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 Bose–Einstein condensation-to-Bardeen–Cooper–Schrieffer crossover to phase separation, Fulde–Ferrell–Larkin–Ovchinnikov 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 with current experiments.
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 Bose–Einstein condensation-to-Bardeen–Cooper–Schrieffer crossover to phase separation, Fulde–Ferrell–Larkin–Ovchinnikov 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 with current experiments.
We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words:
The study of ultracold atomic Fermi gases is a rapidly exploding subject which is defining new directions in condensed matter and atomic physics. Quite generally what makes these gases so important is their remarkable tunability and controllability. Using a Feshbach resonance one can tune the attractive two-body interactions from weak to strong and thereby make a smooth crossover from a BCS superfluid of Cooper pairs to a Bose-Einstein condensed superfluid. Furthermore, one can tune the population of the two spin states, allowing observation of exotic spin-polarized superfluids, such as the Fulde Ferrell Larkin Ovchinnikov (FFLO) phase. A wide array of powerful characterization tools, which often have direct condensed matter analogues, are available to the experimenter. In this Chapter, we present a general review of the status of these Fermi gases with the aim of communicating the excitement and great potential of the field.
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.
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 Fulde-Ferrell-Larkin-Ovchinnikov--like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the Bardeen-Cooper-Schrieffer side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the Bose-Einstein-condensate side of the resonance, the pairing instability is present for scattering lengths larger than a critical value that is only weakly dependent on population imbalance and always smaller than the scattering length at which the Stoner-like spin instability occurs.