Rabi oscillations and magnetization of a mobile spin-1/2 impurity in a Fermi sea

TL;DR

This paper studies a mobile spin-1/2 impurity in a Fermi gas under Rabi coupling, deriving exact thermodynamic relations and analyzing Rabi oscillations, advancing understanding of impurity dynamics and quasiparticle properties.

Contribution

It provides exact thermodynamic relations for a Rabi-coupled impurity in a Fermi sea and introduces a correlation function approach for analyzing Rabi oscillations across various parameters.

Findings

Thermodynamic relations link impurity magnetization to quasiparticle properties.

Analytical results in weak and strong Rabi coupling limits.

Theoretical predictions align with recent experimental observations.

Abstract

We investigate the behavior of a mobile spin-1/2 impurity atom immersed in a Fermi gas, where the interacting spin-$\uparrow$ and non-interacting spin-$\downarrow$ states of the impurity are Rabi coupled via an external field. This scenario resembles the classic problem of a two-state system interacting with a dissipative environment, but with an added dimension provided by the impurity momentum degree of freedom. In this case, the impurity can become "dressed" by excitations of the Fermi sea to form a Fermi polaron quasiparticle. For the steady-state system, where the impurity has thermalized with the medium, we derive exact thermodynamic relations that connect the impurity magnetization with quasiparticle properties such as the number of fermions in the dressing cloud. We show how the thermodynamic properties evolve with increasing Rabi coupling and we present exact analytical results in the limits of weak and strong Rabi coupling. For the dynamics of the Rabi-driven Fermi polaron, we formulate a theoretical approach based on correlation functions that respects conservation laws and allows the efficient calculation of Rabi oscillations for a range of time scales and impurity momenta beyond what has been achieved previously. Our results are in good agreement with recent experiments on the Rabi oscillations of the attractive polaron, and they reveal how the Rabi oscillations are influenced by the interplay between the polaron and its dressing cloud.