We theoretically study a possible 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.
We theoretically study a possible 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.
The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet s-wave pairing, we find that, in the strongly imbalanced regime, the induced intraspecies interaction leads to p-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi-liquid state in this regime is unstable to p-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. We present possible experimental signatures of the p-wave state using radiofrequency spectroscopy as well as density-density correlations after free expansion.
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.
Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at qc inversely proportional to the characteristic length scale in real space, the soft-core radius rc. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with superfluid and density wave orders due to the interplay of the Fermi momentum pF, interaction range rc, and interaction strength u0. For repulsive bare interactions u0>0, the dominant instability is a f-wave superfluid for ${p}_{F}{r}_{c}\ensuremath{\lesssim}2$ and a density wave for ${p}_{F}{r}_{c}\ensuremath{\gtrsim}4$. The f-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism but has a much higher Tc. For attractive bare interactions u0<0, the leading instability is p-wave pairing. The phase diagram is obtained from a functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on an equal footing.
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:
We consider ultracold imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mixtures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species. In both cases, the number of atoms for each component is allowed to be different, leading to a spin imbalance or a polarization. In the second case, the two different species also give rise to a mass imbalance for the particles. Imbalanced Fermi mixtures play a fundamental role in condensed-matter, nuclear and astroparticle physics. Experimentally, the atomic mixtures are made strongly interacting with the use of two-channel Feshbach resonances. We start out by treating these in more detail. We review the relevant scattering theory, and apply it to the well-studied case of resonant s-wave collisions with zero angular momentum. Furthermore, we discuss the less-studied case of p-wave collisions with nonzero angular momentum, and the inhomogeneous case due to a trapping potential. Having discussed the two-body physics, we turn to the many-body physics. The pioneering experimental studies of Cooper pairing in lithium-6 mixtures with a spin imbalance were performed by Zwierlein et al. [Science 311, 492 (2006)] and Partridge et al. [Science 311, 503 (2006)]. We study the mean-field theory for the polarized Fermi mixture to obtain a qualitative understanding of these experiments. In the unitarity limit, where the scattering length of the interatomic interaction diverges, the theory gives rise to two exotic superfluid phases that are absent in the balanced mixture. These are the gapless superfluid Sarma phase and the phase-separated phase. By using renormalization group techniques to account for the effects of strong interactions, we obtain also quantitative agreement with Monte-Carlo calculations and experiments. We then generalize our knowledge of the solely spin-imbalanced mixture to the mass-imbalanced case, where in particular the mixture consisting of lithium-6 and potassium-40 is experimentally promising. We study the mean-field phase diagram for this mixture in the unitarity limit, where we not only find phase separation and Sarma superfluidity, but also a Lifshitz point. The latter signals an instability towards a supersolid phase. We also include the effects of fluctuations, which do not alter the topology of the phase diagram. However, fluctuation effects lower the critical temperatures with an experimentally relevant factor of three. Finally, we study superfluidity in a fully polarized gas of potassium-40 atoms near a p-wave Feshbach resonance. In particular, we consider coherent Josephson oscillations between the superfluid components in the two channels of the resonance, whose frequencies contain a clear signature of the quantum phase transition that occurs as a function of applied magnetic field.
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.