Experimental progress with ultracold atoms has allowed the study of many-body systems far from thermal equilibrium in accessible timescales when compared with solid state systems [1–5]. Moreover, atomic gases offer unique advantages for the control of many of relevant parameters, like the tuning of interactions and the change of internal state, those that have allowed the experimental realization of the Fermi polaron, a impurity immersed in a Fermi sea with Fermi energy $E_{\mathrm{F}}$ [6–14]. By using radio-frequency (RF) the polarons properties have been measured through linear response and Rabi oscillations when the Rabi frequency of the drive $\Omega_{0} < E_{\mathrm{F}}/\hbar$, although little is known about the dynamics and the relaxation between a non-interacting impurity state and the polaron in the strongly driven regime ($ \Omega_{0}\gg E_{\mathrm{F}}/\hbar $).

Here, we study the non-equilibrium dynamics of impurities immersed in a homogeneous Fermi gas. We drive the internal state of the impurities, between one level that does not interact with the Fermi bath, and one that is strongly interacting with it. By using the two-to-lowest Zeeman states of $^{6}$Li we create the two-level system, in which initially the impurities are in $\left|2\right\rangle$ and interact very weakly with the bath in $\left|3\right\rangle$. The minority is then driven to the third internal state $\left|1\right\rangle$ with a RF field, where this state interacts strongly with the bath. We investigate the dynamics of the minority under different drives, from weak $(\Omega_{0}\ll E_{\mathrm{F}}/\hbar)$ to strong $(\Omega_{0}\gg E_{\mathrm{F}}/\hbar)$. We extract the Rabi frequency renormalized by interactions $\Omega_{\mathrm{R}}$ and the relaxation time $T_{2}$ of the effective magnetization $\mathcal{M}$ (the relative population difference) at the resonance of the dressed two-level system. We observe that the system relaxes towards a steady state characterized by a detuning-dependent magnetization, effectively described by a thermalized two-level system [15]. This scenario can be understood as a dissipative two-level system, which evolves to the thermal equilibrium state via interactions with a fermionic bath [16-18]. We also extract the effective $T_{1}$ and $T_{2}$ times characterizing the decay to the steady-state as well as the energy shift of the resonant frequency of the two-level systems. Additionally, we make the connection of this strongly driven impurity-bath system with the (equilibrium) polaron problem and we find that the resonance of the dressed thermalized two-level system, defined as the energy in which this two-level system is equally populated, matches the energy of the polaron as measured by linear-response spectroscopy.

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