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Normal state of highly polarized Fermi gases: simple many-body approaches

We consider the problem of a single \down atom in the presence of a Fermi sea of \up atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the \down atom using two simple approaches: a many-body variational wave function and a T-matrix approximation. These two methods lead to the same results and are in good agreement with existing quantum Monte-Carlo calculations performed at unitarity and, in one dimension, with the known exact solution. Surprisingly, our results suggest that, even at unitarity, the effect of interactions is fairly weak and can be accurately described using single particle-hole excitations. We also consider the case of unequal masses.