Magnetically Controlled Exchange Process in an Ultracold Atom-Dimer Mixture

We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schrödinger equation in the adiabatic hyperspherical representation. The high efficiency of the exchange process is explained by the halo character of both the initial and final molecular states.

Figure 1

(a) Zeeman diagram of the most weakly bound dimer states $A_2$ and $AB$ below the $A+A$ and $A+B$ dissociation thresholds, respectively; here $A$ and $B$ are two hyperfine sublevels of Cs. (b) Schematic representation of a crossing between the $A_2+B$ and $A+AB$ channels. (c) The energy difference $\Delta E$ between the $A_2+B(m_F)$ and $A+AB(m_F)$ channels, with $m_F=2$, 3 or 4, showing channel crossings around 35 G for $m_F=2$ and 3.

Figure 2

Rate coefficient $\beta$ for inelastic atom-molecule collisions for the $B+A_2$ mixtures at a temperature of 50(10) nK as a function of the magnetic field $B$, comparing the experimental results (symbols) with the model calculations (lines). The solid curves represent the total $A_2$ loss rate including relaxation to more deeply bound states, whereas the dashed curve shows the contribution of the exchange process. The error bars contain the uncertainties of the trap frequencies and temperature measurements, required to convert the measured particle numbers into densities.

Figure 3

Measurement of the fraction of $A_2$ molecules (a) and $A$ atoms (b), after a fixed storage time of 22 ms of the $B+A_2$ mixtures at a temperature of 100(10) nK. The fractions are defined as the $A_2$ molecule and $A$ atom number normalized to the initial $A_2$ molecule number (about 4000). The data points are averaged over three to five measurement runs and the error bars represent the statistical uncertainty. The lines are obtained from the rate equations using the theoretical results for the total loss rates (a) and exchange rates (b), as shown in Fig. 2.

Figure 4

Magnetic field dependence of the two-body scattering lengths for the $A+A$ and the three $A+B$ channels, in units of the Bohr radius $a_0$. The nonshaded region represents the universal regime, which for Cs is realized for $a\gg 100a_0$ [10]. Narrow Feshbach resonances resulting from higher partial waves are neglected here.