Boiling a Unitary Fermi Liquid

We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures $T$. In this regime, we observe a characteristic $T^2$ dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high $T$, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, $\propto T^{-1/2}$. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.

Figure 1

(a) Thermal evolution of the minority rf spectra. The impurity concentration is $n_{\downarrow }/n_{\uparrow }=0.10\pm 0.03$, the Rabi frequency ${\mathrm{\Omega }}_R=2\pi \times 0.5\mathrm{kHz}$, and the pulse duration $T_{\text{pulse}}=1\mathrm{ms}$. (b) 2D plot of the minority spectra with maxima highlighted by white points. To reflect the energy of the initial many-body state, the spectra are shown with the inverse frequency $E_{-}/E_{F\uparrow }$, where $E_{-}=-\hslash \omega$. The cross corresponds to the theoretical zero temperature result for the polaron energy, including a correction for final state interactions [3, 4, 5, 8, 38]. (c) FWHM of the rf spectra. (Dotted line) Fourier resolution limit; (dashed red line) single-polaron decay rate $\mathrm{\Gamma }/E_{F\uparrow }=2.71(T/T_{F\uparrow }{)}^2$ [7], offset by the Fourier limit; (dash-dotted black line) FWHM of the rf spectrum in the high-temperature limit $\mathrm{\Gamma }/E_{F\uparrow }=1.2\sqrt{T_{F\uparrow }/T}$ [40, 41], reflecting the scattering rate in the classical, unitary Boltzmann gas. [For the errors in (b) and (c), see the Supplemental Material [33] ].

Figure 2

Contact of the spin-imbalanced Fermi gas. (a) Typical rf spectra of the spin minority (blue circles) and majority (red squares). The impurity concentration is 10%. (Inset) High-frequency tails of the minority and majority spectra together with a fit of Eq. (1). (b) Contact as a function of temperature, obtained by measuring the transferred fraction of atoms as a function of rf pulse duration for frequencies $\hslash \omega /E_{F\uparrow }>5.5$ and use of Eq. (1). The gray dashed line shows the third-order viral expansion [48] and the cross shows the result from the Chevy ansatz [3, 49].

Figure 3

Observation of the majority excess cloud. (a) Density profiles in a harmonically varying external potential $U$. Blue (red) data points indicate the profiles of the minority (majority) spin component. The normalized temperature of the gas is $T/T_{F\uparrow }=0.07$ in the trap center ($U=0$). The green dashed line represents the equation of state of the ideal Fermi gas, the red (blue) solid line is the Fermi liquid ansatz [Eq. (3)] for the majority (minority) component. The red shaded area displays the excess majority density $\mathrm{\Delta }{n}_{\uparrow }$. (Inset) Dependence of the excess majority to minority ratio on the impurity concentration. (b) Temperature dependence of the majority excess cloud. Data points show the excess majority density $\mathrm{\Delta }{n}_{\uparrow }$ for an impurity concentration of $n_{\downarrow }/n_{\uparrow }=0.1$ (squares), $n_{\downarrow }/n_{\uparrow }=0.2$ (triangles), and $n_{\downarrow }/n_{\uparrow }=0.3$ (circles). The cross indicates the low-temperature prediction of the Fermi liquid ansatz $\mathrm{\Delta }{n}_{\uparrow }/n_{\downarrow }=-A=0.615$ [8] and the dashed line shows the third-order virial expansion.

Figure 4

Isothermal minority compressibility. The solid line is the Fermi liquid ansatz for $m^{*}/m=1$, while the dashed line corresponds to a fit with an effective mass of $m^{*}/m=1.25(5)$ assuming $A=-0.615$ [8]. The gray shaded area represents the standard deviation of the fit. For the entire range of temperatures displayed, the majority component is degenerate ($T/T_{F\uparrow }<0.2$).