Quantum nucleation and macroscopic quantum tunneling in cold-atom boson-fermion mixtures

The kinetics of the phase separation transition in boson-fermion cold-atom mixtures is investigated. We identify the parameters at which the transition is governed by a quantum nucleation mechanism, responsible for the formation of critical nuclei of a stable phase. We demonstrate that for low fermion-boson mass ratio the density dependence of the quantum nucleation transition rate is experimentally observable. The crossover to the macroscopic quantum tunneling regime is analyzed. Based on a microscopic description of interacting cold-atom boson-fermion mixtures, we derive an effective action for the critical droplet and obtain an asymptotic expression for the nucleation rate in the vicinity of the phase transition and near the spinodal instability of the mixed phase. We show that dissipation due to excitations in the fermion subsystem play a dominant role close to the transition point.