Collisional relaxation of Feshbach molecules and three-body recombination in ${}^{87}\mathrm{Rb}$ Bose-Einstein condensates

We predict the resonance-enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate close to $1007\mathrm{G}$. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum, causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.

Figure 1

(Color online) Upper panel: elastic (dashed curve) and inelastic (solid curve) atom-dimer scattering rates $K_{\mathrm{ad}}$ associated with a collision energy of $3q_{\mathrm{i}}^2∕\left(4m\right)=k_{\mathrm{B}}\times 10\mathrm{nK}$ $(k_{\mathrm{B}}\times 1\mathrm{mK}=h\times 20.8\mathrm{MHz})$ versus $B$ on the low-field side of $B_0$. Lower panel: energies of the Feshbach molecular (dashed curve) and second highest excited vibrational (dotted curve) dimer states, $E_{-1}$ and $E_{-2}$, respectively. The dot-dashed and solid curves indicate the energies of isotropic metastable ${}^{87}\mathrm{Rb}_3$ states. The highest excited trimer level emerges at about $1003.7\mathrm{G}$ (arrow) in a zero-energy resonance (inset) for collisions between atoms and dimers in the second highest excited vibrational state.

Figure 2

(Color online) Three-body recombination loss rate constant $K_3$ versus $B$. Solid curves refer to the total loss rate constant $K_3^{\mathrm{tot}}$, whereas dashed and dot-dashed curves are its contributions from the final Feshbach molecular and second highest excited vibrational ${}^{87}\mathrm{Rb}_2$ states, respectively. The inset shows an enlargement close to the diatomic resonance whose position $B_0$ is indicated by the dotted line.

Figure 3

(Color online) Comparison between measured (circles and squares) and predicted (solid curve) total three-body recombination loss rate constants $K_3^{\mathrm{tot}}$. Error bars refer to statistical uncertainties only. The inset shows the binary scattering length $a\left(B\right)=a_{\mathrm{bg}}[1-\mathrm{\Delta }B∕(B-B_0\left)\right]$ on the low-field (solid curve) and high-field (dashed curve) sides of the diatomic zero-energy resonance (vertical dotted line). The horizontal dotted line indicates the background scattering length [13, 16] $a_{\mathrm{bg}}=100.5a_{\mathrm{Bohr}}$ $(a_{\mathrm{Bohr}}=0.0529\mathrm{nm})$ whereas the resonance width is $\mathrm{\Delta }B=0.21\mathrm{G}$. All measurements refer to $B<B_0$ where the BEC is stable with respect to collapse.