Lifshitz point in the phase diagram of resonantly interacting 6Li-40K mixtures.

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.

Renormalization group theory for the imbalanced Fermi gas.

We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)10.1038/nature06473].

Theory for p-wave Feshbach molecules.

We determine the physical properties of p-wave Feshbach molecules in doubly spin-polarized 40K and find excellent agreement with recent experiments. We show that these molecules have a large probability Z to be in the closed channel or bare molecular state responsible for the Feshbach resonance. In the superfluid state this allows for observation of Rabi oscillations between the molecular and atomic components of the Bose-Einstein condensed pairs, which contains a characteristic signature of the quantum phase transition that occurs as a function of applied magnetic field.

Sarma phase in trapped unbalanced fermi gases.

We consider a trapped unbalanced Fermi gas at nonzero temperatures where the superfluid Sarma phase is stable. We determine, in particular, the phase boundaries between the superfluid, normal, and phase-separated regions of the trapped unbalanced Fermi mixture. We show that the physics of the Sarma phase is sufficient to understand the recent observations of Zwierlein et al. [Science 311, 492 (2006); Nature (London) 442, 54 (2006)] and indicate how the apparent contradictions between this experiment and the experiment of Partridge et al. [Science 311, 503 (2006)] may be resolved.