Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices

Abstract

Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for a small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long-range order into long-range order by coupling many identical 1D systems, such as in quasi-1D optical lattices

Universal quantum behavior of interacting fermions in one-dimensional traps: From few particles to the trap thermodynamic limit

“…Refs. [48,83]. Moreover, the number n peak of peaks turns out to increase proportionally to ℓ as suggested by the phase term in Eq.…”

BCS-BEC crossover and the disappearance of Fulde-Ferrell-Larkin-Ovchinnikov correlations in a spin-imbalanced one-dimensional Fermi gas

“…In the limit of L → ∞, the density and spin profiles will become flat, while the modulations can then be detected in the respective correlation functions (compare Refs. [33,68] for the attractive Hubbard model). In the experimentally relevant situation of harmonically trapped particles, however, the density profiles themselves should have properties similar to those discussed here for finite systems with open boundary conditions, at least in parts of the particle cloud.…”

Dimer, trimer, and Fulde-Ferrell-Larkin-Ovchinnikov liquids in mass- and spin-imbalanced trapped binary mixtures in one dimension

“…Only recently, it was rigorously shown that the partially polarized phase is the onedimensional analogue of the FFLO state by means of exact numerical methods [49,51,[58][59][60], confirming predictions from mean-field theory [61,62] and bosonization [63]. In 1D, this means that the pair-pair correlation functions are modulated with Q = k F ↑ − k F ↓ and decay as a power law, slower than any competing correlation in the two-particle channel (k F σ = πn σ is the Fermi momentum).…”