Ultracold Fermionic Feshbach Molecules of ${}^{23}\mathrm{Na}{}^{40}\mathbf{K}$

We report on the formation of ultracold weakly bound Feshbach molecules of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$, the first fermionic molecule that is chemically stable in its absolute ground state. The lifetime of the nearly degenerate molecular gas exceeds 100 ms in the vicinity of the Feshbach resonance. The measured dependence of the molecular binding energy on the magnetic field demonstrates the open-channel character of the molecules over a wide field range and implies significant singlet admixture. This will enable efficient transfer into the singlet vibrational ground state, resulting in a stable molecular Fermi gas with strong dipolar interactions.

Figure 1

(a) Association of fermionic Feshbach molecules. Starting with a mixture of $|1,1{⟩}_{\mathrm{Na}}$ and $|9/2,-3/2{⟩}_{\mathrm{K}}$ atoms, rf spectroscopy near the $|9/2,-3/2{⟩}_{\mathrm{K}}$ to $|9/2,-5/2{⟩}_{\mathrm{K}}$ hyperfine transition reveals free ${}^{40}\mathrm{K}$ atoms repulsively interacting with the ${}^{23}\mathrm{Na}$ bath (near zero rf offset), as well as associated molecules (near 85 kHz rf offset). A fit to the molecular association spectrum yields a binding energy of $E_b=h\times 84(6)\mathrm{kHz}$. The magnetic field corresponding to the atomic transition at 34.975 MHz was 129.4 G. (b) Dissociation of Feshbach molecules. Driving the $|9/2,-5/2{⟩}_{\mathrm{K}}$ to $|9/2,-7/2{⟩}_{\mathrm{K}}$ transition yields the molecular dissociation spectrum, showing a sharp onset at an rf frequency shifted by $E_b/h$ from the atomic transition. The solid line shows the fit of a $\mathrm{\text{model}}\propto \theta (\nu -{\nu }_b)\sqrt{\nu -{\nu }_b}/{\nu }^2$ [10], yielding ${\nu }_b=E_b/h=85(8)\mathrm{kHz}$.

Figure 2

(a) Binding energy of NaK Feshbach molecules at the wide Feshbach resonance between $|1,1{⟩}_{\mathrm{Na}}$ and $|9/2,-5/2{⟩}_{\mathrm{K}}$. Binding energies smaller than 200 kHz (circles) are obtained by direct detection of molecules [see Fig. 1a], while larger binding energies (diamonds) with weaker free-bound coupling are measured by detecting simultaneous atom loss in $|1,1{⟩}_{\mathrm{Na}}$ and $|9/2,-3/2{⟩}_{\mathrm{K}}$. The solid line is a one-parameter fit to the model described in the text, and the shaded region displays the uncertainty. (b) Open-channel fraction (dashed line) and singlet admixture of the molecular state (solid line), derived from the binding energy curve in (a), and singlet admixture of unbound pairs (dotted line).

Figure 3

Time-of-flight expansion of leftover ${}^{40}\mathrm{K}$ atoms and associated molecules at 129.4 G (binding energy $h\times 84\mathrm{kHz}$) right after rf association. Assuming a classical gas model, the width of the cloud corresponds to an average kinetic energy of 340 nK for the ${}^{40}\mathrm{K}$ cloud and 500 nK for the molecular cloud. Free atoms are transferred and detected in the $m_F=-1/2$ state, while potassium atoms bound in NaK molecules are imaged in the $m_F=-5/2$ state. The insets show an average of 20 absorption images for K atoms (NaK molecules) after 4.5 ms (4.0 ms) time of flight.

Figure 4

Lifetime of fermionic Feshbach molecules. The measurement is performed at a magnetic field of 132.2 G, corresponding to a binding energy of 32 kHz. The red (black) data points show the number of molecules as a function of hold time with (without) removing sodium from the dipole trap directly after association. Solid lines correspond to exponential fits yielding a $1/e$ time $\tau$ of 54(13) ms and 8(1) ms, respectively. The inset shows the lifetime as a function of the scattering length between bosons and fermions. The maximum observed lifetime is 140(40) ms.