We study mass-imbalanced two-component Fermi mixtures, where one of the components consists of dipolar fermions. We specifically study the mass imbalances corresponding to the atomic ${}^{163}$Dy-${}^{40}$K and ${}^{53}$Cr-${}^{6}$Li mixtures. We study the onset of the $s$-wave superfluid phase, as a function of population imbalance and the dipolar interaction strength. We find the critical temperature and the Fermi surface deformations at the transition to depend on the dipolar interaction strength, where the critical temperature increases (decreases) with dipolar interaction strength for a majority (minority) of dipolar atoms. We present momentum distributions of both components where the Fermi surface deformations are visible.
We study mass-imbalanced two-component Fermi mixtures, where one of the components consists of dipolar fermions. We specifically study the mass imbalances corresponding to the atomic 163Dy-40K and 53Cr-6Li mixtures. We study the onset of the s-wave superfluid phase, as a function of population imbalance and the dipolar interaction strength. We find the critical temperature and the Fermi surface deformations at the transition to depend on the dipolar interaction strength, where the critical temperature increases (decreases) with dipolar interaction strength for a majority (minority) of dipolar atoms. We present momentum distributions of both components where the Fermi surface deformations are visible.
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 investigate the temperature effects in an imbalanced superfluid atomic Fermi gas. We consider a bilayer system of two-component dipolar fermionic atoms with one layer containing atoms of one component and the other layer the atoms of other component with an imbalance between the populations of the two components. This imbalance results in uniform and nonuniform superfluid phases such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and normal Fermi liquid phases for different system parameters. Using the mean-field BCS theory together with the superfluid mass-density criterion we classify different phases in thermodynamic phase diagram. Our results indicate that for a dipolar Fermi system the Sarma phase is stable for large imbalance at finite temperature below the critical temperature, and the FFLO phase is stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The phase diagram in the temperature and population imbalance plane indicate three Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi liquid phase while the other two correspond to the coexistance of the Sarma phase, FFLO phase and normal Fermi phase for dipolar interactions.
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.
Mass imbalance changes not only pairing in a polarized Fermi gas but also the thermodynamic condition under which normal and superfluid components can remain phase separated. The low-temperature properties of mass imbalanced two component Fermi gases are investigated within the local density approximation on the BCS side of the BCS BEC crossover, with an unpolarized superfluid spatially separated from a partially polarized normal component. For each interaction strength and mass ratio, the pairing gap, average chemical potential, Hartree Fock potentials, and imbalance chemical potential are obtained self consistently, with the latter determined by the normal superfluid phase separation condition rather than varied independently. The results show that a larger mass ratio requires a larger imbalance chemical potential to maintain phase separation. For the 163Dy 40K mixture, an increase in the absolute value of the interaction strength raises the average and imbalance chemical potentials while reducing the pairing gap. The resulting changes modify the quasiparticle spectrum and the superfluid density of states and are reflected directly in the thermal response, with the quasiparticle specific heat decreasing at a fixed mass ratio. In contrast, increasing the mass ratio enhances the specific heat, which is associated with the larger density of available states near the Fermi surface of the heavier majority component. The results thus connect the normal superfluid phase separation condition with the quasiparticle spectrum and superfluid density of states, and show that the specific heat provides a clear thermal signature of mass imbalance in the phase separated regime.
We used radio-frequency spectroscopy to study pairing in the normal and superfluid phases of a strongly interacting Fermi gas with imbalanced spin populations. At high spin imbalances, the system does not become superfluid even at zero temperature. In this normal phase, full pairing of the minority atoms was observed. Hence, mismatched Fermi surfaces do not prevent pairing but can quench the superfluid state, thus realizing a system of fermion pairs that do not condense even at the lowest temperature.
We describe the relation between the isothermal atomic compressibility and density fluctuations in mixtures of two-component fermions with population or mass imbalance. We derive a generalized version of the fluctuation-dissipation theorem which is valid for both balanced and imbalanced Fermi-Fermi mixtures. Furthermore, we show that the compressibility, its critical exponents, and phase boundaries can be extracted via an analysis of the density fluctuations as a function of population imbalance, interaction parameter or temperature. Lastly, we demonstrate that in the presence of trapping potentials, the local compressibility and local density-density correlations can be extracted via a generalized fluctuation-dissipation theorem valid within the local density approximation.