Quasiparticle Lifetime of the Repulsive Fermi Polaron

We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi oscillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes to the lower-lying attractive branch. Thus, the theory-experiment agreement demonstrates that the quasiparticle lifetime is dominated by many-body dephasing within the upper repulsive branch rather than by relaxation from the upper branch itself. Our findings shed light on recent experimental observations of persistent repulsive correlations, and have important consequences for the nature and stability of the strongly repulsive Fermi gas.

Figure 1

(a) Two pseudospin states (red and green) of an impurity embedded in a medium (blue) are coupled together and undergo Rabi oscillations with an effective frequency $\mathrm{\Omega }$ and damping rate ${\mathrm{\Gamma }}_R$. (b) The impurity spectral function of a nearly free impurity (left) is coupled to that of an impurity that strongly interacts with the Fermi gas (right). The repulsive polaron peak is centered at energy $E_{+}$ above the molecule-hole continuum and is characterized by the residue $Z$ (dark green area) and width $\mathrm{\Gamma }$ [35].

Figure 2

Rabi oscillations calculated using the TBM (solid lines) and compared with the data (black dots) from the 2D ${}^{173}\mathrm{Yb}$ experiment [16] (top row) and the 3D ${}^6\mathrm{Li}$ experiment [14] (bottom row). In the top row, ${\mathrm{\Omega }}_0/E_F\simeq 0.95$ and $T/T_F\simeq 0.16$ while, from left to right, $\ln (1/k_F{a}_{2\mathrm{D}})=0.73$,0.57, and 0.25. In the bottom row, ${\mathrm{\Omega }}_0/E_F\simeq 0.68$ and $T/T_F\simeq 0.13$ while, from left to right, $1/(k_{F}a)=2.63$,1.27, and 0.22. The shaded regions correspond to the estimated uncertainty in the detuning around the repulsive polaron energy [46]. In the top row, the data is calculated from the sole measurement of ${\mathcal{N}}_{\downarrow }(t)$, and the normalization of each data point to ${\mathcal{N}}_{\downarrow }(t=0)$ [46]. We define the Fermi time ${\tau }_F\equiv 1/E_F$.

Figure 3

The extracted frequency $(\mathrm{\Omega }/{\mathrm{\Omega }}_0{)}^2$ and damping ${\mathrm{\Gamma }}_R$ of the Rabi oscillations as determined from the TBM (blue circles) and in the 2D (a),(c) and 3D (b),(d) experiments (black dots). The TBM error bars are derived from the uncertainty in detuning [46], which tends to increase the oscillation frequency. The extracted Rabi parameters are also compared with the quasiparticle residue $Z\simeq (\mathrm{\Omega }/{\mathrm{\Omega }}_0{)}^2$ (top row) and quasiparticle inverse lifetime $\mathrm{\Gamma }\simeq {\mathrm{\Gamma }}_R$ (bottom row) obtained directly from the finite-temperature impurity Green’s function (green solid line). The TBM simulations are set to match the experimental parameters [46]. Inset: data in (d) plotted on a log-log scale, together with the result of a zero-temperature Green’s function calculation (green dashed line).