Ground-state phase transitions in spin-1 Bose-Einstein condensates with spin-orbit coupling

TL;DR

This paper studies how spin-orbit coupling and magnetic field gradients induce phase transitions in the ground state of spin-1 Bose-Einstein condensates, revealing that excited states can become ground states under certain conditions.

Contribution

It provides an exact solution for the linear system and demonstrates the persistence of phase transitions in the nonlinear regime, including effects of attractive interactions.

Findings

Excited states can transition into the ground state with varying SOC and magnetic field gradient.

Ground state phase transitions occur even with nonlinear repulsive interactions.

Weak attraction leads to mixed states near transition points; strong attraction causes edge states.

Abstract

We investigate phase transitions of the ground state (GS) of spin-1 Bose-Einstein condensates under the combined action of the spin-orbit coupling (SOC) and gradient magnetic field. Introducing appropariate raising and lowering operators, we exactly solve the linear system. Analyzing the obtained energy spectrum, we conclude that simultaneous variation of the magnetic-field gradient and SOC strength leads to the transition of excited states into the GS. As a result, any excited state can transition to the GS, at appropriate values of the system's parameters. The nonlinear system is solved numerically, showing that the GS phase transition, similar to the one in the linear system, still exists under the action of the repulsive nonlinearity. In the case of weak attraction, a mixed state appears near the GS transition point, while the GS transitions into an edge state under the action of strong attractive interaction.