Feshbach spectroscopy and scattering properties of ultracold Li + Na mixtures

We have observed 26 interspecies Feshbach resonances at fields up to 2050 G in ultracold ${}^6\text{Li}+{}^{23}\text{Na}$ mixtures for different spin-state combinations. Applying the asymptotic bound-state model to assign the resonances, we found that most resonances have $d$-wave character. This analysis serves as guidance for a coupled-channel calculation, which uses modified interaction potentials to describe the positions of the Feshbach resonances well within the experimental uncertainty and to calculate their widths. The scattering length derived from the improved interaction potentials is experimentally confirmed and deviates from previously reported values in sign and magnitude. We give prospects for ${}^7\text{Li}+{}^{23}\text{Na}$ and predict broad Feshbach resonances suitable for tuning.

Figure 1

Magnetic field dependence of atomic ground-state energies of $6$Li and ${}^{23}$Na. The indicated labeling of the different Zeeman levels is used throughout the paper.

Figure 2

Measured ${}^6\text{Li}+\text{Na}$ trap loss spectrum around 850 G, showing the remaining Na (a) and $6$Li (b) atom numbers after a hold time of 1 s. The solid lines are Gaussian fits. Three-body loss associated with the NaNa resonance in $|1\rangle$ at 851 G [25] can involve a Na or a Li atom as third partner and thus leads to loss of Li atoms at resonance, independent of the Li spin channel (gray symbols for Li $|6\rangle$ shifted by an offset for clarity). The loss feature at 852 G exclusively appears when Li is in the $|3\rangle$ state and can thus be identified as interspecies resonance.

Figure 3

Near-threshold molecular spectra for different $M_F$ from ABM, showing the molecular states $l=0$ (thick blue) and 2 (solid red) states, and the observed $s$- (large blue) and $d$-wave (small red) Feshbach resonances as filled circles. Atomic thresholds are depicted as black and gray dashed lines. The black and labeled ($|6\mathrm{Li}\rangle +|\mathrm{Na}\rangle$) thresholds are those relevant for the observed Feshbach resonances. The inset in panel (b) shows the resonances in the $|1\rangle +|1\rangle$ channel, which also have been previously observed [9]. In (c) a zoom in of four $d$-wave resonances around 900 G exemplarily highlights the fit quality in the $|1\rangle +|3\rangle$ and $|3\rangle +|1\rangle$ channel. A negative magnetic field corresponds to a sign change in $M_F$.

Figure 4

Scattering length of ${}^7\text{Li}+\text{Na}$ in energetically lowest spin channel, derived from interaction potentials. The spectrum shows much broader $s$-wave Feshbach resonances than found in ${}^6\text{Li}+\text{Na}$, most notably a 5.4-G-broad resonance around 1220 G.