High-polarization limit of the quasi-two-dimensional Fermi gas

We demonstrate that the theoretical description of current experiments of quasi-two-dimensional (quasi-2D) Fermi gases requires going beyond the usual 2D theories. We provide such a theory for the highly spin-imbalanced quasi-2D Fermi gas. For typical experimental conditions, we find that the location of the recently predicted polaron-molecule transition is shifted to lower values of the vacuum binding energy due to the interplay between transverse confinement and many-body physics. The energy of the attractive polaron is calculated in the two-dimensional to three-dimensional (2D-3D) crossover and displays a series of cusps before converging towards the 3D limit. The repulsive polaron is shown to be accurately described by a 2D theory with a single interaction parameter.