Exploring Exotic Microphases in Simulated Spin-Orbit Coupled Boson Systems*

We assess the robustness of a novel quantum microemulsion phase in Rashba spin-orbit coupled (SOC) Bose-Einstein condensates using finite-temperature, field-theoretic simulations. Our goal is to motivate experimental progress in realizing Rashba SOC in ultracold gases—an engineered 2D isotropic interplay between spin and momentum that has yet to be successfully realized experimentally—by clarifying the microemulsion's broad viability. Our group's previous research suggests that the microemulsion phase only exists under immiscible conditions, which may limit realistic experiments. Contrary to our expectations, we find that similar to the immiscible stripe superfluid phase, the miscible plane-wave phase undergoes a Kosterlitz Thouless-like transition into the microemulsion, losing superfluidity at elevated temperature. We conclude with a phase diagram that demonstrates the existence of the microemulsion, regardless of miscibility.