Association of ultracold double-species bosonic molecules

We report on the creation of heterospecies bosonic molecules, associated from an ultracold Bose-Bose mixture of ${}^{41}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$, by using a resonantly modulated magnetic field close to two Feshbach resonances. We measure the binding energy of the weakly bound molecular states versus the Feshbach field and compare our results to theoretical predictions. We observe the broadening and asymmetry of the association spectrum due to the thermal distribution of the atoms and a frequency shift occurring when the binding energy depends nonlinearly on the Feshbach field. A simple model is developed to quantitatively describe the association process. This work represents a required step toward Bose-Einstein condensates of dipolar molecules.

Figure 1

(Color online) (a) Molecular radio-frequency association: two free atoms with relative kinetic energy $E_{\mathrm{kin}}$ are resonantly transferred to a molecular level by modulating the magnetic field. The inset shows the remaining atom number after a variable association time. The solid line is an nonexponential fit to data (see text). (b) Spectrum for an association time of $30\mathrm{ms}$, $B=78.25\mathrm{G}$. The solid line is a fit with the line shape described in the text.

Figure 2

(Color online) (a) KRb binding energy and three-body losses for the Feshbach resonance at $79\mathrm{G}$: triangles show the experimental binding energies, circles the atom number. The dash-dotted black line shows the theoretical prediction for $E_b$; the solid blue line is the same curve, but translated by $-0.24\mathrm{G}$. The solid red line represents a Gaussian fit to the atom number. The vertical dashed lines show the position of the FR as determined by the three-body losses (red, left) and the binding energy (blue, right). (b) Same as above, for the FR at $39\mathrm{G}$. Note the widely different scale of $x$ axis. Here the theoretical model for $E_b$ is shifted by $-1\mathrm{G}$.

Figure 3

(Color online) Line shapes of the molecular association process for different values of temperature. Solid circles represent data, taken after $30\mathrm{ms}$ of rf pulse length around $B=78.2\mathrm{G}$. Solid lines represent the fitted line shape with the model described in the text: we take the binding energy $E_b$, the decay rate $\gamma$, and the coupling strength $\Omega$ as free fit parameters. The temperature is measured from the ballistic expansion of the clouds. Dashed lines show the fits assuming $\gamma =0$.

Figure 4

(Color online) Shift of the resonant modulation frequency as a function of the modulation amplitude, measured at $B=78.30\mathrm{G}$ with $15\mathrm{ms}$ of rf pulse length and a temperature of $350\mathrm{nK}$. The solid line represents the parabolic fit.