Structures and proximity effects of inhomogeneous population-imbalanced Fermi gases with pairing interactions

TL;DR

This paper investigates how spatial variations in pairing interactions and spin polarization influence the coexistence and structure of different phases in inhomogeneous, population-imbalanced Fermi gases, revealing complex phase transitions and proximity effects.

Contribution

It introduces a detailed analysis of phase coexistence and transitions in inhomogeneous Fermi gases using the Bogoliubov--de Gennes framework, highlighting novel phase behaviors and proximity phenomena.

Findings

Spatial inhomogeneity drives phase transitions between BCS, FFLO, and normal phases.

FFLO phase exhibits characteristic modulated order parameter and proximity effects.

A buffer FFLO phase appears at phase interfaces in the presence of spin polarization.

Abstract

By introducing spatially varying profiles of pairing interaction or spin polarization to quasi one-dimensional two-component atomic Fermi gases confined in box potentials, we analyze the ground state structures and properties when multiple phases coexist in real space by implementing the Bogoliubov--de~Gennes equation suitable for describing inhomogeneous fermion systems. While the BCS, Fulde--Ferrell--Larkin--Ovchinnikov (FFLO), and normal phases occupy different regions on the phase diagram when the parameters are uniform, a spatial change of pairing strength or spin polarization can drive the system from the FFLO phase to a normal gas or from a BCS superfluid to the FFLO phase in real space. The FFLO phase exhibits its signature modulating order parameter at the FFLO momentum due to population imbalance, and the pair correlation penetrates the polarized normal phase and exhibits proximity effects. Meanwhile, the BCS phase tends to repel population imbalance and maintain a plateau of pairing. Interestingly, a buffer FFLO phase emerges when the spatial change attempts to join the BCS and normal phase in the presence of spin polarization. By analyzing the pairing correlations, interfacial properties, and momentum-space spectra of the inhomogeneous structures, relevant length- and momentum- scales and their interplay are characterized. We also briefly discuss implications of inhomogeneous multi-phase atomic Fermi gases with population imbalance.