Real space mean-field theory of a spin-1 Bose gas in synthetic dimensions

TL;DR

This paper uses mean-field theory to analyze the ground states of a spin-1 Bose gas with synthetic dimensions, revealing phase diagrams with charge and spin density waves influenced by interactions and spin-orbit coupling.

Contribution

It provides a comprehensive mean-field analysis of phase behavior in spin-1 Bose gases with synthetic dimensions, considering various interaction types and experimental parameters.

Findings

Identification of charge and spin density wave phases

Phase diagram dependence on spin-orbit coupling and interactions

Relevance to current ultracold atom experiments

Abstract

The internal degrees of freedom provided by ultracold atoms give a route for realizing higher dimensional physics in systems with limited spatial dimensions. Non-spatial degrees of freedom in these systems are dubbed "synthetic dimensions". This connection is useful from an experimental standpoint but complicated by the fact that interactions alter the condensate ground state. Here we use the Gross-Pitaevskii equation to study ground state properties of a spin-1 Bose gas under the combined influence of an optical lattice, spin-orbit coupling, and interactions at the mean field level. The associated phases depend on the sign of the spin-dependent interaction parameter and the strength of the optical lattice potential. We find "charge" and spin density wave phases which are directly related to helical spin order in real space and affect the behavior of edge currents in the synthetic dimension. We determine the resulting phase diagram as a function of the spin-orbit coupling and spin-dependent interaction strength, considering both attractive (ferromagnetic) and repulsive (polar) spin-dependent interactions. Our results are applicable to current and future experiments, specifically with $^{87}$Rb, $^{7}$Li, $^{41}$K, and $^{23}$Na.