Tomographic rf Spectroscopy of a Trapped Fermi Gas at Unitarity

We present spatially resolved radio-frequency spectroscopy of a trapped Fermi gas with resonant interactions and observe a spectral gap at low temperatures. The spatial distribution of the spectral response of the trapped gas is obtained using in situ phase-contrast imaging and 3D image reconstruction. At the lowest temperature, the homogeneous rf spectrum shows an asymmetric excitation line shape with a peak at $0.48(4){\epsilon }_F$ with respect to the free atomic line, where ${\epsilon }_F$ is the local Fermi energy.

Figure 1

Radio-frequency (rf) spectroscopy of a Fermi gas with in situ phase-contrast imaging. (a) After applying an rf pulse, the spatial distribution of the density difference between state $|1⟩$ and $|2⟩$ is recorded with the phase-contrast imaging technique [17]. The density depletion reflects the spin excitation induced by the rf pulse. The dashed line indicates the size of the trapped sample. (b) An absorption image of an equal mixture without applying an rf pulse. The field of view for each image is $205\mu \mathrm{m}\times 680\mu \mathrm{m}$. (c) rf spectrum of the inhomogeneous sample is obtained by integrating the signal in the phase-contrast images. The red (or gray) line is a Gaussian fit to the spectrum.

Figure 2

Spatially resolved rf spectroscopy of a trapped Fermi gas. (a) The spectral intensity $I(r,\Delta \nu )$ was obtained from the reconstructed 3D profiles of the density difference. See text for the description of the reconstruction method. Local rf spectra are shown for (b) $r=0\mu \mathrm{m}$, (c) $r=24\mu \mathrm{m}$, and (d) $r=40\mu \mathrm{m}$, whose positions are marked by vertical dashed lines in (a). Each spectrum is obtained by spatially averaging over $2.5\mu \mathrm{m}$. $R_{\mathrm{TF}}$ is the radial Thomas-Fermi radius for a noninteracting Fermi gas with the same atom number. The peak position $\Delta {\nu }_p(r)$ in the local rf spectra is determined from the moderately smoothed spectra and marked by the black line in (a). The determination of $\Delta {\nu }_p$ is limited to $|r|<48\mu \mathrm{m}$ due to the signal-to-noise ratio. The yellow (or light gray) line is a parabolic fit to $\Delta {\nu }_p(r)$. The radius determined by extrapolating the fit to zero rf offset is $R_p=53.6\mu \mathrm{m}$ indicated by the white down arrow. The black up arrow indicates the radius of the trapped sample, $R=56.6\mu \mathrm{m}$, measured independently from absorption images like Fig. 1b.