Anisotropic superfluidity in the stripe phase found in spin-orbit coupled Bose-Einstein condensates

Spin-orbit coupled Bose-Einstein condensates host unconventional superfluid phases in bulk, such as a stripe phase with smectic character. Despite much progress in the mean-field and zero temperature limits, the precise superfluid character of the stripe phase is poorly understood at finite temperature. To investigate and quantify finite temperature effects, this work numerically samples a (2 + 1)-dimensional coherent state statistical field theory via the Complex Langevin algorithm, capturing T>0 thermodynamics without approximation. Employing the phase twist method, the superfluid density tensor is calculated and studied as a function of temperature, spin-orbit coupling anisotropy, and spin-orbit coupling strength. Low but finite temperature results suggest a significant reduction in superfluidity in the direction parallel to the stripes in the limit of isotropic spin-orbit coupling.