a critical interaction strength, the superfluid phase becomes unstable and gives way to checkerboard, stripe, or incompressible phases depending on
θ. For
θ≳62∘, we find that half filling becomes unstable and only the empty state,
n=0, and the fully filled state,
n=1, are stable. Unlike recent experimental reports of a self-bound insulator at half filling, the homogeneous ground state does not support such a phase, but instead exhibits a direct first-order transition between
n=0 and
n=1. At finite temperature, thermal fluctuations shift the onset of density instabilities to larger
θ and stabilize intermediate fillings in the regime where half filling is unstable in the ground state. This leads to phase-separated states consisting of empty and fully filled regions that resemble the experimentally observed "self-bound insulator." In a harmonic trap, similar structures also emerge from phase coexistence associated with the underlying first-order transition.
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study the ground state properties of dipolar bosons trapped in a two-dimensional lattice with density-induced hopping and where the dipoles are tilted along the
xz plane. We present ground state phase diagrams of the above system at different tilt angles. We find that, as the dipolar interaction increases, the superfluid phase at half filling factor is destroyed in favor of either a checkerboard or stripe solid phase for tilt angle
θ≲35.3∘ or
θ≳35.3∘ respectively. More interesting physics happens at tilt angles
θ≳58∘ where we find that, as the dipolar interaction strength increases, solid phases first appear at filling factor lower than
0.5. Moreover, unlike what observed at lower tilt angles at half filling, we find that the superfluid gives way to a stripe solid through a stripe supersolid phase.