Proximity effects in spatially quenched population-imbalanced Fermi gases with pairing interactions 

By introducing spatially inhomogeneous profiles of the pairing interaction or spin polarization, separation of different phases of Fermi gases can form in real space. We implement the Bogoliubov-de Gennes (BdG) formalism to investigate the ground-state structures and properties induced by inhomogeneity. For a spatial quench between the Fulde-Ferrell-Larkin-Ovchinikov (FFLO) and polarized normal phases, the modulating FFLO pairing correlation penetrates the normal region, showing a peak at the FFLO momentum in the Fourier transform of the pair correlation function. When the BCS and FFLO superfluids are joined by inhomogeneity, the BCS region expels population imbalance to the FFLO side while the two sides exhibit zero-momentum and finite-momentum pair correlations. If the BCS and normal phases are joined in the presence of spin polarization, a buffer of the FFLO phase emerges and leads to modulating pair correlations in the normal region. The proxy effects in inhomogeneous Fermi gases with pairing and spin polarization thus provide a versatile platform for testing the response of superfluids and polarized Fermi gases in real space.