Spin-orbit coupled Bose-Einstein condensates in a double well

TL;DR

This paper investigates the quantum dynamics of spin-orbit coupled Bose-Einstein condensates in a double-well potential, providing analytical solutions and predicting a detectable spin Josephson effect for experimental realization.

Contribution

It offers an analytical treatment of the two-site Bose-Hubbard model with spin-orbit coupling, exploring various regimes and predicting observable spin Josephson phenomena.

Findings

Analytical solutions for different coupling regimes.

Prediction of a measurable spin Josephson effect.

Computation of atomic and spin currents in the system.

Abstract

We study the quantum dynamics of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) in a double-well potential inspired by the experimental protocol recently developed by NIST group. We focus on the regime where the number of atoms is very large and perform a two-mode approximation. An analytical solution of the two-site Bose-Hubbard-like Hamiltonian is found for several limiting cases, which range from a strong Raman coupling to a strong Josephson coupling, ending with the complete model in the presence of weak nonlinear interactions. Depending on the particular limit, different approaches are chosen: a mapping onto an SU(2) spin problem together with a Holstein-Primakoff transformation in the first two cases and a rotating wave approximation (RWA) when dealing with the complete model. The quantum evolution of the number difference of bosons with equal or different spin between the two wells is investigated in a wide range of parameters; finally the corresponding total atomic current and the spin current are computed. We show a spin Josephson effect which could be detected in experiments and employed to build up realistic devices.