We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e., unitarity, regime. The Bogoliubov-de Gennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and Fulde-Ferrel-Larkin-Ovchinnikov-type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter.
We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e., unitarity, regime. The Bogoliubov-de Gennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and Fulde-Ferrel-Larkin-Ovchinnikov-type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter.
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.
We theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS-BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov-de Gennes equation coupled with the regularized gap and number equations. The zero-temperature phase diagram in the crossover regime is presented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state governs the weak-coupling BCS region of a resonance. It is found that the FFLO oscillation vanishes in the BEC side, in which the system under population imbalance turns into a phase separation (PS) between locally binding superfluid and fully polarized spin domains. We also demonstrate numerical calculations with a large particle number O(10^5), comparable to that observed in recent experiments. The resulting density profile on a resonance yields the PS, which is in good agreement with the recent experiments, while the FFLO modulation exists in the pairing field. It is also proposed that the most favorable location for the detection of the FFLO oscillation is in the vicinity of the critical population imbalance in the weak coupling BCS regime, where the oscillation periodicity becomes much larger than the interparticle spacing. Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced system. The clear difference in the RF spectroscopy between BCS and BEC sides reveals the structure of the pairing field and local ``magnetization''.
The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced two-component fermion mixtures in harmonically trapped optical lattices. In the low density limit, the superfluid order parameter has Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type oscillations 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 has oscillations in the radial direction towards the trap center for low imbalances, it also has oscillations 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 imbalances, but leads to double peaks for intermediate imbalances.
Ultracold atomic gases have emerged as an ideal laboratory system to emulate many-body physics in an unprecedentedly controllable manner. Numerous many-body quantum states and phases have been experimentally explored and characterized using the ultracold atomic gases, offering new insights into many exciting physics ranging from condensed matters to cosmology. In this thesis, we will present a systematic numerical study of a novel experimental system, population imbalanced two-component ultracold Fermi gases. We explore the phase diagram of this system in both 3D and 1D especially focusing on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by a spatially oscillating order parameter. In 3D, we solve for the stationary states of trapped imbalanced Fermi gases in a wide range of parameter space with a home-made parallel eigen-solver for Bogoliubov-de Gennes (BdG) equations. Our results show that there exists a metastable state with a FFLO type oscillating order parameter. In 1D, we simulate the dynamical expansion of the population imbalanced Fermi gases from the trap. A numerically quasi-exact scheme, time-evolving block decimation (TEBD), is introduced for the comparative studies with the solution of the time-dependent BdG equation. Our results predict that the existence of FFLO states will leave conspicuous signatures in the density profiles during the expansion. For further understanding of the interplay between the population imbalance and two-body pairing interaction between two spin components, we also study the spin transport properties through trapped ultracold Fermi gases. The preliminary results will be discussed.
We calculate the mean-field thermodynamics of a spherically trapped Fermi gas with unequal spin populations in the unitarity limit, comparing results from the Bogoliubov--de Gennes equations and the local density approximation. We follow the usual mean-field decoupling in deriving the Bogoliubov--de Gennes equations and set up an efficient and accurate method for solving these equations. In the local density approximation we consider locally homogeneous solutions, with a slowly varying order parameter. With a large particle number these two approximation schemes give rise to essentially the same results for various thermodynamic quantities, including the density profiles. This excellent agreement strongly indicates that the small oscillation of order parameters near the edge of trap, sometimes interpreted as spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states in previous studies of Bogoliubov--de Gennes equations, is a finite-size effect. We find that a bimodal structure emerges in the density profile of the minority-spin state at finite temperature, as observed in experiments. The superfluid transition temperature as a function of the population imbalance is determined and is shown to be consistent with recent experimental measurements. The temperature dependence of the equation of state is discussed.
Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or---potentially---to exotic forms of superfluidity such as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, Sarma state, or breached pair state. We consider ultracold Fermi gases with polarization, i.e., spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the Bardeen-Cooper-Schrieffer (BCS) superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior.