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arXiv:2201.03756 · Physical Review A

Supersolid phases of lattice dipoles tilted in three dimensions

Jin Zhang, Chao Zhang, Jin Yang, Barbara Capogrosso-Sansone

Published Jun 3, 2022• 16 citations
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Abstract

By means of quantum Monte Carlo simulations we study phase diagrams of dipolar bosons in a square optical lattice. The dipoles in the system are parallel to each other and their orientation can be fixed in any direction in the three-dimensional space. Starting from experimentally tunable parameters like scattering length and dipolar interaction strength, we derive the parameters entering the effective Hamiltonian. Depending on the direction of the dipoles, various types of supersolids (e.g., checkerboard, stripe) and solids (checkerboard, stripe, diagonal stripe, and an incompressible phase) can be stabilized. Remarkably, we find a cluster supersolid characterized by the formation of horizontal clusters of particles. These clusters order along a direction at an angle with the horizontal. Moreover, we find what we call a grain-boundary superfluid. In this phase, regions with solid order are separated by extended defects---grain boundaries---which support superfluidity. We also investigate the robustness of the stripe supersolid against thermal fluctuations. Finally, we comment on the experimental realization of the phases found.

DOI
10.1103/physreva.105.063302

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By means of quantum Monte Carlo simulations we study phase diagrams of dipolar bosons in a square optical lattice. The dipoles in the system are parallel to each other and their orientation can be fixed in any direction in the three-dimensional space. Starting from experimentally tunable parameters like scattering length and dipolar interaction strength, we derive the parameters entering the effective Hamiltonian. Depending on the direction of the dipoles, various types of supersolids (e.g., checkerboard, stripe) and solids (checkerboard, stripe, diagonal stripe, and an incompressible phase) can be stabilized. Remarkably, we find a cluster supersolid characterized by the formation of horizontal clusters of particles. These clusters order along a direction at an angle with the horizontal. Moreover, we find what we call a grain-boundary superfluid. In this phase, regions with solid order are separated by extended defects---grain boundaries---which support superfluidity. We also investigate the robustness of the stripe supersolid against thermal fluctuations. Finally, we comment on the experimental realization of the phases found.
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.
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform Path Integral Quantum Monte Carlo simulations using the Worm Algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighboring interaction, supersolid phases are stabilized not only by doping the solids with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and suggest experimental conditions under which the pair checkerboard phase can be observed.
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, by means of quantum Monte Carlo, 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 xzxzxz 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 $\ensuremath{\theta}\ensuremath{\lesssim}{30}^{\ensuremath{\circ}}$ or $\ensuremath{\theta}\ensuremath{\gtrsim}{30}^{\ensuremath{\circ}}$, respectively. More interesting physics happens at tilt angles $\ensuremath{\theta}\ensuremath{\gtrsim}{58}^{\ensuremath{\circ}}$, where we find that as the dipolar interaction strength increases, solid phases first appear at filling factor lower than 0.5. Moreover, unlike what is observed at lower tilt angles, we find that at half filling, a stripe supersolid intervenes between the superfluid and stripe solid phase.
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 xzxzxz 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∘\theta \lesssim 35.3^{\circ}θ≲35.3∘ or θ≳35.3∘\theta \gtrsim 35.3^{\circ}θ≳35.3∘ respectively. More interesting physics happens at tilt angles θ≳58∘\theta \gtrsim 58^{\circ}θ≳58∘ where we find that, as the dipolar interaction strength increases, solid phases first appear at filling factor lower than 0.50.50.5. 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.
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform path-integral quantum Monte Carlo simulations using the worm algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighbor interaction, supersolid phases are stabilized by doping the solids not only with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and we suggest experimental conditions under which the pair checkerboard phase can be observed.
We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $\ensuremath{\theta}$ of the dipolar bosons. At low tilt angles, ${0}^{\ensuremath{\circ}}\ensuremath{\leqslant}\ensuremath{\theta}\ensuremath{\lesssim}{25}^{\ensuremath{\circ}}$, the ground states of the system are phases with checkerboard order, which can be either checkerboard supersolids or checkerboard density waves. For high tilt angles, ${35}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{55}^{\ensuremath{\circ}}$, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, ${25}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{35}^{\ensuremath{\circ}}$, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at $\ensuremath{\theta}\ensuremath{\gtrsim}{55}^{\ensuremath{\circ}}$, which renders the system unstable, and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second-order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results. In our study, the incompressible phases have an average occupancy per site $\ensuremath{\rho}\ensuremath{\le}1$, but the compressible phases can have $\ensuremath{\rho}>1$.