Ground state of spin-1 Bose-Einstein condensates with spin-orbit coupling in a Zeeman field

TL;DR

This paper explores the ground states of spin-1 Bose-Einstein condensates with spin-orbit coupling under Zeeman fields, revealing phase transitions and unique magnetization behaviors influenced by external magnetic fields.

Contribution

It provides a systematic analysis of phase boundaries and magnetization responses in spin-1 BECs with spin-orbit coupling under Zeeman effects, combining analytical and numerical methods.

Findings

Zeeman field induces phase transitions between standing wave and plane wave phases.

Magnetization responds differently to linear and quadratic Zeeman effects.

Beyond a critical Zeeman strength, the system becomes fully polarized in ferromagnetic or polar states.

Abstract

We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing wave phase or plane wave phase when the strength of Zeeman field is below a critical value related to the strength of spin-orbit coupling. Zeeman field can induce the phase transition between standing wave and plane wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner, the linear Zeeman effect magnetizes the standing wave phase along the direction of the magnetic field, but the quadratic one demagnetizes the plane wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.