Quantum Phases for Finite-Temperature Gases of Bosonic Polar Molecules Shielded by Dual Microwaves

We investigate the finite-temperature phase diagram of polar molecules shielded by dual microwave fields using the path integral Monte Carlo method combined with the worm algorithm. We determine the critical temperature Tc for Bose-Einstein condensations (BECs) and identify two distinct phases below Tc: the expanding gas (EG) phase and the self-bound gas (SBG) phase. We further analyze the temperature and interaction-strength dependence of the condensate and superfluid fractions. Notably, in contrast to dilute atomic BECs, the SBG phase displays a low condensate fraction and a high superfluid fraction, resembling the behavior of strongly correlated 4He superfluids. These significant many-body correlations arise from the interplay between long-range dipole-dipole interactions and the short-range shielding potential. Furthermore, we demonstrate that the aspect ratio of the gas provides a characteristic geometric signature to accurately determine the EG-to-SBG transition, robust against external trapping potentials. Our findings provide unbiased and numerically exact results to guide upcoming experiments with polar molecules.