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arXiv:1206.5050 · Physical Review A

Pairing in a two-dimensional Fermi gas with population imbalance

Mathew Wolak, Benoît Grémaud, Richard T. Scalettar, G. G. Batrouni

Published Aug 23, 2012• 36 citations
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Abstract

Pairing in a population-imbalanced Fermi system in a two-dimensional optical lattice is studied using determinant quantum Monte Carlo simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovchinnikov phase. Contrary to claims of fragility with increased dimensionality, we find that this phase is stable across a wide range of values for the polarization, temperature, and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center-of-mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold-atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels, which can be seen as the analog of the finite center-of-mass momentum pairing in the translationally invariant case. Finally, we perform mean-field calculations for the uniform and confined systems and show the results to be in good agreement with quantum Monte Carlo. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.

DOI
10.1103/physreva.86.023630

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Pairing in a population-imbalanced Fermi system in a two-dimensional optical lattice is studied using determinant quantum Monte Carlo simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovchinnikov phase. Contrary to claims of fragility with increased dimensionality, we find that this phase is stable across a wide range of values for the polarization, temperature, and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center-of-mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold-atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels, which can be seen as the analog of the finite center-of-mass momentum pairing in the translationally invariant case. Finally, we perform mean-field calculations for the uniform and confined systems and show the results to be in good agreement with quantum Monte Carlo. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.
We study the pairing states in a largely imbalanced two-component Fermi gas loaded in an anisotropic two-dimensional optical lattice, where the spin-up and spin-down fermions are filled to the s- and p x -orbital bands, respectively. We show that owing to the relative inversion of the band structures of the s and p x orbitals, the system favors pairing between two fermions on the same side of the Brillouin zone, leading to a large stable regime for states with a finite center-of-mass momentum, i.e., the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. In particular, when two Fermi surfaces are close in momentum space, a nesting effect stabilizes a special type of π-FFLO phase with a spatial modulation of π along the easily tunneled x direction. We map out the zero-temperature phase diagrams within the mean-field approach for various aspect ratios within the two-dimensional plane and calculate the Berezinskii–Kosterlitz–Thouless (BKT) transition temperatures T BKT for different phases.
We consider a two-component gas of fermions in optical lattices in the presence of a population imbalance within a mean-field theory. We study phase transitions from a normal gas of unpaired fermions to a superfluid phase of Bose-condensed Cooper pairs. The possibility of Cooper pairs with a nonzero centre-of-mass momentum is included, which corresponds to a so-called Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) state. We find that for population-imbalanced systems such states can form the ground state. The FF and LO state are compared and it is shown that actually the LO state is energetically more favourable. We complete the mean-field phase diagram for the LO phase and show that it is qualitatively in excellent agreement with recent diagrammatic Monte Carlo calculations. Subsequently, we calculate the atomic density modulations in the LO phase.
We investigate exotic paired states of spin-imbalanced Fermi gases in anisotropic lattices, tuning the dimension between one and three. We calculate the finite temperature phase diagram of the system using real-space dynamical mean-field theory in combination with the quantum Monte Carlo method. We find that regardless of the intermediate dimensions examined, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state survives to reach about one third of the BCS critical temperature of the spin-density balanced case. We show how the gapless nature of the state found is reflected in the local spectral function. While the FFLO state is found at a wide range of polarizations at low temperatures across the dimensional crossover, with increasing temperature we find out strongly dimensionality-dependent melting characteristics of shell structures related to harmonic confinement. Moreover, we show that intermediate dimension can help to stabilize an extremely uniform finite temperature FFLO state despite the presence of harmonic confinement.
We consider pairing in a two-component atomic Fermi gas, in a three-dimensional optical lattice, when the components have unequal densities, i.e. the gas is polarized. We show that a superfluid where the translational symmetry is broken by a finite Cooper pair momentum, namely a Fulde–Ferrel–Larkin–Ovchinnikov (FFLO)-type state, minimizes the Helmholtz free energy of the system. We demonstrate that such a state is clearly visible in the observable momentum distribution of the atoms, and analyse the dependence of the order parameter and the momentum distribution on the filling fraction and the interaction strength.
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.
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.