Spontaneous Dissociation of Long-Range Feshbach Molecules

We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for ${}^{85}\mathrm{R}\mathrm{b}$ dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of ${{}^{85}\mathrm{R}\mathrm{b}}_2$.

Figure 1

Magnetic field dependence of the real (solid curve) and imaginary (dashed curve) parts of the complex scattering length $a(B)-ib(B)$. The dotted line indicates the length scale [13] $r_{\mathrm{v}\mathrm{d}\mathrm{W}}=(m{C}_6/{\hslash }^2{)}^{1/4}/2$ set by the long-range asymptotic $-C_6/r^6$ van der Waals tail of the background scattering potential. We note that $b(B)$ is multiplied by a factor of 1000.

Figure 2

Two-body decay lifetime $\tau (B)$ of the ${{}^{85}\mathrm{R}\mathrm{b}}_2$ Feshbach molecules [2, 5] versus magnetic field strength $B$ near 15.5 mT. The squares indicate the experimental data of Thompson et al. [1]. The circles indicate exact predictions of coupled channels calculations, whereas the solid and dotted curves show the results of the universal formulas (9) and (12), respectively. The magnitude of the bare state lifetime ${\tau }_{\mathrm{r}\mathrm{e}\mathrm{s}}$ is indicated by the dotted line. For the purpose of comparison, we have slightly corrected the axis of the magnetic field strength in such a way that the theoretical resonance position recovers the measured value of $B_0=15.5041\mathrm{m}\mathrm{T}$ [5].