Radio-frequency association of heteronuclear Feshbach molecules

We present a detailed analysis of the production efficiency of weakly bound heteronuclear ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ Feshbach molecules using radio-frequency association in a harmonic trap. The efficiency was measured in a wide range of temperatures, binding energies, and radio frequencies. A comprehensive analytical model is presented, explaining the observed asymmetric spectra and achieving good quantitative agreement with the measured production rates. This model provides a deep understanding of the molecule association process and paves the way for future experiments which rely on Feshbach molecules, e.g., for the production of deeply bound molecules.

Figure 1

(Color online) Number of associated molecules versus radio frequency for various binding energies. The solid lines show the theoretical model. All measurements were taken at a temperature of $730\mathrm{nK}$. The duration of the radio-frequency pulses is indicated in the legend. The inset illustrates the association process including the relevant energies and the wave functions of the molecule and atom pair (not shown to scale).

Figure 2

(Color online) The molecular binding energies as a function of magnetic field are shown in the top frame. A value of $B_0=546.618\left(6\right)\mathrm{G}$ is obtained for the position of the resonance (dotted line). The bottom shows the obtained number of molecules per pulse length.

Figure 3

(Color online) Scale factor versus binding energy (a) and temperature (b). The solid lines are guides to the eye.

Figure 4

(Color online) Number of associated molecules versus radio frequency for various temperatures. The solid lines show the theoretical model. All measurements were taken at a fixed magnetic field of $545.994\mathrm{G}$.