We develop an accurate theory of resonantly interacting Fermi mixtures with both spin and mass imbalance. We consider Fermi mixtures with arbitrary mass imbalances but focus, in particular, on the experimentally available $^{6}\mathrm{Li}$-$^{40}\mathrm{K}$ mixture. We determine the phase diagram of the mixture for different interactions strengths that lie on the BCS side of the Feshbach resonance. We also determine the universal phase diagram at unitarity. We find, for the mixtures with a sufficiently large mass imbalance, which includes the $^{6}\mathrm{Li}$-$^{40}\mathrm{K}$ mixture, a Lifshitz point in the universal phase diagram that signals an instability toward a supersolid phase.
We develop an accurate theory of resonantly interacting Fermi mixtures with both spin and mass imbalance. We consider Fermi mixtures with arbitrary mass imbalances but focus, in particular, on the experimentally available 6Li-40K mixture. We determine the phase diagram of the mixture for different interactions strengths that lie on the BCS side of the Feshbach resonance. We also determine the universal phase diagram at unitarity. We find, for the mixtures with a sufficiently large mass imbalance, which includes the 6Li-40K mixture, a Lifshitz point in the universal phase diagram that signals an instability toward a supersolid phase.
In this thesis, we study two-component Fermi mixtures in the presence of both a mass and a population imbalance. For a large part we focus on the experimentally available 6Li-40K mixture and on the phase transitions that can occur in this mixture. In the first part of this thesis, we study the extremely polarized two-component Fermi gas with a mass imbalance in the strongly interacting regime. Specifically, we focus on the mixture of 6Li and 40K atoms. In this interaction regime spin polarons, i.e., dressed minority atoms, form. We consider the spectral function for the minority atoms, from which the lifetime and the effective mass of the spin polaron can be determined. Moreover, we predict the radio-frequency spectrum and the momentum distribution for the spin polarons for experiments with 6Li and 40K atoms. Subsequently we study the relaxation of the motion of the Fermi polaron due to spin drag. In the second part, we develop an accurate theory of resonantly interacting Fermi mixtures with both spin and mass imbalance. We consider Fermi mixtures with arbitrary mass imbalances, but focus in particular on the 6Li-40K mixture. We determine the phase diagram of the mixture for different interaction strengths that lie on the BCS side of the Feshbach resonance. We also determine the universal phase diagram at unitarity. We find for the mixtures with a sufficiently large mass imbalance, that includes the 6Li-40K mixture, a Lifshitz point in the universal phase diagram that signals an instability towards a supersolid phase. In the last part of the thesis, we show that the ultracold three-dimensional 6Li-40K mixture at unitarity can exhibit the highly exotic Larkin-Ovchinnikov superfluid phase. We determine the phase diagram for majorities of 40K atoms within mean-field theory taking the inhomogeneities of the fermion states into account exactly. We find two different inhomogeneous superfluid phases in mixtures with a majority of 40K atoms, namely the Larkin-Ovchinnikov (LO) phase with one inhomogeneous direction and a cubic phase (LO3) where three spatial translational symmetries are broken. We determine the transition between these two phases by solving the Bogoliubov-de Gennes equations in the superfluid LO phase. Subsequently, we calculate the atomic density modulation of the atoms in the LO phase and show that it is sufficiently large to be visible in experiment.
We consider a strongly interacting 6Li-40K mixture, which is imbalanced both in the masses and the densities of the two fermionic species. At present, it is the experimentalist's favorite for reaching the superfluid regime. We construct an effective thermodynamic potential that leads to excellent agreement with Monte Carlo results for the normal state. We use it to determine the universal phase diagram of the mixture in the unitarity limit, where we find, in contrast to the mass-balanced case, the presence of a Lifshitz point. This point is characterized by the effective mass of the Cooper pairs becoming negative, which signals an instability towards a supersolid phase.
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 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 a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. By using many-body diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced mixture 87Rb-40K for different values of the density imbalance. We then analyze the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation, the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.
We present phase diagrams for population-imbalanced, trapped Fermi superfluids near unitarity. In addition to providing quantitative values for the superfluid transition temperature, the pairing onset temperature, and the transition line (separating the Sarma and phase separation regimes), we study experimental signatures of these transitions based on density profiles and density differences at the center. Predictions on the BCS side of resonance show unexpected behavior, which should be searched for experimentally.