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arXiv:0903.2346 · Physical Review B

Phase diagram of imbalanced fermions in optical lattices

Xiaoling Cui, Yupeng Wang

Published May 22, 2009• 6 citations
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Abstract

The zero-temperature phase diagrams of imbalanced fermions in three-dimensional optical lattices are investigated to evaluate the validity of the Fermi-Hubbard model. It is found that depending on the filling factor, $s$-wave scattering strength, and lattice potential, the system may fall into the normal $(N)$ phase, magnetized superfluid $({\text{SF}}_{M})$, or phase separation of $N$ and Bardeen-Cooper-Schrieffer state. By tuning these parameters, the superfluidity could be favorable by enhanced effective couplings or suppressed by the increased band gap. The phase profiles in the presence of a harmonic trap are also investigated under LDA, which show some exotic shell structures compared to those without the optical lattice.

DOI
10.1103/physrevb.79.180509

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The zero-temperature phase diagrams of imbalanced fermions in three-dimensional optical lattices are investigated to evaluate the validity of the Fermi-Hubbard model. It is found that depending on the filling factor, sss-wave scattering strength, and lattice potential, the system may fall into the normal (N)(N)(N) phase, magnetized superfluid (SFM)({\text{SF}}_{M})(SFM​), or phase separation of NNN and Bardeen-Cooper-Schrieffer state. By tuning these parameters, the superfluidity could be favorable by enhanced effective couplings or suppressed by the increased band gap. The phase profiles in the presence of a harmonic trap are also investigated under LDA, which show some exotic shell structures compared to those without the optical lattice.
The zero-temperature phase diagrams of imbalanced two-species Fermi gases are investigated in asymmetric optical lattices with arbitrary potential depths, based on the exact spectrum instead of the Fermi-Hubbard model. We study the effect of lattice potentials and atomic densities to the fully paired Bardeen-Cooper-Schrieffer (BCS) state and particularly the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. It is found that the increasing lattice potential favors BCS at low densities because of the enhanced effective coupling, whereas FFLO is favored at intermediate densities when the system undergoes a dimensional crossover. Finally, using the local density approximation, we study the evolution of the phase profile in the presence of external harmonic traps by merely tuning the lattice potentials.
We study fermion pairing in a population-imbalanced mixture of 6{}^{6}6Li atomic gas loaded in a three-dimensional lattice at very low temperatures. Using the number equation for each population, the gap equation, and the equation for the Helmholtz free energy, we determine the gap, chemical potentials, and pair-momentum as functions of polarization. These parameters define the stability regions for a Fulde-Ferrell-Larkin-Ovchinnikov phase, a phase separation region where Bardeen-Cooper-Schrieffer and normal phases coexist, a Sarma phase when the pair-momentum vanishes, and the transition to the normal phase when the gap disappears. The collective-mode energies are then calculated using a Bethe-Salpeter approach in the generalized random-phase approximation assuming that the system is well described by the single-band Hubbard model. An interesting result is that this fermionic gas has a superfluid phase revealed by rotonlike minima in the asymmetric collective-mode energy spectrum.
We investigate a one-dimensional two-component system in an optical lattice of attractive interactions under a spin-dependent external potential. Based on the density-matrix renormalization group methods, we obtain its phase diagram as a function of the external potential imbalance and the strength of the attractive interaction through the analysis on the density profiles and the momentum pair correlation functions. We find that there are three different phases in the system, a coexisted fully polarized and Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase, a normal polarized phase, and a Bardeen–Cooper–Schrieffer (BCS) phase. Different from the systems of spin-independent external potential, where the FFLO phase is normally favored by the attractive interactions, in the present situation, the FFLO phases are easily destroyed by the attractive interactions, leading to the normal polarized or the BCS phase.
The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced fermion mixtures in harmonically trapped two-dimensional optical lattices. In the low density limit the superfluid order parameter modulates in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However, in the high density limit while the order parameter modulates in the radial direction towards the trap center for low imbalance, it also modulates towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalance, but leads to double peaks for intermediate imbalance.
We study the phase diagram of an imbalanced two-component Fermi gas in optical lattices of 1–3 dimensions (1D–3D), considering the possibilities of the Fulde–Ferrel–Larkin–Ovchinnikov (FFLO), Sarma/breached pair, BCS and normal states as well as phase separation, at finite and zero temperatures. In particular, phase diagrams with respect to average chemical potential and the chemical potential difference of the two components are considered, because this gives the essential information about the shell structures of phases that will occur in the presence of an additional (harmonic) confinement. These phase diagrams in 1D, 2D and 3D show in a striking way the effect of Van Hove singularities on the FFLO state. Although we focus on population imbalanced gases, the results are relevant also for the (effective) mass imbalanced case. We demonstrate by LDA calculations that various shell structures such as normal–FFLO–BCS–FFLO–normal, or FFLO–normal, are possible in presence of a background harmonic trap. The phases are reflected in noise correlations: especially in 1D the unpaired atoms leave a clear signature of the FFLO state as a zero-correlation area ('breach') within the Fermi sea. This strong signature occurs both for a 1D lattice as well as for a 1D continuum. We also discuss the effect of Hartree energies and the Gorkov correction on the phase diagrams.
The ground-state phase diagram of Fermi-Fermi mixtures in optical lattices is analyzed as a function of interaction strength, population imbalance, filling fraction, and tunneling parameters. It is shown that population imbalanced Fermi-Fermi mixtures reduce to strongly interacting Bose-Fermi mixtures in the molecular limit, in sharp contrast to homogeneous or harmonically trapped systems, where the resulting Bose-Fermi mixture is weakly interacting. Furthermore, insulating phases are found in optical lattices of Fermi-Fermi mixtures in addition to the standard phase-separated or coexisting superfluid--excess-fermion phases found in homogeneous systems. The insulating states can be a molecular Bose-Mott insulator (BMI), a Fermi-Pauli insulator (FPI), a phase-separated BMI-FPI mixture, or a Bose-Fermi checkerboard.