We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast to the unpolarized BEC which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the unpolarized superfluid favor the stabilization of a polarized superfluid phase.
Whether it occurs in superconductors, helium-3 or inside a neutron star, fermionic superfluidity requires pairing of fermions, particles with half-integer spin. For an equal mixture of two states of fermions ("spin up" and "spin down"), pairing can be complete and the entire system will become superfluid. When the two populations of fermions are unequal, not every particle can find a partner. Will the system nevertheless stay superfluid? Here we study this intriguing question in an unequal mixture of strongly interacting ultracold fermionic atoms. The superfluid region vs population imbalance …
We derive the underlying finite temperature theory which describes Fermi gas superfluidity with population imbalance in a homogeneous system. We compute the pair formation temperature and superfluid transition temperature $T_c$ and superfluid density in a manner consistent with the standard ground state equations, and thereby present a complete phase diagram. Finite temperature stabilizes superfluidity, as manifested by two solutions for $T_c$, or by low $T$ instabilities. At unitarity the polarized state is an ``intermediate temperature superfluid".
We study fermionic superfluidity in strongly anisotropic optical lattices with attractive interactions utilizing the cluster DMFT method, and focusing in particular on the role of non-local quantum fluctuations. We show that non-local quantum fluctuations impact the BCS superfluid transition dramatically. Moreover, we show that exotic superfluid states with delicate order parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase driven by spin population imbalance, can emerge even in the presence of such strong fluctuations.
We study the superfluid behavior of a population imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a one-dimensional (1D) optical lattice, using a pairing fluctuation theory. We show that, besides widespread pseudogap phenomena and intermediate temperature superfluidity, the superfluid phase is readily destroyed except in a limited region of the parameter space. We find a new mechanism for pair hopping, assisted by the excessive majority fermions, in the presence of continuum-lattice mixing, which leads to an unusual constant BEC asymptote for $T_c$ that is i…
Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in real space. By exploiting a BCS mean-field theory for the nearly-flat butterfly-bands regime of low magnetic-flux limit, here we reveal a number of unusual superfluid properties both in the ground state and at finite temperatures. Our thorough analysis includes but is not limited to the order parameter, condensate and superfluid fractions, and the critical BC…
We investigate the properties of entanglement in one-dimensional fermionic lattices at the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid regime. By analyzing occupation probabilities, which are concepts closely related to FFLO and entanglement, we obtain approximate analytical expressions for the spin-flip processes at the FFLO regime. We also apply density matrix renormalization group calculations to obtain the exact ground-state entanglement of the system in superfluid and non-superfluid regimes. Our results reveal a breaking pairs avalanche appearing precisely at the FFLO-normal phase …
The induced interaction among the majority spin species, due to the presence of the minority species, is computed for the case of a population-imbalanced resonantly-interacting Fermi gas. It is shown that this interaction leads to an instability, at low temperatures, of the recently observed polaron Fermi liquid phase of strongly imbalanced Fermi gases to a p-wave superfluid state. We find that the associated transition temperature, while quite small in the weakly interacting BCS regime, is experimentally accessible in the strongly interacting unitary regime.
In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of $T_\text{c}$. For large $d$ and/or small $t$, which yield an open Fer…
We theoretically study a possible new pairing mechanism for a two-dimensional population imbalanced Fermi gas with short-range repulsive interactions which can be realized on the upper branch of a Feshbach resonance. We use a well-controlled renormalization group approach, which allows an unbiased study of the instabilities of imbalanced Fermi liquid without assumption of a broken symmetry and gives a numerical calculation of the transition temperature from microscopic parameters. Our results show a leading superfluid instability in the p-wave channel for the majority species. The correspondin…
We analyze the finite-temperature phase diagram of the boson-fermion-Hubbard model with Feshbach converting interaction, using the coherent-state path-integral method. We show that depending on the position of the bosonic band, this type of interaction, even if weak, can drive the system into the resonant superfluid phase in the strong bosonic interaction limit. It turns out that this phase can exist for an arbitrary number of fermions (i.e., fermionic concentration between 0 and 2) but with the bosonic particle number very close to an integer value. We point out that the standard time-of-flig…
We study the zero temperature phase diagram of an imbalanced bilayer of dipolar fermions. We consider perpendicularly aligned identical dipoles in two layers and investigate the effect of population imbalance on the ground state phase at different layer spacings and average densities. The attractive part of the interlayer interaction could lead to the BEC-BCS crossover and the Fermi surface mismatch between two layers results in interesting uniform and nonuniform superfluid phases, which we have investigated here using the BCS mean-field theory together with the superfluid-mass density criteri…
We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the…
We investigate the one-dimensional Hubbard ring with attractive interaction in the presence of imbalanced spin populations by using the exact diagonalization method. The singlet pairing correlation function is found to show spatial oscillations with power-law decay as expected in the Fulde-Ferrell-Larkin-Ovchinnikov state of a Tomonaga-Luttinger liquid. In the strong coupling regime, the system shows an anomalous flux quantization of period h=4e, half of the superconducting flux quantum of h=2e, as recently predicted by mean-field analysis, together with various flux quanta smaller than h=4e. …
We study superconducting properties of population-imbalanced ultracold Fermi mixtures in the honeycomb lattice that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain ground state phase diagrams including some unconventional superconducting phases such as the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase. We show that this phase is characterized by atypical behaviour of the Cooper pairs total momentum in the external magnetic field. We show that the momentum changes its valu…
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.
The quantum dynamics of two-species bosons in an optical lattice is studied within the mean-field theory. The quantum coherence experiences periodical collapses and revivals, which depends on the relative strength of the inter-and intra-species interactions. The paired superfluidity and the counterflow superfluidity are identified and are verified by exact diagonaliztion in the two-site Hubbard model. We suggest a dynamical method of implementation and detection for the paired superfluid and the counterflow superfluidity in the optical lattices.
Singlet pairing in a Fermi superfluid is frustrated when the amounts of fermions of each pairing partner are unequal. The resulting `imbalanced superfluid' has been realized experimentally for ultracold atomic gases with s-wave interactions. Inspired by high-temperature superconductivity, we investigate the case of d-wave interactions, and find marked differences from the s-wave superfluid. Whereas s-wave imbalanced Fermi gases tend to phase separate in real space, in a balanced condensate and an imbalanced normal halo, we show that the d-wave gas can phase separate in reciprocal space so that…
We utilize the Hubbard model to demonstrate that doping of the antiferromagnetic parent compounds of cuprate superconductors stabilizes a spin liquid state. Superconductivity in such a state emerges due to the spin-orbit coupling between charge current and superfluidity of spinon condensate, resulting in a chiral relation between the order parameter phase gradient and supercurrent. We propose simple experimental tests for the presented mechanism.
We investigate the superfluid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic field. We analyze the temperature and magnetic field dependencies of the order parameter. We find that in the two-dimensional case, the spatially homogeneous spin polarized superfluidity ($SC(P\neq0)$) is stable in the weak coupling limit, at T=0, as opposed to the s-wave pairing symmetry case in 2D. We construct the ground state phase diagrams both for fixed chemical potential ($μ$) and electron concentration ($n$). Furthermore, we obtain the temperature vs. magnetic field…
We analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability region for uniform superfluidity when the lighter fermions are in excess. In addition, we find topological quantum phase transitions associated with the disappearance or appearance of momentum space …
We study the interplay between the Hofstadter butterfly, strong interactions and Zeeman field within the mean-field Bogoliubov-de Gennes theory in real space, and explore the ground states of the attractive single-band Hofstadter-Hubbard Hamiltonian on a square lattice, including the exotic possibility of imbalanced vector potentials. We find that the cooperation between the vector potential and superfluid order breaks the spatial symmetry of the system, and flourish stripe-ordered Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like superfluid and supersolid phases that can be distinguished and chara…
Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak-coupling, we find that the maximum mean field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence …
We study superfluidity of strongly repulsive fermionic atoms in optical lattices. The atoms are paired up through a correlated tunneling mechanism, which induces superfluidity when repulsive nearest-neighbor interactions are included in the Hubbard model. This paired superfluid is a metastable state which persists for a long time as the pair-broken process is severely suppressed. The mean-field phase diagram and low energy excitations are investigated in a square lattice system. Intriguingly, spontaneous superflows may appear in the ground state of a triangular optical lattice system due to an…
We study the occurrence of excitonic superfluidity in electron-hole bilayers at zero temperature. We not only identify the crossover in the phase diagram from the BCS limit of overlapping pairs to the BEC limit of non-overlapping tightly-bound pairs but also, by varying the electron and hole densities independently, we can analyze a number of phases that occur mainly in the crossover region. With different electron and hole effective masses, the phase diagram is asymmetric with respect to excess electron or hole densities. We propose as the criterion for the onset of superfluidity, the jump of…
We use microscopic Bogoliubov-de Gennes formalism to explore the ground-state phase diagram of the single-band attractive Hofstadter-Hubbard model on a square lattice. We show that the interplay between the Hofstadter butterfly and superfluidity breaks spatial symmetry, and gives rise to stripe-ordered superfluid and supersolid phases in large parameter spaces. We also discuss the effects of a trapping potential and comment on the viability of observing stripe-ordered phases with cold Fermi gases.
We present a pairing fluctuation theory which self-consistently incorporates finite momentum pair excitations in the context of BCS--Bose-Einstein condensation (BEC) crossover, and we apply this theory to high $T_c$ superconductors and ultracold Fermi gases. There are strong similarities between Fermi gases in the unitary regime and high Tc superconductors. Here we address key issues of common interest, especially the pseudogap. In the Fermi gases we summarize recent experiments including various phase diagrams (with and without population imbalance), as well as evidence for a pseudogap in the…
We study the zero temperature mean-field phase diagram of the Bose-Hubbard model in the presence of local coupling between the bosons and an external bath. We consider a coupling that conserves the on-site occupation number, preserving the robustness of the Mott and superfluid phases. We show that the coupling to the bath renormalizes the chemical potential and the interaction between the bosons and reduces the size of the superfluid regions between the insulating lobes. For strong enough coupling, a finite value of hopping is required to obtain superfluidity around the degeneracy points where…
We show that a nearest-neighbor singlet phase results (from an effective Hamiltonian) for the one-dimensional Hubbard-Holstein model in the regime of strong electron-electron and electron-phonon interactions and under non-adiabatic conditions ($t/ω_0 \leq 1$). By mapping the system of nearest-neighbor singlets at a filling $N_p/N$ onto a hard-core-boson (HCB) $t$-$V$ model at a filling $N_p/(N-N_p)$, we demonstrate explicitly that superfluidity and charge-density-wave (CDW) occur mutually exclusively with the diagonal long range order manifesting itself only at one-third filling. Furthermore, …
We determine the critical Zeeman energy splitting for Fermi superfluidity at infinite s-wave scattering length according to the Monte Carlo and experimental results of the equations of state. Based on the universality hypothesis, we show that there exist two critical fields $H_{c1}$ and $H_{c2}$, between which a superfluid-normal mixed phase is energetically favored, and model-independent formulae for $H_{c1}$, $H_{c2}$ and the critical population imbalance $P_c$ are derived. Using recent Monte Carlo and experimental results of $P_c$, $H_{c1}$ and $H_{c2}$ are determined. It is found $H_{c1}=0…
We present a study of the attractive Hubbard model based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). For this study the NRG method is extended to deal with self-consistent solutions of effective impurity models with superconducting symmetry breaking. We give details of this extension and validate our calculations with DMFT results with antiferromagnetic ordering. We also present results for static and integrated quantities for different filling factors in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. We study the ev…
We analyze the evolution of two-band superfluidity from the weak coupling Bardeen-Cooper-Schrieffer (BCS) to the strong coupling Bose-Einstein condensation (BEC) limit. When the interband interaction is tuned from negative to positive values, a quantum phase transition occurs from a 0-phase to a $π$-phase state, depending on the relative phase of two order parameters. Furthermore, population imbalances between the two bands can be created by tuning the intraband or interband interactions. We also find two undamped low energy collective excitations corresponding to in-phase and out-of-phase mod…
We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the superconducting state in free space, as well as on the lattice in the framework of the Fermi-gas model with hard-core repulsion, the Hubbard model, the Shubin-Vonsovsky model, and the $t-J$ model. We demonstrate that the critical superconducting temperature can be greatly increased in the spin-polarized case or in a two-band situation already at low densities. The…
Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction, while one component is confined on a one-dimensional (1D) optical lattice whereas the other is in a homogeneous 3D continuum. We study the phase diagram and the pseudogap phenomena throughout the entire BCS-BEC crossover, using a pairing fluctuation t…
The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough th…
Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Mueller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-Tc superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wave-function. In this review article, we revisit the Hub…
We explore novel features of a nonrelativistic fermionic superfluid in which the pairing interaction includes a contribution from the exchange of a dynamical bosonic mode. We show that the dynamical boson exchange (DBE), which causes a retarded pairing interaction and thus violates the Galilean invariance of the fermion sector, generically leads to a quantum reduction of the superfluid density and hence a nonzero normal fraction even at zero temperature. For spin-singlet pairing, the DBE also leads to a nonvanishing spin susceptibility at zero temperature, providing a mechanism for the coexist…
Superfluidity in atomic Fermi gases with population imbalance has recently become an exciting research focus. There is considerable disagreement in the literature about the appropriate stability conditions for states in the phase diagram throughout the BCS to Bose-Einstein condensation (BEC) crossover. Here we discuss these stability conditions for homogeneous polarized superfluid phases, and compare with recent alternative proposals. The requirement of a positive second order partial derivative of the thermodynamic potential with respect to the fermionic excitation gap $Δ$ (at fixed chemical …
The superfluid properties of a two-state Fermi mixture in an optical lattice are profoundly modified when an imbalance in the population of the two states is present.We present analytical solutions for the free energy, and for the gap and number equations in the saddle-point approximation describing resonant superfluidity in the quasi-two-dimensional gas. Inhomogeneities due to the trapping potentials can be taken into account using the local density approximation. Analyzing the free energy in this approximation, we find that phase separation occurs in the layers. The phase diagram of the supe…
Larkin-Ovchinnikov (LO) state which combines the superfluidity and spatial periodicity of pairing order parameter and exhibits the supersolid properties has been attracting intense attention in both condensed matter physics and ultracold atoms. Conventionally, realization of LO state from an intrinsic s-wave interacting system necessitates to break the time-reversal (TR) and sometimes spatial-inversion (SI) symmetries. Here we report a novel prediction that the LO state can be realized in a TR and SI symmetric system representing a bilayer Fermi gas subjected to a laserassisted interlayer tunn…
We study the effects of dipole interaction on the superfluidity in a homogeneous Fermi gas with population imbalance. We show that the Larkin-Ovchinnikov-Fulde-Ferrell phase is replaced by another nonuniform superfluid phase, in which the order parameter has a nonzero triplet component induced by the dipole interaction.
We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) with increasing attraction, in the presence of the Zeeman magnetic field ($h$) for $d=2$, within the spin-polarized attractive Hubbard model. The broken symmetry Hartree approximation {as well as the} strong coupling expansion are used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. For spin independent hopping integrals ($t^{\uparrow}=t^{\downarrow}$), we find no stable homogeneous polarized superfluid (SC$_M$) stat…
Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here, we provide a general result for the superfluid weight $D_{\rm s}$ of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number $C$. We find that the integral over the Brillouin zone of the quantum metric, an invariant calculated from the Bloch functions, …
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 …
Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位束设施）；Department of Physics and Astronomy, Michigan State University（密歇根州立大学物理与天文学系）；TRIUMF（特利安夫实验室）；Department of Physics, University of Guelph（圭尔夫大学物理系）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）；Department of Physics, Arizona State University（亚利桑那州立大学物理系）；Department of Physics and Quantum Theory Project, University of Florida（佛罗里达大学物理与量子理论项目）
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…
Based on consideration of the system symmetry and its Hilbert space, we show that strongly interacting fermions in an optical lattice or superlattice can be generically described by a lattice resonance Hamiltonian. The latter can be mapped to a general Hubbard model with particle assisted tunneling rates. We investigate the model under population imbalance and show the attractive and the repulsive models have the same complexity in phase diagram under the particle-hole mapping. Using this mapping, we propose an experimental method to detect possible exotic superfluid/magnetic phases for this s…
Fermionic superfluidity in atomic Fermi gases across a Feshbach resonance is normally described by the atom-molecule theory, which treats the closed channel as a noninteracting point boson. In this work we present a theoretical description of the resonant superfluidity in analogy to the two-band superconductors. We employ the underlying two-channel scattering model of Feshbach resonance where the closed channel is treated as a composite boson with binding energy $\varepsilon_0$ and the resonance is triggered by the microscopic interchannel coupling $U_{12}$. The binding energy $\varepsilon_0$ …
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 m…
In this paper, we study a system of two-component Bose gas in an artificial magnetic field trapped by concentric harmonic and annular potentials, respectively. The system is realized by gases with two-internal states like the hyperfine states of $^{87}$Rb. We are interested in effects of a Rabi oscillation between them. Two-component Bose Hubbard model is introduced to describe the system, and Gross-Pitaevskii equations are used to study the system. We first study the Bose gas system in the annular trap by varying the width of the annulus and strength of the magnetic field, in particular, we f…
