Quench Dynamics of the Ideal Bose Polaron at Zero and Nonzero Temperatures

TL;DR

This paper provides an exact analytical study of the ideal Bose polaron's dynamics at various temperatures, revealing that many features of real BECs are already present in this simplified model, including thermalization and Tan contact behavior.

Contribution

It offers explicit formulas for the time evolution of the condensate wave function and density matrix, and relates the rf spectrum to the two-body problem, advancing understanding of impurity dynamics in ideal BECs.

Findings

System thermalizes even with coherent dynamics at negative scattering length.

Tan contact diverges at unitarity when a condensate exists.

Exact solutions for time evolution and rf spectrum are derived.

Abstract

We give a detailed account of a stationary impurity in an ideal Bose-Einstein condensate, which we call the ideal Bose polaron, at both zero and non-zero temperatures and arbitrary strength of the impurity-boson coupling. The time evolution is solved exactly and it is found that, surprisingly, many of the features that have been predicted for the real BEC are already present in this simpler setting and can be understood analytically therein. We obtain explicit formulae for the time evolution of the condensate wave function at $T=0$ and of the one-particle density matrix at $T>0$. For negative scattering length, the system is found to thermalize even though the dynamics are perfectly coherent. The time evolution and thermal values of the Tan contact are derived and compared to a recent experiment. We find that contrary to the Fermi polaron, the contact is not bounded at unitarity as long as a condensate exists. An explicit formula for the dynamical overlap at $T=0$ allows us to compute the rf spectrum which can be understood in detail by relating it to the two-body problem of one boson and the impurity.