Effects of Dipolar Interaction on Spin–Orbit Coupled Dynamics in Spin-1 Ultracold Atoms

Abstract

In this paper, we investigate the spin–orbit coupling of F = 1 dipolar Bose–Einstein condensates in a quasi-one-dimensional trap by solving the mean field Gross–Pitaevskii equation. We focus on the two phases, ferromagnetic and antiferromagnetic. For the former, we find that the spin echo signal emerges gradually as the spin–orbit coupling strength increases, which favors miscibility in density profile. The dipolar interaction plays a tiny role in the spin dynamics process, the qualitative behavior remains almost unchanged. Nevertheless, for the antiferromagnetic phase, the physical picture greatly changes. The spin echo signal abruptly increases with the increase in spin–orbit coupling strength, and the density structure exhibits phase separation. With the emergence of dipolar interaction, the spin echo signal vanishes, and the evolution of the three components is ruleless. Meanwhile, the condensate deviates from the property of phase separation. Also, we analyze the effect of the number of atoms on spin dynamics. It is obvious that the reduction of atoms increases the number of spin echo signals for the ferromagnetic phase regardless of the nature of dipolar interaction. In addition, for the antiferromagnetic phase, such a decrease gives rise to the disappearance of the spin echo signal in the absence of dipolar interaction, and its influence is small when dipolar interaction is added.