Non-equilibrium Dynamics of Fermi Polarons Driven by Time-dependent Interaction

We systematically studied the dynamics of Fermi polarons driven by time-dependent scattering length using a time-dependent variational method. Starting from the non-interacting initial state, we calculated the evolution behavior of the contact, energy, and quasiparticle residue of this system as the scattering length $a_s(t)$ increases from zero. In the short-time evolution, we obtained analytical results, verifying that when $a_s(t)$ grows as $\sqrt{t}$, the contact $C(t)$ and energy $E(t)$ exhibit the maximum growth rate. Furthermore, we numerically solved the long-time evolution, when $a_s(t)$ is diven with a strength $\beta$ and a power $\alpha$ as $a_s(t) = {\sqrt{2}\beta}/{k_F} {(\epsilon_Ft)}^{\alpha}$. For large driving strength, due to the interference between the polaron states and the non-interacting states, $C(t)$ and $Z(t)$ exhibit oscillatory behavior; For small $\beta$, the oscillatory behavior disappears due to the decay of the repulsive polaron into the continuum, and $C(t)$ and $Z(t)$ gradually relax to zero. The energy always saturates over long times for different driving strength. Additionally, our method is applicable to any time-dependent form of the scattering length.