Quantum Corrections to Dilute Bose Liquids

TL;DR

This paper extends the mean-field analysis of tunable quantum liquids made from bosons, fermions, and mixtures by calculating quantum corrections to their ground state energy and condensate depletion, showing these corrections are small.

Contribution

It provides the first calculation of quantum corrections beyond mean-field for these tunable quantum liquids, including estimates of higher-order effects.

Findings

Quantum corrections are small and controlled by the diluteness parameter.

The corrections remain small despite the absence of a strict low-density regime.

Higher order corrections are estimated to be manageable.

Abstract

It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002)) that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons (boselets), fermions (fermilets) and their mixtures (ferbolets) by controlling their interaction properties by the means of a Feshbach resonance. 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 higher order corrections as well. We show that the quantum corrections are relatively small and controlled by the diluteness parameter $\sqrt{n|a|^3} \ll 1$, even though strictly speaking in this case there is no low density expansion.