Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS-BEC Crossover Regime

TL;DR

This paper provides a comprehensive theoretical analysis of imbalanced Fermi gases in the BCS-BEC crossover, revealing phase behaviors, density profiles, and RF spectroscopy signatures across different interaction regimes.

Contribution

It introduces detailed numerical calculations of the ground state phases, including FFLO and phase separation, in large systems with population imbalance, aligning with recent experimental observations.

Findings

FFLO phase exists in the weak-coupling BCS regime

Phase separation occurs on the BEC side with population imbalance

RF spectroscopy distinguishes pairing structures across regimes

Abstract

We theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS-BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov-de Gennes equation coupled with the regularized gap and number equations. The zero-temperature phase diagram in the crossover regime is presented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state governs the weak-coupling BCS region of a resonance. It is found that the FFLO oscillation vanishes in the BEC side, in which the system under population imbalance turns into a phase separation (PS) between locally binding superfluid and fully polarized spin domains. We also demonstrate numerical calculations with a large particle number O(10^5), comparable to that observed in recent experiments. The resulting density profile on a resonance yields the PS, which is in good agreement with the recent experiments, while the FFLO modulation exists in the pairing field. It is also proposed that the most favorable location for the detection of the FFLO oscillation is in the vicinity of the critical population imbalance in the weak coupling BCS regime, where the oscillation periodicity becomes much larger than the interparticle spacing. Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced system. The clear difference in the RF spectroscopy between BCS and BEC sides reveals the structure of the pairing field and local ``magnetization''.