Polar molecules in bilayers with high population imbalance

We investigate a dilute Fermi gas of polar molecules confined into a bilayer setup with dipole moments polarized perpendicular to the layers. In particular, we consider the extreme case of population imbalance, where we have only one particle in one layer and many particles in the other one. The single molecule is attracted by the dilute Fermi gas through the interlayer dipole-dipole force, presenting an interesting impurity problem with long-range anisotropic interaction. We characterize the quasiparticle, calculating its chemical potential with a Brueckner-Hartree-Fock approach. Moreover, we determine the momentum relaxation rate for finite momentum and temperature. The latter is reminiscent of Coulomb drag in bilayer electronic systems. For a confined system we relate the results for the chemical potential with the measurement of the oscillation frequency of the impurity. The momentum relaxation rate provides instead an estimate on how quickly the oscillations are damped.