  We consider a spin impurity with multiple energy levels moving in a
non-interacting Fermi sea, and theoretically solve this Fermi spin polaron
problem at nonzero temperature by using a non-self-consistent many-body
$T$-matrix theory. We focus on the simplest case with spin half, where the two
energy states of the impurity are coupled by a Rabi flip term. At small Rabi
coupling, the impurity exhibits damped Rabi oscillations, where the decoherence
is caused by the interaction with the Fermi sea, as recently reported in Fermi
polaron experiments with ultracold atoms. We investigate the dependence of Rabi
oscillations on the Rabi coupling strength and examine the additional nonlinear
damping due to large Rabi coupling. At finite temperature and at nonzero
impurity concentration, the impurity can acquire a pronounced momentum
distribution. We show that the momentum/thermal average can sizably reduce the
visibility of Rabi oscillations. We compare our theoretical predictions to the
recent experimental data and find a good agreement without any adjustable
parameter.
