Precise Characterization of ${}^6\mathrm{Li}$ Feshbach Resonances Using Trap-Sideband-Resolved RF Spectroscopy of Weakly Bound Molecules

We perform radio-frequency dissociation spectroscopy of weakly bound ${}^6\mathrm{Li}_2$ Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability, this allows us to resolve the discrete trap levels in the radio-frequency dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the ${}^6\mathrm{Li}$ scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of the broad ${}^6\mathrm{Li}$ Feshbach resonances with an accuracy better than $7\times {10}^{-4}$ of the resonance widths. This eliminates the dominant uncertainty for current precision measurements of the equation of state of strongly interacting Fermi gases. As an important consequence, our results imply a corrected value for the Bertsch parameter $\xi$ measured by Ku et al. [Science 335, 563 (2012)], which is $\xi =0.370(5)(8)$.

Figure 1

RF spectra for the free-free (red dots, left axis) and bound-free (blue squares, right axis) spectra at a magnetic field of $B=811.139\mathrm{G}$. The line shape of the free-free transition is well described by a Lorentzian (solid line). The bound-free spectrum shows distinct peaks spaced by $2{\nu }_{\mathrm{r}}$, corresponding to different radial trap levels. The errors are the standard errors of the mean of about 40 individual measurements.

Figure 2

Molecular dissociation spectra at four different magnetic fields. The lines show fits according to the model described in the text, with the solid parts indicating the range of the data points included in the fit.