We present a numerical study of the one-dimensional BCS-BEC crossover of a spin-imbalanced Fermi gas. The crossover is described by the Bose-Fermi resonance model in a real space representation. Our main interest is in the behavior of the pair correlations, which, in the BCS limit, are of the Fulde-Ferrell-Larkin-Ovchinnikov type, while in the BEC limit, a superfluid of diatomic molecules forms that exhibits quasi-condensation at zero momentum. We use the density matrix renormalization group method to compute the phase diagram as a function of the detuning of the molecular level and the polarization. As a main result, we show that FFLO-like correlations disappear well below full polarization close to the resonance. The critical polarization depends on both the detuning and the filling.
We study the effect of high population imbalance in the two dimensional attractive Hubbard model, in the coupling regime corresponding to BCS-BEC crossover, and focus on thermal effects on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Using a method that retains all the classical thermal fluctuations on the FFLO state we estimate a very low $T_c$ and infer a strongly first order normal state to FFLO transition. The $T_c$ is an order of magnitude below the mean field estimate. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into th…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with non-zero total momentum Cooper pairs in a strong magnetic field, was predicted more than 50 years ago and now becomes an important concept in many branches of physics. However, no unambiguous experimental evidences for the existence of FFLO phases have been observed yet. Recently, spin-imbalanced ultracold degenerate Fermi gases have emerged as a new powerful platform for the observation of FFLO phases due to their high experimental controllability and the lack of disorder. However, in three dimensional degenerate …
We study the phase diagram of a two-dimensional ultracold Fermi gas with the synthetic spin-orbit coupling (SOC) that has recently been realized at NIST. Due to the coexistence of anisotropic SOC and effective Zeeman fields in the NIST scheme, the system shows rich structure of phase separation involving exotic gapless superfluid and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states with different center-of-mass momentum. In particular, we characterize the stability region of FFLO states and demonstrate their unique features under SOC. We then show that the effective transverse Zeeman fie…
We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the $ab$ plane. At low temperatures, the upper critical field $μ_0 H_{c2}^{ab}$ shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at $μ_0 H^{\ast}\approx 24$ T well below $μ_0 H_{c2}^{ab}$, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes…
We study s-wave superconductivity in the two dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via Monte Carlo. The method requires iterative solution of the Bogoliubov-de-Gennes (BdG) equations for amplitude and phase fluctuating configurations of the pairing field. We establish the full thermal phase diagram …
We examine the existence and characteristics of the exotic Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in a one-dimensional Fermi gas with attractive Hubbard interactions, in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that a robust FFLO phase can be created in the presence of attractive on-site interactions and Zeeman field, and that the addition of SOC suppresses the FFLO order and enhances the pair formation. In absence of SOC, the system shows four phases: Bardeen-Cooper-Schrieffer (BCS), FFLO, multi- mode pairing and fully polarized phases by tuning the Zeeman fie…
Increasing the spin imbalance in superconductors can spatially modulate the gap by forming Cooper pairs with finite momentum. For large imbalances compared to the Fermi energy, the inhomogeneous FFLO superconductor ultimately becomes a normal metal. There is mounting experimental evidence for this scenario in 2D organic superconductors in large in-plane magnetic fields; this is complemented by ongoing efforts to realize this scenario in coupled tubes of atomic Fermi gases with spin imbalance. Yet, a theory for the phase transition from a metal to an FFLO superconductor has not been developed s…
Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent opportunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of great interest in condensed matter physics. However, the FFLO states have not been observed experimentally in Fermi gases in three dimensions (3D), possibly due to their small phase space volume and extremely low temperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainly in a $^6$Li--$^{40}$K mixture, on the one-plane-wave FFLO phases for a 3D ho…
We consider the quasi-one dimensional system realized by an array of weakly coupled parallel one-dimensional "tubes" in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin orbit coupling (SOC), and an s-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (T=0) Bogoliubov-de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes, and show that the T=0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov …
We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional (1D) optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model (AHM) in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground state phase diagrams including some unconventional superconducting phases such as the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase, and the $η$ phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. I…
The possibility of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a population imbalanced Fermi gas with a vortex is proposed. Employing the Bogoliubov-de-Gennes formalism we self-consistently determine the superfluid order parameter and the particle number density in the presence of a vortex. We find that as increasing population imbalance, the superfluid order parameter spatially oscillates around the vortex core in the radial direction, indicating that the FFLO state becomes stable. We find that the radial FFLO states cover a wide region of the phase diagram in the weak-coupling regime …
The evolution of an attractive polarized two-component Fermi gas at zero temperature is analyzed as its polarization is progressively decreased, from full polarization (corresponding to the polaronic limit) down to a critical polarization when superfluidity sets in. This critical polarization and the nature of the associated superfluid instability are determined within a fully self-consistent $t$-matrix approach implemented exactly at zero temperature. In this way, the polarization-vs-coupling phase diagram at zero temperature is constructed throughout the whole BCS-BEC crossover. Depending on…
In three dimensional Fermi gases with spin imbalance, a competition exists between Cooper pairing with zero and with finite momentum. The latter gives rise to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase, which only exists in a restricted area of the phase diagram as a function of chemical potential imbalance and interaction strength. Applying an optical potential along one direction enhances the FFLO region in this phase diagram. In this paper, we construct the phase diagram as a function of polarization and interaction strength in order to study the competition between the FF…
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 unde…
Using the time-dependent density matrix renormalization group method and exact diagonalization, we study the non-equilibrium dynamics of the one-dimensional Fermi-Hubbard model following a quantum quench or a ramp of the onsite interaction strength. For quenches from the non-interacting to the attractive regime, we investigate the dynamical emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which at finite spin polarizations are the dominant two-body correlations in the ground state, and their signatures in the pair quasi-momentum distribution function. We observe that the post…
We study the attractive Hubbard model with spin imbalance on two lattices featuring a flat band: the Lieb and kagome lattices. We present mean-field phase diagrams featuring exotic superfluid phases, similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose stability is confirmed by dynamical mean-field theory (DMFT). The nature of the pairing is found to be richer than just the Fermi surface shift responsible for the usual FFLO state. The presence of a flat band allows for changes in the particle momentum distributions at null energy cost. This facilitates formation of nontrivial su…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with non-zero total momentum Cooper pairs in a large magnetic field, was first predicted about 50 years ago, and since then became an important concept in many branches of physics. Despite intensive search in various materials, unambiguous experimental evidence for the FFLO phase is still lacking in experiments. In this paper, we show that both FF (uniform order parameter with plane-wave phase) and LO phase (spatially varying order parameter amplitude) can be observed using fermionic cold atoms in spin-orbit coupled opt…
We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the non-equilibrium steady state, being coupled with two fermion baths. By developing a non-equilibrium strong-coupling theory based on the combined $T$-matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the …
We present an overview of recent developments in species-imbalanced ("polarized") Feshbach-resonant Fermi gases. We summarize the current status of thermodynamics of these systems in terms of a phase diagram as a function of the Feshbach resonance detuning, polarization and temperature. We review instabilities of the s-wave superfluidity across the BEC-BCS crossover to phase separation, FFLO states, polarized molecular superfluidity and the normal state, driven by the species imbalance. We discuss different models and approximations of this system and compare their predictions to current exper…
We calculate the pair correlation function and the order parameter correlation function, which probe, respectively, the intra-pair and inter-pair correlations of a Fermi gas with attractive inter-particle interaction, in terms of a diagrammatic approach as a function of coupling throughout the BCS-BEC crossover and of temperature, both in the superfluid and normal phase across the critical temperature $T_{c}$. Several physical quantities are obtained from this calculation, including the pair coherence and healing lengths, the Tan's contact, the crossover temperature $T^{*}$ below which inter-p…
We study mixtures of a population-imbalanced strongly-interacting Fermi gas and of a Bose-Einstein condensed gas at zero temperature. In the homogeneous case, we find that the Chandrasekhar-Clogston critical polarization for the onset of instability of Fermi superfluidity is enhanced due to the interaction with the bosons. Predictions for the critical polarization are also given in the trapped case, with a special focus to the situation of equal Fermi-Bose and Bose-Bose coupling constants, where the density of fermions becomes flat in the center of the trap. This regime can be realized experim…
We study the persistent currents of an attractive Fermi gas confined in a tightly-confining ring trap and subjected to an artificial gauge field all through the BCS-BEC crossover. At weak attractions, on the BCS side, fermions display a parity effect in the persistent currents, ie their response to the gauge field is paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on the BEC side of the crossover we find a doubling of the periodicity of the ground-state energy as a function of the artificial gauge field and disappearance of the parity effect, indicati…
We study the influence of population imbalance on the pairing, spin, and density instabilities of a two component ideal Fermi gas after a sudden quench of interactions near a Feshbach resonance. Over a large region of parameters the pairing instability is dominated by finite momentum pairing, suggesting the possibility of observing FFLO-like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the BCS side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the BEC side of the resonance, the pairing ins…
We study the mass imbalanced Fermi-Fermi mixture within the framework of a two-dimensional lattice fermion model. Based on the thermodynamic and species dependent quasiparticle behavior we map out the finite temperature phase diagram of this system and show that unlike the balanced Fermi superfluid there are now two different pseudogap regimes as PG-I and PG-II. While within the PG-I regime both the fermionic species are pseudogapped, PG-II corresponds to the regime where pseudogap feature survives only in the light species. We believe that the single particle spectral features that we discuss…
We analyze the BCS-BEC crossover for a Fermi gas made of neutral atoms in three hyperfine states with a SU(3) invariant attractive interaction. By solving the extended BCS equations for the total number of particles and the pairing gap, we calculate at zero temperature the pairing gap, the population imbalance, the condensate fraction and the first sound velocity of the uniform system as a function of the interaction strength in both three and two dimensions. Contrary to the three-dimensional case, in two dimensions the condensate fraction approaches the value 1 only for an extremely large int…
Twodimensional spin-orbit-coupled Fermi gases subject to s-wave pairing can be driven into a topological phase by increasing the Zeeman spin splitting beyond a critical value. In the topological phase, the system exhibits the hallmarks of chiral p-wave superfluidity, including exotic Majorana excitations. Previous theoretical studies of this realization of a twodimensional topological Fermi superfluid have focused on the BCS regime where the s-wave Cooper pairs are only weakly bound and, hence, the induced chiral p-wave order parameter has a small magnitude. Motivated by the goal to identify p…
We analyze the effects of in- and out-of-plane Zeeman fields on the BCS-BEC evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves novel gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly-degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly-degenerate circles, …
In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. We find that quasi-condensation mirrors Berezinskii-Kosterlitz-Thouless behavior in many ways, including the emergence of a strong zero momentum peak in the pair momentum distribution. Importantly, the disappearance of this quasi-condensate occurs at a reasonably well defined crossover temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible wit…
We use the Bogoliubov-de Gennes formalism to analyze harmonically trapped Fermi gases with Rashba-type spin-orbit coupling in two dimensions. We consider both population-balanced and -imbalanced Fermi gases throughout the BCS-BEC evolution, and study the effects of spin-orbit coupling on the spontaneously induced countercirculating mass currents and the associated intrinsic angular momentum. In particular, we find that even a small spin-orbit coupling destabilizes Fulde-Ferrel-Larkin-Ovchinnikov (FFLO)-type spatially modulated superfluid phases as well as the phase-separated states against the…
We study the superfluid state of two-species heteronuclear Fermi gases with isotropic contact and anisotropic long-range dipolar interactions. By explicitly taking account of Fock exchange contribution, we derive self-consistent equations describing the pairing states in the system. Exploiting the symmetry of the system, we developed an efficient way of solving the self-consistent equations by exploiting the symmetries. We find that the temperature tends to increase the anisotropy of the pairing state, which is rather counterintuitive. We study the anisotropic properties of the system by exami…
Ultracold fermionic gases in optical lattices give a great opportunity for creating different types of novel states. One of them is phase separation induced by a trapping potential between different types of superfluid phases. The core-shell structures, occurring in systems with a trapping potential, are a good example of such separations. The types and the sequences of phases which emerge in such structures can depend on spin-imbalance, shape of the trap and on-site interaction strength. In this work, we investigate the properties of such structures within an attractive Fermi gas loaded in th…
