Finite-temperature quasicrystalline state in spin-orbit coupled dipolar Bose-Einstein condensates: Supersolid?

Supersolidity — a counterintuitive concept that combines superfluidity with crystalline ordering — has caught the attention of contemporary cold atom and condensed matter physics. While experiments have so far realized striped and dipolar supersolids in Bose-Einstein condensates (BEC), mean-field treatments of two-dimensional Rashba spin-orbit coupled dipolar BECs have proposed the existence of aperiodic "quasicrystal" analogues. However, the massive single-particle degeneracy of the Rashba Hamiltonian highlights the importance of fluctuations in this system. As such, beyond-mean-field investigations of the quasicrystal BEC state are necessary to resolve their precise equilibrium behavior and properties. Here, we use coherent states complex Langevin numerical simulations to study two-dimensional quasicrystalline BEC phases under realistic quantum and thermal fluctuations. We discuss whether superfluidity persists at low temperature in the quasicrystalline state as well as the nature of finite-temperature phase transitions, shedding light on whether this quasicrystal BEC state constitutes a new type of supersolid.