Universal Bose Gases Near Resonance: A Rigorous Solution

TL;DR

This paper provides a rigorous analytical solution for universal Bose gases near resonance using an epsilon expansion, addressing a key challenge in quantum gases at large scattering lengths.

Contribution

It introduces a novel epsilon expansion approach near four dimensions to solve for properties of Bose gases near resonance, overcoming the limitations of dilute theory.

Findings

Chemical potential approaches a universal value near resonance.

Condensation fraction is approximately 2/3 with small corrections.

Results have implications for ultra-cold gases in physical dimensions.

Abstract

We obtain a rigorous solution of universal Bose gases near resonance and offer an answer to one of the long-standing challenges of quantum gases at large scattering lengths, where the standard dilute theory breaks down. The solution was obtained by using an $\epsilon$ expansion near four spatial dimension. In dimension $d = 4 - \epsilon$, the chemical potential of Bose gases near resonances is shown to approach the universal value $\epsilon^{(2/(4-\epsilon))} \epsilon_F \sqrt{2/3} (1 + 0.474 \epsilon - i 1.217 \epsilon + ...)$, where $\epsilon_F$ is the Fermi energy defined for a Fermi gas of density $n$, and the condensation fraction is equal to $2/3 (1 + 0.0877 \epsilon + ...)$. We also discuss the implications on ultra-cold gases in physical dimensions.