Decoherence and Momentum Relaxation in Fermi-Polaron Rabi Dynamics: A Kinetic Equation Approach

Despite the paradigmatic nature of the Fermi-polaron model, the theoretical description of its nonlinear dynamics poses challenges. Here, we apply a quantum kinetic theory of driven polarons to recent experiments with ultracold atoms, where Rabi oscillations between a Fermi-polaron state and a noninteracting level were reported. The resulting equations separate decoherence from momentum relaxation, with the corresponding rates showing a different dependence on microscopic scattering processes and quasiparticle properties. We describe both the polaron ground state and the excited repulsive-polaron state and we find a good quantitative agreement between our predictions and the available experimental data without any fitting parameter. Our approach not only takes into account collisional phenomena, but also it can be used to study the different roles played by decoherence and the collisional integral in the strongly interacting highly imbalanced mixture of Fermi gases.

Figure 1

(a) A highly imbalanced mixture of atoms in state $|1⟩$ (majority, blue) and $|2⟩$ (minority, red dot in a circle) is held at temperature $T$ with zero interspecies interaction. The Rabi coupling $\mathrm{\Omega }$ drives the transitions between states $|2⟩$ and $|3⟩$. In the latter, minority atoms occupy repulsive and attractive Fermi-polaron branches, formed due to the interaction with the majority component, while ${\delta }_{\alpha }$ is the detuning between the noninteracting state and the polaron levels (here, only $\alpha =a$ is shown). (b) Polaron dispersion relations for atoms in state $|3⟩$. The interaction with the majority atoms induces inter- and intraband transitions, with rates $W^{\alpha \beta }$, where $\alpha ,\beta \in \{a,r\}$.

Figure 2

Rabi oscillations of the attractive polarons for $1/(k_{F}a)=0$ (a) and 0.25 (b) as a function of time $t$ (in units of $t_F=1/{ϵ}_F$) and of the repulsive polaron for $1/(k_{F}a)=1.27$ (c). The red dots are from the experiment [10]. The solid red line is from Eq. (6) and the non-self-consistent $T$-matrix approximation in Eq. (6). The red shaded region shows the confidence interval for 20% relative uncertainty in the temperature. The parameters: $\mathrm{\Omega }=0.7{ϵ}_F$, $T=0.135{ϵ}_F$.

Figure 3

Thermalization and violation of the detailed balance for attractive polarons. The main panel shows the degree of the violation of the detailed balance as quantified by $\surd ⟨[B(\mathbf{k},{\mathbf{k}}^{\prime })-1{]}^2⟩$. Inset shows the inferred temperature $T_K$ (in the units of the bath temperature $T$) from the Kullback-Leibler divergence. Here, the parameters are $1/k_{F}a=-0.25$ (dashed blue), 0 (solid green), 0.25 (dotted red); $\mathrm{\Omega }=0.7{ϵ}_F$, $T=0.135{ϵ}_F$, ${\delta }_a(0)=0$.