# Dynamics of relaxation and dressing of a quenched Bose polaron

## TL;DR

This paper investigates the non-equilibrium relaxation and dressing dynamics of a mobile impurity in a Bose-Einstein condensate, revealing critical phenomena near the speed of sound and universal features related to phonon emission.

## Contribution

It introduces a many-body generalization of Weisskopf-Wigner theory to analyze impurity dynamics, uncovering universal critical behavior near the Mach number one.

## Key findings

- Quantum Zeno behavior at early times
- Power-law slowing of dressing dynamics near 
- Discontinuous entanglement entropy at 

## Abstract

We study the non-equilibrium dynamics of relaxation and dressing of a mobile impurity suddenly immersed--or quenched-- into a zero temperature homogeneous Bose Einstein condensate (BEC) with velocity $v$. A many body generalization of Weisskopf-Wigner theory is implemented to obtain the impurity fidelity, reduced density matrix and entanglement entropy. The dynamics depend crucially on the Mach number $\beta =v/c$, with $c$ the speed of sound of superfluid phonons and features many different time scales. Quantum Zeno behavior at early time is followed by relaxational and dressing dynamics determined by Cerenkov emission of long-wavelength phonons for $\beta >1$ with a decay rate $\Gamma_p \propto (\beta-1)^3$. The polaron dressing dynamics \emph{slows-down} as $\beta \rightarrow 1$ and is characterized by power laws $t^{-\alpha}$ with different exponents for $\beta \lessgtr 1$. The asymptotic entanglement entropy features a sharp discontinuity and the residue features a cusp at $\beta =1$. These non-equilibrium features suggest \emph{universal} dynamical critical phenomena near $\beta \simeq 1$, 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 $\beta \leq 1$.