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arXiv:1906.07483 · Physical Review A

Quantum phases of canted dipolar bosons in a two-dimensional square optical lattice

Soumik Bandyopadhyay, Rukmani Bai, Sukla Pal, Kuldeep Suthar, Rejish Nath, D. Angom

Published Nov 25, 2019• 34 citations
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Abstract

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 $\ensuremath{\rho}>1$.

DOI
10.1103/physreva.100.053623

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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 \ensuremathθ\ensuremath{\theta}\ensuremathθ of the dipolar bosons. At low tilt angles, 0\ensuremath∘\ensuremath⩽\ensuremathθ\ensuremath≲25\ensuremath∘{0}^{\ensuremath{\circ}}\ensuremath{\leqslant}\ensuremath{\theta}\ensuremath{\lesssim}{25}^{\ensuremath{\circ}}0\ensuremath∘\ensuremath⩽\ensuremathθ\ensuremath≲25\ensuremath∘, 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∘\ensuremath≲\ensuremathθ\ensuremath≲55\ensuremath∘{35}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{55}^{\ensuremath{\circ}}35\ensuremath∘\ensuremath≲\ensuremathθ\ensuremath≲55\ensuremath∘, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, 25\ensuremath∘\ensuremath≲\ensuremathθ\ensuremath≲35\ensuremath∘{25}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{35}^{\ensuremath{\circ}}25\ensuremath∘\ensuremath≲\ensuremathθ\ensuremath≲35\ensuremath∘, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at \ensuremathθ\ensuremath≳55\ensuremath∘\ensuremath{\theta}\ensuremath{\gtrsim}{55}^{\ensuremath{\circ}}\ensuremathθ\ensuremath≳55\ensuremath∘, 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 \ensuremathρ\ensuremath≤1\ensuremath{\rho}\ensuremath{\le}1\ensuremathρ\ensuremath≤1, but the compressible phases can have \ensuremathρ>1\ensuremath{\rho}>1\ensuremathρ>1.
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.
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 investigate the quench dynamics of the dipolar bosons in two dimensional optical lattice of square geometry using the time dependent Gutzwiller method. The system exhibits different density orders like the checkerboard and the striped pattern, depending upon the polarization angle of the dipoles. We quench the hopping parameter across the striped density wave (SDW) to striped supersolid (SSS) phase transition, and obtain the scaling laws for the correlation length and topological vortex density, as function of the quench rate. The results are reminiscent of the Kibble-Zurek mechanism (KZM). We also investigate the dynamics from the striped supersolid phase to the checkerboard supersolid phase, obtained by quenching the dipole tilt angle θθθ. This is a first order structural quantum phase transition, and we study the non-equilibrium dynamics from the perspective of the KZM. In particular, we find the number of the domains with checkerboard order follows a power law scaling with the quench rate. This indicates the applicability of the KZM to this first order quantum phase 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 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 perform a stability analysis of superfluid (SF) and supersolid (SS) phases of polarized dipolar bosons in two-dimensional optical lattices at high filling factors and zero temperature, and obtain the phase boundaries between SF, checkerboard SS (CSS), striped SS (SSS), and collapse. We show that the phase diagram can be explored through the application of an external field and the tuning of its direction with respect to the optical lattice plane. In particular, we find a transition between the CSS and SSS phases.
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∘φ=45^\circφ=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 θθθ. For weak interactions, the system remains superfluid for all θθθ. Above a critical interaction strength, the superfluid phase becomes unstable and gives way to checkerboard, stripe, or incompressible phases depending on θθθ. For θ≳62∘θ\gtrsim 62^\circθ≳62∘, we find that half filling becomes unstable and only the empty state, n=0n=0n=0, and the fully filled state, n=1n=1n=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=0n=0n=0 and n=1n=1n=1. At finite temperature, thermal fluctuations shift the onset of density instabilities to larger θθθ 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.