LAUSR

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 $\ensuremath{\beta}=v/c$, 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 $\ensuremath{\beta}g1$ with a relaxation rate ${\mathrm{\ensuremath{\Gamma}}}_{p}\ensuremath{\propto}{(\ensuremath{\beta}\ensuremath{-}1)}^{3}$. The polaron dressing dynamics slows down as $\ensuremath{\beta}\ensuremath{\rightarrow}1$ and is characterized by power laws ${t}^{\ensuremath{-}\ensuremath{\alpha}}$ with exponents $\ensuremath{\alpha}=3/2,1/2,2$ for $\ensuremath{\beta}g1,=1,l1,$ respectively. The asymptotic entanglement entropy features a sharp discontinuity, and the residue features a cusp at $\ensuremath{\beta}=1$. These nonequilibrium features suggest universal dynamical critical phenomena near $\ensuremath{\beta}\ensuremath{\simeq}1$ 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 $\ensuremath{\beta}\ensuremath{\le}1$.