Emergence of a Spin Microemulsion in Spin-Orbit Coupled Bose-Einstein Condensates

Abstract

We report the first numerical prediction of a “spin microemulsion”—a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions—in two-dimensional systems of spinor Bose-Einstein condensates with isotropic Rashba spin-orbit coupling. Using field-theoretic numerical simulations, we investigated the melting of a low-temperature stripe phase with supersolid character and find that the stripes lose their superfluidity at elevated temperature and undergo a Kosterlitz-Thouless-like transition into a spin microemulsion. Momentum distribution calculations highlight a thermally broadened occupation of the Rashba circle of low-energy states with macroscopic and isotropic occupation around the ring. We provide a finite-temperature phase diagram that positions the emulsion as an intermediate, structured isotropic phase with residual quantum character before transitioning at higher temperature into a structureless normal fluid.Received 20 June 2023Revised 14 August 2023Accepted 1 September 2023DOI:https://doi.org/10.1103/PhysRevLett.131.173403© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMagnetic texturePhase transitionsSpin-orbit couplingStripesPhysical SystemsSpinor Bose-Einstein condensatesSupersolidsTechniquesFinite temperature field theoryFinite-size scalingLangevin algorithmPath-integral methodsAtomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics