Analytical limits for cold atom Bose gases with tunable interactions

TL;DR

This paper analyzes the equilibrium properties of dilute Bose gases with tunable interactions using a non-perturbative auxiliary field formalism, providing analytical results near the critical point and in the unitarity limit.

Contribution

It introduces the LOAF approximation for Bose gases, showing its consistency with known results and providing new analytical insights in the unitarity regime.

Findings

LOAF reproduces known zero-temperature results for dilute gases.

Near the critical point, LOAF matches large-N effective field theory predictions.

In the unitarity limit, the equation of state differs from Fermi gases, with E/(pV)=1.

Abstract

We discuss the equilibrium properties of dilute Bose gases using a non-perturbative formalism based on auxiliary fields related to the normal and anomalous densities. We show analytically that for a dilute Bose gas of weakly-interacting particles at zero temperature, the leading-order auxiliary field (LOAF) approximation leads to well-known analytical results. Close to the critical point the LOAF predictions are the same as those obtained using an effective field theory in the large-N approximation. We also report analytical approximations for the LOAF results in the unitarity limit, which compare favorably with our numerical results. LOAF predicts that the equation of state for the Bose gas in the unitarity limit is E / (p V) = 1, unlike the case of the Fermi gas when E / (p V) = 3/2.