Vortex, stripe, Skyrmion lattice, and localized states in a spin–orbit coupled dipolar condensate

Abstract

We investigate a spin-1/2 system containing both dipolar and non-dipolar components in a 52Cr Bose–Einstein condensate with spin–orbit coupling. Combined with energy analysis, phase diagram between contact interaction and Rashba spin–orbit coupling reveals four distinctive ground-state phases: vortex state phase, stripe phase, Skyrmion lattice phase, and localized Skyrmion phase. We adopt the condensate order parameter to characterize the supersolidity and topological charges of the quantum states of matter. In particular, we predict the emergence of a Skyrmion lattice phase with supersolidity which is justified by calculating the crystalline order. Moreover, we find that the critical value of the spin–orbit coupling from stripe to Skyrmion lattice increases with decreasing relative strength of the dipolar and contact interactions. Our results demonstrate the possibility for physicists to realize a wealth of controllable topological configurations in dipolar condensates, including Skyrmion lattices with both supersolidity and different topological charges adjusted by changing the strength of spin–orbit coupling. The topological phases we predict in this work can be realized by using state-of-the-art techniques in ultracold atomic experiments, such as using pulsed magnetic fields to induce and adjust spin–orbit couplings on atom chips of chromium, erbium, or dysprosium condensates.