BCS-BEC crossover with unequal mass fermions

TL;DR

This paper explores the BCS-BEC crossover in a two-fermion-species system with unequal masses, analyzing the equation of state, ground state energy, and scattering properties across the crossover, with implications for experiments involving mixed atomic gases.

Contribution

It provides a detailed theoretical analysis of the BCS-BEC crossover with unequal masses, including Gaussian fluctuation effects and comparisons with quantum Monte Carlo and four-body results.

Findings

Excellent agreement with quantum Monte Carlo results for mass ratio 6.67.

Dimer scattering length matches four-body calculations across mass ratios.

Derived conditions for trapping frequencies to achieve unpolarized gases.

Abstract

We investigate the crossover from BCS pairing to molecular BEC in an atomic gas with two fermion species with masses $m_\up \ne m_\dn$ tuned through a Feshbach resonance. We present results for the T=0 equation of state as a function of the scattering length including the effects of Gaussian fluctuations about the mean field ground state. We compute the ground state energy as a function of $m_\up/m_\dn$ at unitarity and find excellent agreement with the quantum Monte Carlo result for $m_\up/m_\dn = 6.67$ for a $^{40}$K-$^6$Li mixture. We show that the dimer scattering length in the BEC limit as a function of $m_\up/m_\dn$ compares well with exact four-body results of Petrov {\it et al}. We also derive the condition for trapping frequencies to obtain an unpolarized gas in a harmonic trap.