Polaron-to-molecule transition in a strongly imbalanced Fermi gas

A single down-spin fermion with an attractive zero-range interaction with a Fermi sea of up-spin fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wave function in the molecular limit, we determine the critical value for the polaron-to-molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirotzek [Phys. Rev. Lett. 102, 230402 (2009)]. In addition, we calculate the contact coefficient of the strongly imbalanced gas, using the adiabatic theorem of Tan and discuss the implications of the polaron-to-molecule transition for the phase diagram of the attractive Fermi gas at finite imbalance.