Dynamics of relaxation and dressing of a quenched Bose polaron

We study the nonequilibrium dynamics of relaxation and dressing of a mobile impurity with velocity v, suddenly immersed, or quenched, into a zero-temperature homogeneous Bose-Einstein condensate. A many-body generalization of Weisskopf-Wigner theory is implemented to obtain the impurity fidelity, reduced density matrix and entanglement entropy. The dynamics depends crucially on the Mach number beta = v/c, with c the speed of sound of superfluid phonons, and features many different timescales. Quantum Zeno behavior at early time is followed by nonequilibrium dynamics determined by Cerenkov emission of long-wavelength phonons for beta > 1 with a relaxation rate Gamma(p) proportional to (beta - 1)(3). The polaron dressing dynamics slows down as beta -> 1 and is characterized by power laws t(-alpha) with exponents alpha = 3/2, 1/2, 2 for beta > 1, = 1, < 1, respectively. The asymptotic entanglement entropy features a sharp discontinuity, and the residue features a cusp at beta = 1. These nonequilibrium features suggest universal dynamical critical phenomena near beta similar or equal to 1 and are a direct consequence of the linear dispersion relation of long-wavelength superfluid phonons. We conjecture on the emergence of an asymptotic dynamical attractor with beta <= 1.