Recent finite-temperature numerical simulations have unveiled a quantum “spin” microemulsion analog, found by raising the temperature of a stripe supersolid phase in a Rashba spin-orbit coupled Bose gas. This microemulsion state is a highly correlated, isotropic normal fluid where atoms self-arrange based on their internal pseudospin into patterns that resemble bicontinuous microemulsions. This finding leaves several open questions regarding the broader accessibility of this phase in experiments. Here, we use equilibrium finite-temperature numerical simulations based on a coherent-state path integral representation to perform a computational investigation into the thermodynamic stability of the spin microemulsion state. Numerical simulations emphasize the requirement of a nearly, but not perfectly, isotropic spin-orbit coupling in order to achieve the microemulsion phase in cold-atom experiments. Moreover, the microemulsion state exists independent of miscibility of the pseudospin components and for a wide range of pseudospin population imbalance, suggesting a high degree of flexibility in choosing the atom and hyperfine states in an experimental realization. Finally, we demonstrate this feasibility by mimicking a Rashba spin-orbit-coupled ${}^{87}\mathrm{Rb}$ experiment in an isotropic harmonic trap, where we confirm the microemulsion's existence via its density profile and equilibrium quasimomentum distribution.

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• Phase diagrams
• Spin-orbit coupling
• Spinor Bose-Einstein condensates
• Supersolids
• Complex Langevin dynamics
• Finite temperature field theory
• Finite-size scaling
• Path-integral methods