Population-imbalanced Fermi Research Articles

Radial Fulde-Ferrell-Larkin-Ovchinnikov-like state in a population-imbalanced Fermi gas

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 at $T=0$ in contrast to the conventional case without a vortex. We show that this inhomogeneous superfluidity can be detected as peak structures of the local polarization rate associated with the node structure of the superfluid order parameter. Since the vortex in the 3D Fermi gas with population imbalance has been already realized in experiments, our proposal is a promising candidate of the FFLO state in cold atom physics.

Shear Viscosity of Uniform Fermi Gases with Population Imbalance

The shear viscosity has been an important topic in ultracold Fermi gases, and it has served as a diagnostic of various theories. Due to the complicated phase structures of population-imbalanced (polarized) Fermi gases with tunable attraction, past works on the shear viscosity mainly focused on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi superfluid at finite temperatures by a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. The Cooper pairs lead to the anomalous shear viscosity analogous to the shear viscosity. We derive an exact relation connecting certain thermodynamic quantities and transport coefficients at the mean-field level for polarized unitary Fermi superfluids. An approximate relation beyond mean-field is proposed and only exhibits mild deviations from our numerical results. In the unitary and Bose-Einstein condensation (BEC) regimes, the total shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. Moreover, competition among the excess fermions, noncondensed pairs, and fermionic quasiparticles may lead to non-monotonic behavior of the ratio between the shear viscosity and relaxation time as the polarization increases.

Exotic superfluidity and pairing phenomena in atomic Fermi gases in mixed dimensions

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 theory. We find that the effective dimensionality of the non-interacting lattice component can evolve from quasi-3D to quasi-1D, leading to strong Fermi surface mismatch. Upon pairing, the system becomes effectively quasi-two dimensional in the BEC regime. The behavior of Tc bears similarity to that of a regular 3D population imbalanced Fermi gas, but with a more drastic departure from the regular 3D balanced case, featuring both intermediate temperature superfluidity and possible pair density wave ground state. Unlike a simple 1D optical lattice case, Tc in the mixed dimensions has a constant BEC asymptote.

Pairing in a two-dimensional Fermi gas with population imbalance

Pairing in a population imbalanced Fermi system in a two-dimensional optical lattice is studied using Determinant Quantum Monte Carlo (DQMC) simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovshinnikov (FFLO) phase. Contrary to claims of fragility with increased dimensionality we find that this phase is stable across wide range of values for the polarization, temperature and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center of mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels which can be seen as the analog of the finite center of mass momentum pairing in the translationally invariant case. Finally, we perform mean field calculations for the uniform and confined systems and show the results to be in good agreement with QMC. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.

Imbalanced ultracold Fermi gas in the weakly repulsive regime: Renormalization-group approach forp-wave superfluidity

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 corresponding mechanism is that there are effective attractive interactions for the majority species, induced by the particle-hole susceptibility of the minority species, where the mismatch of the Fermi surfaces of the two species plays an important role. We also propose an experimental protocol for detecting the p-wave superfluidity and discuss the corresponding experimental signatures.

Probing the homogeneous spectral function of a strongly interacting superfluid atomic Fermi gas in a trap using phase separation and momentum-resolved radio-frequency spectroscopy

It is of central importance to probe the \emph{local} spectral function $A(\mathbf{k},\omega)$ of a strongly interacting Fermi gas in a trap. Momentum resolved rf spectroscopy has been demonstrated to be able to probe the trap averaged $A(\mathbf{k},\omega)$. However, the usefulness of this technique was limited by the trap inhomogeneity. Independent of a specific theory, here we propose that by studying the momentum resolved rf spectra of the minority fermions of a phase separated, population imbalanced Fermi gas at low temperature, one can effectively extract $A(\mathbf{k},\omega)$ of a homogeneous superfluid Fermi gas (at the trap center). In support, we present calculated spectral functions and spectral intensity maps for various cases from BCS through BEC regimes using different theories.

Stability of Spin-Orbit Coupled Fermi Gases with Population Imbalance

We use the self-consistent mean-field theory to analyze the effects of Rashba-type spin-orbit coupling (SOC) on the ground-state phase diagram of population-imbalanced Fermi gases throughout the BCS-Bose-Einstein condensate evolution. We find that the SOC and population imbalance are counteracting, and that this competition tends to stabilize the uniform superfluid phase against the phase separation. However, we also show that the SOC stabilizes (destabilizes) the uniform superfluid phase against the normal phase for low (high) population imbalances. In addition, we find topological quantum phase transitions associated with the appearance of momentum-space regions with zero quasiparticle energies, and study their signatures in the momentum distribution.

Ground states and dynamics of population-imbalanced Fermi condensates in one dimension

By using the numerically exact density-matrix renormalization group (DMRG) approach, we investigate the ground states of harmonically trapped one-dimensional (1D) fermions with population imbalance and find that the Larkin–Ovchinnikov (LO) state, which is a condensed state of fermion pairs with nonzero center-of-mass momentum, is realized for a wide range of parameters. The phase diagram comprising the two phases of (i) an LO state at the trap center and a balanced condensate at the periphery and (ii) an LO state at the trap center and a pure majority component at the periphery is obtained. The reduced two-body density matrix indicates that most of the minority atoms contribute to the LO-type quasi-condensate. With the time-dependent DMRG, we also investigate the real-time dynamics of a system of 1D fermions in response to a spin-flip excitation.

Superfluid transition temperature in a dilute Bose–Fermi mixture with imbalanced two-component Fermi gas

We study s- and p-wave pairing of population imbalanced Fermi atoms in a dilute Bose–Fermi mixture. s-wave pairing takes place only between atoms of different spins, while p-wave Cooper pair is formed by atoms in the same spin component. We calculate the transition temperature of this system in the presence of all interactions between two-spin states. The effective interaction between two-spin states is the sum of the direct one g FF , the one arising from polarization of the bosonic medium g FBF and that due to polarization of the fermionic medium itself g FFF . The p-wave channel can exist due to polarization of the bosonic medium with the effective attractive interaction and we estimate of the transition temperature increase due to this effect.

Population imbalanced Fermi gases in quasi two dimensions

We study s-wave pairing of population imbalanced Fermi atoms in quasi two dimensions using a mean-field theory. At zero temperature, we map out the phase diagram in the entire Bardeen, Cooper and Schrieffer–Bose–Einstein condensation (BCS–BEC) crossover region by investigating the effect of weak atom tunnelling between layers. We find that the superfluid phase stabilizes as one decreases the atom tunnelling between layers. This allows one to control the superfluid–normal first-order phase transition by tuning a single experimental parameter. Further, we find that a tunnelling induced polarized superfluid phase appears in a narrow parameter region in the BEC regime. At finite temperatures, we use a Landau–Ginzberg functional approach to investigate the possibility of a spatially inhomogeneous Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) phase in the weakly interacting BCS limit near the tricritical point of spatially homogenous superfluid, FFLO and normal phases. We find that the normal–FFLO phase transition is the first-order transition as opposed to the continuous transition predicted in zero-temperature theories.

Determination of the equation of state of a polarized Fermi gas at unitarity

We report on the measurement of the equation of state of a two-component Fermi gas of $^{6}\mathrm{Li}$ atoms with resonant interactions. By analyzing the in situ density distributions of a population-imbalanced Fermi mixture reported in a recent experiment [Y. Shin et al., Nature 451, 689 (2008)], we determine the energy density of a resonantly interacting Fermi gas as a function of the densities of the two components. We present a method to determine the equation of state directly from the shape of the trapped cloud, where the fully polarized, noninteracting ideal Fermi gas in the outer region provides the absolute calibration of particle density. From the density profiles obtained at the lowest temperature, we estimate the zero-temperature equation of state.

Radio-frequency spectroscopy of trapped Fermi gases with population imbalance

Motivated by recent experiments, we address the behavior and evolution of radio-frequency (RF) spectra as temperature and polarization are varied in population-imbalanced Fermi gases from above to below ${T}_{c}$. We discuss a series of scenarios for the experimentally observed zero-temperature pseudogap phase and show how present and future RF experiments may help in its elucidation. We conclude that the experiments of Zwierlein and co-workers at the lowest $T$ may well reflect ground-state properties, but take issue with their claim that the pairing gap survives up to temperatures of the order of the degeneracy temperature ${T}_{F}$ at unitarity.