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

TL;DR

This paper investigates the non-equilibrium dynamics of Fermi polarons under time-varying interactions using a variational approach, revealing how contact, energy, and quasiparticle residue evolve with different driving protocols.

Contribution

The study introduces a systematic variational method to analyze Fermi polaron dynamics with arbitrary time-dependent interactions, providing analytical and numerical insights into their evolution.

Findings

Contact and energy grow maximally when scattering length scales as √t.

Oscillations in contact and residue occur at high driving strength due to interference effects.

Energy saturates over time regardless of driving strength.

Abstract

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.