Resonant Association of Feshbach Molecules

In recent experiments, Feshbach molecules have been associated using resonant modulation of a magnetic field close to a zero-energy resonance [1, 2]. We analyse the dependence of this process upon the duration, amplitude and frequency of the modulation, as well as the temperature and density of the gas. A modulation of angular frequency $\omega_{\mbox{L}}$ resonantly couples a pair of atoms with relative kinetic energy $p^2/m$ = $\bar{h}\omega_{\mbox{L}$ + $E_{\mbox{b}}^{\mbox{av}}$ to the molecular state, where $E_{\mbox{b}}^{\mbox{av}}$ is the molecular bound state energy. The presence of a continuum of modes around this energy has a strong influence on the final conversion efficiency. Shifts in the modulation frequency giving maximum conversion are created by the amplitude of the modulation and the temperature of the gas. We discuss the importance of mean-field effects at short times, and predict that resonant association can be effective for binding energies of order $h \times 1$ MHz. \newline \newline [1] S. T. Thompson, E. Hodby and C. E. Wieman, Phys. Rev. Lett. \textbf{95}, 190404 (2005). \newline [2] S. B. Papp and C. E. Wieman, Phys. Rev. Lett. \textbf{97}, 180404 (2006).