The Universality and stability for a dilute Bose gas with a Feshbach resonance

TL;DR

This paper analyzes the zero-temperature behavior of a dilute Bose gas near a Feshbach resonance, revealing universal properties, instability of the atomic superfluid, and an equivalence to ideal Fermi gas thermodynamics in the unitary limit.

Contribution

It provides a renormalization group analysis showing the universal scaling and thermodynamic equivalence of a dilute Bose gas with Feshbach resonance at zero temperature.

Findings

The system always collapses in the dilute limit.

Atomic superfluid is unstable in the dilute limit.

Thermodynamics matches that of an ideal Fermi gas at unitarity.

Abstract

We study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero density fixed point. Moreover, we find that the T=0 thermodynamics of this system in the unitary limit is exactly identical to the one for an ideal Fermi gas.