The superfluid-insulator transitions of the fermionic atoms in optical lattices are investigated by the two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of the multiband effects. The quasiparticle weight in the superfluid state decreases significantly, as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model.
We study the multiband superfluid and the superfluid (SF) to band insulator (BI) transition of strongly interacting fermionic atoms in an optical lattice at a filling of two fermions per well. We present physical arguments to show that a consistent mean field description of this problem is obtained by retaining only intraband pairing between the fermions. Using this approach we obtain a reasonable account of the experimentally observed critical lattice depth for the SF-BI transition and the modulated components of the condensate density, and make predictions for the lattice depth dependence of…
In the fermionic Hubbard model, doubly occupied states have an exponentially large lifetime for strong repulsive interactions U. We show that this property can be used to prepare a metastable s-wave superfluid state for fermionic atoms in optical lattices described by a large-U Hubbard model. When an initial band-insulating state is expanded, the doubly occupied sites Bose condense. A mapping to the ferromagnetic Heisenberg model in an external field allows for a reliable solution of the problem. Nearest-neighbor repulsion and pair hopping are important in stabilizing superfluidity.
We investigate different physical properties of a spin imbalanced fermionic superfluid described by an attractive Hubbard model in presence of a harmonic trap. To characterize the ground state of such a system, we compute various correlation functions, such as pairing, density and current correlations To underscore the effect of the trap, we compute these quantities as a function of strength of the trapping potential. A distinguishing feature of a superfluid state with population imbalance, is the appearance of a phase with spatially modulating gap function, called the Fulde- Ferrell-Larkin-Ov…
We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multi-band effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of weakly bound molecular bosons to the region of strongly bound atomic bosons. Here the crossover can be controlled by attractive fermion interaction. One of the present models is a case with attractive fermion interaction, where an insulator-superfluid transition takes place. The transition is characterized as the transition between a band insulator and a Bose-Ei…
We study the stability of the paired fermionic p-wave superfluid made out of identical atoms all in the same hyperfine state close to a p-wave Feshbach resonance. First we reproduce known results concerning the lifetime of a 3D superfluid, in particular, we show that it decays at the same rate as its interaction energy, thus precluding its equilibration before it decays. Then we proceed to study its stability in case when the superfluid is confined to 2D by means of an optical harmonic potential. We find that the relative stability is somewhat improved in 2D in the BCS regime, such that the de…
We study the phase diagram of a three-component Fermi gas with weak attractive interactions, which shows three superfluid and one normal phases. At weak symmetry breaking between the components the existence of domain walls interpolating between two superfluids introduces a new length scale much larger than the coherence length of each superfluid. This, in particular, limits the applicability of the local density approximation in the trapped case, which we also discuss. In the same regime the system hosts soft collective modes with a mass much smaller than the energy gaps of individual superfl…
We analyze the dynamics of a condensate of ultra-cold atomic fermions following an abrupt change of the pairing strength. At long times, the system goes to a non-stationary steady state, which we determine exactly. The superfluid order parameter asymptotes to a constant value. We show that the order parameter vanishes when the pairing strength is decreased below a certain critical value. In this case, the steady state of the system combines properties of normal and superfluid states - the gap and the condensate fraction vanish, while the superfluid density is nonzero.
We discuss various superfluid properties of a two-component Fermi system in the presence of a tight one-dimensional periodic potential in a three-dimensional system. We use a zero temperature mean field theory and derive analytical expressions for the Josephson current, the sound velocity and the center of mass oscillations in the BCS-Bose Einstein condensation crossover region.
We investigate the harmonically trapped 2D fermionic systems with a effective spin-orbit coupling and intrinsic s-wave superfluidity under the local density approximation, and find that there is a critical value for Zeeman field. When the Zeeman field larger than the critical value, the topological superfluid phases emerge and coexist with the normal superfluid phase, topological phase separation, in the trapped region. Otherwise, the superfluid phase is topologically trivial.
In a recent article, Kwon et al. [Nature (London) {\bf 600}, 64 (2021)] revealed nonuniversal dissipative dynamics of quantum vortices in a fermionic superfluid. The enhancement of the dissipative process is pronounced for the Bardeen-Cooper-Schrieffer interaction regime, and it was suggested that the effect is due to the presence of quasiparticles localized inside the vortex core. We test this hypothesis through numerical simulations with time-dependent density-functional theory: a fully microscopic framework with fermionic degrees of freedom. The results of fully microscopic calculations exp…
We determine the superfluid transition temperature $T_c$ and related finite temperature phase diagrams for the entire BCS-Bose Einstein condensation crossover in a homogeneous mixture of $^{6}$Li and $^{40}$K atoms with population imbalance. Our work is motivated by the recent observation of an inter-species Feshbach resonance. Pairing fluctuation effects, which significantly reduce $T_c$ from the onset temperature for pairing ($T^*$), provide reasonable estimates of $T_c$ and indicate that the inter-species superfluid phase should be accessible in future experiments. Although a generalized-Sa…
We use hydrodynamic equations to study the formation of Faraday waves in a superfluid Fermi gas at zero temperature confined in a strongly elongated cigar-shaped trap. First, we treat the role of the radial density profile in the limit of an infinite cylindrical geometry and analytically evaluate the wavelength of the Faraday pattern. The effect of the axial confinement is fully taken into account in the numerical solution of hydrodynamic equations and shows that the infinite cylinder geometry provides a very good description of the phenomena.
We study a gas of repulsively interacting bosons in an optical lattice and explore the physics beyond the lowest band Hubbard model. Utilizing a generalized Gutzwiller ansatz, we find how the lowest band physics is modified by the inclusion of the first excited bands. In contrast to the prediction of the lowest band Bose-Hubbard model, a reentrant behavior of superfluidity is envisaged as well as decreasing width of the Mott lobes at strong coupling.
Using the functional integral formulation of a nonequilibrium quantum many-body theory we develop a regular description of a Fermi system with a strong attractive interaction in the presence of an external time-dependent potential. In the strong coupling limit this fermionic system is equivalent to a noequilibrium dilute Bose gas of diatomic molecules. We also consider a nonequilibrim strongly coupled Bardeen-Cooper-Schrieffer (BCS) theory and show that it reduces to the full nonlinear time-dependent Gross-Pitaevski (GP) equation, which determines an evolution of the condensate wave function.
We study the superfluid phases of quasi-2D atomic Fermi gases interacting via a p-wave Feshbach resonance. We calculate the absorption spectra of these phases under a hyperfine transition, for both non-rotating and rotating superfluids. We show that one can identify the different phases of the p-wave superfluid from the absorption spectrum. The absorption spectrum shows clear signatures of the existence of Majorana zero modes at the cores of vortices of the weakly-pairing $p_x+ip_y$ phase.
We study fermionic superfluidity in a boson-single-species-fermion cold atom mixture. We argue that apart from the standard p-wave fermion pairing mediated by the phonon field of the boson gas, the system also exhibits s-wave pairing with the anomalous correlator being an odd function of time or frequency. We show that such a superfluid phase can have a much higher transition temperature than the p-wave and may exist for sufficiently strong couplings between fermions and bosons. These conditions for odd-frequency pairing are favorable close to the value of the coupling at which the mixture pha…
A consistent microscopic theory for the response of strongly-coupled superfluid fermionic systems is formulated. After defining the response as a two-point two-fermion correlation function in the basis of the Bogolyubov's quasiparticles, the equation of motion (EOM) method is applied using the most general fermionic Hamiltonian with a bare two-body interaction, also transformed to the quasiparticle space. As a superfluid extension of the case of the normal phase, the resulting EOM is of the Bethe-Salpeter-Dyson form with the static and dynamical interaction kernels, where the former determines…
We investigate the Bose-Einstein condensation (BEC, superfluidity) of particle-hole pairs in ultracold Fermionic atoms with repulsive interactionsand arbitrary polarization, which are trapped within optical lattices. Near a Feshbach resonance, the dynamics of particle-hole pairs can be described by a hard-core Bose-Hubbard model. The insulator - superfluid and charge-density-wave (CDW) - superfluid phase transitions can be induced by decreasing and increasing the potential depths with controlling the trapping laser intensity, respectively. The parameter and polarization dependence of the criti…
We study a system of ultracold fermionic Potassium (40K) atoms in a three-dimensional optical lattice in the vicinity of an s-wave Feshbach resonance. Close to resonance, the system is described by a multi-band Bose-Fermi Hubbard Hamiltonian. We derive an effective lowest-band Hamiltonian in which the effect of the higher bands is incorporated by a self-consistent mean-field approximation. The resulting model is solved by means of Generalized Dynamical Mean-Field Theory. In addition to the BEC/BCS crossover we find a phase transition to a fermionic Mott insulator at half filling, induced by th…
In this paper we argue that the strongly coupled quark-gluon plasma can be considered as a chiral superfluid. The "normal" component of the fluid is the thermalized matter in common sense, while the "superfluid" part consists of long wavelength (chiral) fermionic states moving independently. We use several nonperturbative techniques to demonstrate that. First, we analyze the fermionic spectrum in the deconfinement phase (Tc < T < 2 Tc) using lattice (overlap) fermions and observe a gap between near-zero modes and the bulk of the spectrum. Second, we use the bosonization procedure with a finite…
