Emergence of $\eta$-pairing ground-state in population-imbalanced attractive Fermi-gases filling $p$ orbitals on 1-D optical lattice

TL;DR

This paper demonstrates that population-imbalanced attractive fermionic gases in 1D optical lattices exhibit an $ ext{eta}$-pairing ground state with spatially oscillating pair correlations, distinct from known Fulde-Ferrel-Larkin-Ovchinikov states.

Contribution

It reveals the emergence of an $ ext{eta}$-pair condensate in 1D optical lattices with population imbalance, confirmed through DMRG calculations and analysis of harmonic trap effects.

Findings

$ ext{eta}$-pairing order observed at the trap center.

Pair correlation oscillates with a fixed period of $ ext{ extpi}$.

Distinct from Fulde-Ferrel-Larkin-Ovchinikov pairing.

Abstract

We explore the ground states in population-imbalanced attractive 1-D fermionic optical lattice filling $p$ orbitals over the lowest $s$ one by using the density-matrix-renormalization-group (DMRG) method. The DMRG calculations find the occurrence of spatially non-uniform off-diagonal long-range order. In contrast to Fulde-Ferrel Larkin-Ovchinikov pair as observed in the single-band Hubbard model. The spatial oscillation period of the pair correlation function is widely fixed to be $\pi$ irrespective of the mismatch between spin-split Fermi surfaces. The ground-state $\pi$ order corresponds to $\eta$-pair condensate predicted by Yang [Phys. Rev. Lett. \textbf{63}, 2144 (1989)]. Taking account of the effects of harmonic traps, we confirm that the $\eta$-pair state distinctly emerges at the center of the trap potential surrounded by perfectly-polarized states even in the trapped cases.