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

Abstract

We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional (2D) 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 θ of the dipolar bosons. At low tilt angles 0 • θ 25 • , the ground state of the system are phases with checkerboard order, which could be either checkerboard supersolid or checkerboard density wave. For high tilt angles 55 • θ 35 • , phases with striped order of supersolid or density wave are preferred. In the intermediate domain 25 • θ 35 • an emulsion or SF phase intervenes the transition between the checkerboard and striped phases. The attractive interaction dominates for θ 55 • , 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.

Dipolar Bose-Hubbard Model in finite-size real-space cylindrical lattices

“…For example, if θ = π 2 , the local dipole-dipole interaction at φ c = 0, π is isotropically repulsive in the lattice plane, which is known to support density waves such as checkerboard and star solids, and supersolid phases [19,40,62]. Meanwhile, the same physical polarisation angle θ causes the polarisation to be along the φ lattice vector at φ c = π 2 , 3π 2 , which supports a stripe density wave state [47,48] and a supersolid with the same density order for soft-core bosons [63][64][65]. At intermediate θ and φ c , the polarisation can point diagonally between ẑ and φ with a perpendicular component in R providing isotropic repulsion, which has recently been shown to support diagonal stripe and superstripe phases with a 3 × 3 unit cell driven by next-nearest-neighbour interactions [66].…”

Supersolid phases of lattice dipoles tilted in three-dimensions

“…Supersolid structures have also been theoretically predicted in dipolar gases trapped in optical lattices [19][20][21][22][23][24][25][26][27][28][29]. As optical lattices already impose a crystalline structure, solid order in these systems is realized when a discrete symmetry is also broken as particles arrange themselves in a crystalline structure different than the one of the underlining optical lattice, e.g.…”

Quantum quench dynamics of tilted dipolar bosons in 2D optical lattices

“…1. At zero temperature, the physics of the system is well described by the lowest band BHM with the dipolar interaction and the Hamiltonian of the system is [19,24,[59][60][61]…”

“…The ultracold atoms in optical lattice simulate the Bose-Hubbard model (BHM) [15,16], which is a minimal model to study the physics of in-teracting bosons in a lattice. These systems are used to understand various equilibrium quantum phases [19][20][21][22][23][24][25][26][27][28], collective excitations [29][30][31][32][33][34] etc. In the context of the KZM, there are many works done using the system of ultracold atoms.…”