Comment on "Fermi-Bose Mixtures near Broad Interspecies Feshbach Resonances"

TL;DR

This paper critiques a recent variational approach to boson-fermion mixtures, demonstrating its inaccuracies and showing through an exactly solvable model that multiple correlated pairs cannot form as previously claimed.

Contribution

It provides a critical analysis of the prior theory and introduces an exactly solvable model to refute the existence of multiple correlated boson-fermion pairs.

Findings

The variational approach is incorrect.

Only one correlated BF pair can form at Q=0.

Multiple pairs as predicted are impossible.

Abstract

In a recent Letter (Phys. Rev. lett. 105, 195301 (2010)), Song et al. introduced a new variational approach to treat strong attractive boson-fermion (BF) correlations in BF atomic mixtures. The proposed theory predicts a first order phase transition to a condensate of composite BF pairs with center of mass momentum Q=0 as opposed to a composite fermionic molecular Fermi gas. We show in this comment that their approach is incorrect and moreover, by resorting to an exactly solvable model we demonstrate that there cannot be more than one correlated Q=0 BF pair in complete contradiction with their conclusions.