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We consider 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 both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be different, 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 review, 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 sophisticated 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.
We investigate the phase structure of spin-imbalanced unitary Fermi gases beyond mean-field theory by means of the Functional Renormalization Group. In this approach, quantum and thermal fluctuations are resolved in a systematic manner. The discretiz
The spectra of low-lying pair excitations for an imbalanced two-component superfluid Fermi gas are analytically derived within the path-integral formalism taking into account Gaussian fluctuations about the saddle point. The spectra are obtained for
We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techni
We study spin- and mass-imbalanced mixtures of spin-$tfrac{1}{2}$ fermions interacting via an attractive contact potential in one spatial dimension. Specifically, we address the influence of unequal particle masses on the pair formation by means of t
We study a trapped two-dimensional spin-imbalanced Fermi gas over a range of temperatures. In the moderate temperature regime, associated with current experiments, we find reasonable semi-quantitative agreement with the measured density profiles as f