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We investigate the behavior of a mobile spin-1/2 impurity atom immersed in aFermi gas, where the interacting spin-$\uparrow$ and non-interactingspin-$\downarrow$ states of the impurity are Rabi coupled via an externalfield. This scenario resembles the classic problem of a two-state systeminteracting with a dissipative environment, but with an added dimensionprovided by the impurity momentum degree of freedom. In this case, the impuritycan become "dressed" by excitations of the Fermi sea to form a Fermi polaronquasiparticle. For the steady-state system, where the impurity has thermalizedwith the medium, we derive exact thermodynamic relations that connect theimpurity magnetization with quasiparticle properties such as the number offermions in the dressing cloud. We show how the thermodynamic properties evolvewith increasing Rabi coupling and we present exact analytical results in thelimits of weak and strong Rabi coupling. For the dynamics of the Rabi-drivenFermi polaron, we formulate a theoretical approach based on correlationfunctions that respects conservation laws and allows the efficient calculationof Rabi oscillations for a range of time scales and impurity momenta beyondwhat has been achieved previously. Our results are in good agreement withrecent experiments on the Rabi oscillations of the attractive polaron, and theyreveal how the Rabi oscillations are influenced by the interplay between thepolaron and its dressing cloud.

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