Quantum dynamics of impurities coupled to a Fermi sea

TL;DR

This paper investigates the quantum dynamics of an impurity in a Fermi gas after a sudden interaction change, using a truncated basis approach to model short-time evolution and analyze many-body phenomena.

Contribution

It introduces a truncated basis method for modeling impurity dynamics in a Fermi sea, capturing short-time behavior and enabling computation of spectral functions and quantum quenches.

Findings

Exact short-time dynamics following a quench are captured by the method.

Universal non-analytic time dependence of the overlap is observed.

The method can compute impurity spectral functions and describe Rabi oscillations.

Abstract

We consider the dynamics of an impurity atom immersed in an ideal Fermi gas at zero temperature. We focus on the coherent quantum evolution of the impurity following a quench to strong impurity-fermion interactions, where the interactions are assumed to be short range like in cold-atom experiments. To approximately model the many-body time evolution, we use a truncated basis method, where at most two particle-hole excitations of the Fermi sea are included. When the system is initially non-interacting, we show that our method exactly captures the short-time dynamics following the quench, and we find that the overlap between initial and final states displays a universal non-analytic dependence on time in this limit. We further demonstrate how our method can be used to compute the impurity spectral function, as well as describe many-body phenomena involving coupled impurity spin states, such as Rabi oscillations in a medium or highly engineered quantum quenches.