Repulsive Fermi Polarons in a Resonant Mixture of Ultracold ${}^6\mathrm{Li}$ Atoms

We employ radio-frequency spectroscopy to investigate a polarized spin mixture of ultracold ${}^6\mathrm{Li}$ atoms close to a broad Feshbach scattering resonance. Focusing on the regime of strong repulsive interactions, we observe well-defined coherent quasiparticles even for unitarity-limited interactions. We characterize the many-body system by extracting the key properties of repulsive Fermi polarons: the energy $E_{+}$, the effective mass $m^{*}$, the residue $Z$, and the decay rate $\mathrm{\Gamma }$. Above a critical interaction, $E_{+}$ is found to exceed the Fermi energy of the bath, while $m^{*}$ diverges and even turns negative, thereby indicating that the repulsive Fermi liquid state becomes energetically and thermodynamically unstable.

Figure 1

(a) Scattering properties of the initial 1–2 and final 1–3 state mixtures. The rf pulse pumps impurities from the weakly interacting into the resonant state. Inset: In situ absorption images of the state $|1⟩$ (red) and $|2⟩$ (blue) atomic clouds for $x=0.10(1)$. The rectangles mark the central region where the spectroscopy signal is recorded. (b) Left: Energy $E_{\downarrow }$ landscape of a zero-momentum impurity interacting with a homogeneous Fermi gas. The shaded area denotes the dressed dimer continuum, and the vertical dashed line marks the polaron-molecule crossing. Right: Sketch of the momentum dependence of the impurity resonance frequency. The blue (green) curve depicts the dispersion of bare (dressed) impurities.

Figure 2

Examples of the repulsive polaron spectral response recorded (a) at different $1/({\kappa }_{F}a)$ values with concentration $x=0.15(3)$ and (b) at different $x$ values with ${\kappa }_{F}a\simeq 2$. (c) Resonance position ${\mathrm{\Delta }}_{+}$ as a function of $\overline{ϵ}$ for various $1/({\kappa }_{F}a)$ values (see the legend). The linear fits used to extract $E_{+}$ and $m/m^{*}$ are shown. Error bars denote the standard errors of the fitted ${\mathrm{\Delta }}_{+}$.

Figure 3

(a) Zero-momentum repulsive polaron energy $E_{+}$ as a function of $1/({\kappa }_{F}a)$ (symbols). Inset: Attractive polaron energy $E_{-}$. Theory predictions from Refs. [23] (dot-dashed yellow line), [25] (dotted green line), and [26] (dashed red line) are shown in both panels. Empty symbols denote points obtained by averaging measurements at different $\overline{ϵ}$ rather than by zero-energy extrapolation [38]. (b) Inverse effective mass $m/m^{*}$ of the repulsive polaron as a function of $1/{\kappa }_{F}a$ (symbols), together with theory predictions from Ref. [25] (dotted green line). Error bars combine the linear fit parameter errors with the standard error of the mean (s.e.m.) of binned data.

Figure 4

(a) Decay rate $\mathrm{\Gamma }$ of the repulsive branch population measured as a function of $1/({\kappa }_{F}a)$. Theory predictions for three-body recombination ${\mathrm{\Gamma }}_3$ [56] (yellow line), polaron-to-polaron ${\mathrm{\Gamma }}_{\mathrm{PP}}$ [25] (green line), and polaron-to-bare atom ${\mathrm{\Gamma }}_{\mathrm{PF}}$ [38] (gray line) decay processes are plotted within their respective regimes of validity. Inset: Examples of polaron population decay for ${\kappa }_{F}a\simeq 1$ (yellow squares), 1.3 (red circles), and 3 (purple diamonds), together with the exponential fits. (b) $(\mathrm{\Omega }/{\mathrm{\Omega }}_0{)}^2$ for the repulsive (blue triangles) and attractive (yellow squares) polarons at various $1/({\kappa }_{F}a)$. Solid curves are our theory predictions for $(\mathrm{\Omega }/{\mathrm{\Omega }}_0{)}^2$ obtained within the ladder approximation [38], while dotted curves depict the lowest-order results $\sqrt{Z_{+2}{Z}_{\pm 3}}$. Inset: Repulsive polaron Rabi oscillations at $x=0.15(3)$ for ${\kappa }_{F}a\simeq 0$ (empty gray circles), 1.1 (yellow squares), 1.3 (red circles), and 1.7 (purple diamonds). Error bars combine the fit parameter errors with binned data s.e.m.