Bose-Bose gases with nonuniversal corrections to the interactions: A droplet phase

Abstract

Through an effective quantum field theory within Bogoliubov’s framework and taking into account nonuniversal effects of the interatomic potential we analytically derive the leading Gaussian zero- and finite-temperature corrections to the equation of state of ultracold interacting Bose-Bose gases. We calculate the ground-state energy per particle at zero and low temperature for three- two- and one-dimensional two-component bosonic gases. By tuning the nonuniversal contribution to the interactions we address and establish conditions under which the formation and stability of a self-bound liquidlike phase or droplet with nonuniversal corrections to the interactions (DNUC) is favorable. At zero temperature in three-dimensions and considering the nonuniversal corrections to the attractive interactions as a fitting parameter the energy per particle for DNUC is in good agreement with some diffusion Monte Carlo results. In two dimensions the DNUC present small deviations regarding conventional droplets. For the one-dimensional DNUC the handling of the nonuniversal effects to the interactions achieves a qualitative agreement with the trend of some available Monte Carlo data in usual droplets. We also introduce some improved Gross–Pitaevskii equations to describe self-trapped DNUC in three, two and one dimension. We briefly discuss some aspects at low temperature regarding nonuniversal corrections to the interactions in Bose-Bose gases. We derive the dependencies on the nonuniversal contribution to the interactions but also on the difference between intra- and inter-species coupling constants. This last dependence crucially affect the three- and the two-dimensional DNUC driving thus to a thermal-induced instability. This thermal instability is also present in one-dimensional Bose-Bose gases, but it is not relevant on the formation of DNUC. This is explained because the necessary attraction mechanism to achieve this phase naturally arises in the fluctuations at zero temperature without major restrictions as it happens in the other dimensions.