Quantum droplets with topological textures in a dipolar condensate

We investigate a spin–orbit coupled Bose–Einstein condensate containing both dipolar and non-dipolar components. Combined with Rashba spin–orbit coupling, the competition between contact and dipolar interaction reveals four distinctive exotic phases: droplet lattice phase, stripe phase, oblique stripe phase, and labyrinthine stripe phase. In particular, we adopt a condensate order parameter ansatz to characterize the superstripe phase in a harmonic trap through minimizing the analytical total energy. Furthermore, we find that the energy analysis of the dipolar condensate in the trap uncovers a higher order transition from lattice to stripe phases when contact interaction increases. Our results demonstrate the possibility for physicists to realize a wealth of controllable configurations in spin–orbit coupled dipolar condensates, including droplet lattice with topology and superstripe adjusted by changing the strength of contact and dipolar interactions. The topological phases we predict in this work can be realized by using state-of-the-art techniques in ultracold atomic experiments of chromium, erbium, or dysprosium condensates.