Quantum corrections to dilute Bose liquids

It was recently shown [A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002)] that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons, fermions, and their mixtures by controlling their interaction properties by means of a Feshbach resonance. Since the quantum fluctuations in this regime could, in principle, destabilize these objects, we extend the previous mean-field analysis of these quantum liquids by computing the lowest-order quantum corrections to the ground-state energy and the depletion of the Bose-Einstein condensate and by estimating the higher-order corrections as well. We show that the quantum corrections are relatively small, do not lead to the destabilization of the droplets and are controlled by the diluteness parameter $\sqrt{n|a{|}^3}\ll 1,$ even though strictly speaking in this case there is no low density expansion.