Bose-Bose mixtures with synthetic spin-orbit coupling in optical lattices

Abstract

We investigate the ground state properties of Bose-Bose mixtures with Rashba-type spin-orbit (SO) coupling in a square lattice. The system displays rich physics from the deep Mott-insulator (MI) all the way to the superfluid (SF) regime. In the deep MI regime, novel spin-ordered phases arise due to the effective Dzyaloshinskii-Moriya type super-exchange interactions. By employing the non-perturbative Bosonic Dynamical Mean-Field-Theory (BDMFT), we numerically study and establish the stability of these magnetic phases against increasing hopping amplitude. We show that as hopping is increased across the MI to SF transition, exotic superfluid phases with magnetic textures emerge. In particular, we identify a new spin-spiral magnetic texture with spatial period 3 in the superfluid close to the MI-SF transition.

Thermodynamics of the Bose-Hubbard model in aBogoliubov+Utheory

“…The anomalous term 12 , containing processes of the type δb 2 , is explicitly taken to be finite in this notation, since it is known from the Bogoliubov theory that deep in the superfluid phase it becomes equally important to the normal (diagonal) term 11 , containing the δb † δb terms. By (6) we arrive at the effective impurity Hamiltonian…”

“…For the broken phase, 11 and μ are combined with different operators. They control the density of the condensed and depleted atoms, whereas 12 mainly determines the anomalous density. According to the Bogoliubov theory of the weakly interacting Bose gas, the anomalous propagator is equally important (but opposite in sign) as the normal propagator deep in the superfluid phase.…”

“…B-DMFT is hence a promising candidate to deal with more complicated dispersions: The hope is that it deals with the local interactions as accurately as in the standard Bose-Hubbard model whereas a small cluster could treat the full dispersion. Furthermore, one would expect that a cluster method goes beyond real-space DMFT for multicomponent systems and systems with long-range interactions and/or dispersions [12,13].…”

Variational study of phase diagrams of spin–orbit coupled bosons

“…Combined with the controllability of interactions and geometries of ultracold bosons, the manipulation ofspin-orbit coupling (SOC) gives rise to a lot of novel quantum states, especially the MI-SF phase transition and the magnetic orders in the deep MI and superfluid regimes [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. For example, one can derive an effective super-exchange spin model with the Dzyaloshinskii-Moriya type (DM-type) interactions [50,51] in the deep MI regime via the second-order perturbation theory.…”

“…MI regimeIn the deep MI regime ( = t U 0.01) with commensurate filling, the spin fluctuations are determined by an effective magnetic Hamiltonian that is derived from the quantum perturbation theory. The effective Hamiltonian is written as[25][26][27][39][40][41][42] …”