Resonant atom-dimer collisions in cesium: Testing universality at positive scattering lengths

We study the collisional properties of an ultracold mixture of cesium atoms and dimers close to a Feshbach resonance near 550 G in the regime of positive $s$-wave scattering lengths. We observe an atom-dimer loss resonance that is related to Efimov's scenario of trimer states. The resonance is found at a value of the scattering length that is different from a previous observation at low magnetic fields. This indicates nonuniversal behavior of the Efimov spectrum for positive scattering lengths. We compare our observations with predictions from effective field theory and with a recent model based on the van der Waals interaction. We present additional measurements on pure atomic samples in order to check for the presence of a resonant loss feature related to an avalanche effect, as suggested by observations in other atomic species. We could not confirm the presence of such a feature.

Figure 1

Near-threshold energy spectrum of ${\mathrm{Cs}}_2$ in the magnetic-field region around 560 G. (a) The spectrum results from three $g$-, two $i$-, and two $s$-wave molecular states. The bent $s$-wave state is our target state for atom-dimer decay measurements and the $g$-wave states are used to prepare molecules in the $s$-wave state. The paths for molecule creation are indicated by the dashed and dash-dotted arrows. The dotted frame indicates the region of interest as magnified in (b). (b) The large $i/s$ avoided crossing is highlighted by the difference between the uncoupled states ($s$, $d$, $g$ basis set and $i$-wave state [35]), shown as dashed lines, and the coupled states (solid lines); for details, see text. The hatched region marks the range of $B$ for which the $s$-wave character of the states is below 90%.

Figure 2

Atom-dimer vs dimer-dimer loss. The number $N_D$ of remaining dimers after a variable hold time for $B=557.7$ G ($a\approx 400a_0$) for a pure molecular sample (circles) and for an atom-dimer mixture (squares). The dashed line is the result of the fit according to a two-body decay rate equation ${\dot{N}}_D=-\alpha N_D^2/V$, giving $\alpha =2.4\left(3\right)\times {10}^{-10}{\mathrm{cm}}^3/\mathrm{s}$. The solid line is a fit according to Eq. (2). The error bars represent the standard deviation for $N_D$ given five to ten experimental runs. Note that in this particular set of measurements, the initial number of dimers is two times higher than under usual experimental conditions, which enhances dimer-dimer losses.

Figure 3

Measured dimer-dimer and atom-dimer loss rate coefficients. (a) The dimer-dimer loss rate coefficient $\alpha$ and (b) the atom-dimer loss rate coefficient $\beta$ are plotted as a function of $B$. They are determined from measurements as shown in Fig. 2. The data in (a) is obtained for hold times of up to 10 ms at the lower side of the avoided crossing (gray squares) and up to 20 ms at the upper side (filled squares). In (b), gray diamonds are data obtained on the lower side of the avoided crossing and filled diamonds are data on the upper side. The error bars contain the statistical uncertainties on the number of atoms and dimers, trap frequencies, and temperature. As in Fig. 1, the hatched region indicates the range of $B$ in which the $s$-wave character of the states is below 90%.

Figure 4

Atom-dimer loss rate coefficient $\beta$ for Cs as a function of the scattering length $a$ in the (a) high- and (b) low-magnetic-field regions. (a) The filled (gray) diamonds result from the measurements performed on the upper (lower) side of the avoided crossing at 175 nK, as in Fig. 3. (b) The filled squares are data from Ref. [4] acquired at 170 nK. In both panels, the dashed and the solid lines represent the EFT fit and the prediction of the vdW model scaled by the factors $D$ and $D^{\prime }$ (see text), respectively. Error bars include statistical uncertainties on temperature, trap frequencies, and atom numbers and the fitting uncertainties.

Figure 5

Loss measurements in pure atomic samples. The loss fraction is measured with samples of (a) $1.5\times {10}^5$ atoms at a temperature of about 170 nK and (b) $4\times {10}^4$ atoms at 40 nK. (a) The hold time is 2 s for the open symbols and 400 ms for the filled ones. (b) The hold time is 1 s for the open symbols and 50 ms for the filled ones. (c) The recombination rate coefficient $L_3$ is extracted from the data set with a hold time of 2 s from (a). The dashed line is the prediction from EFT [16], while the solid one is derived within the vdW model [48]. The error bars include the statistical uncertainties on the atom number. In all three panels, the gray region indicates the position of the loss resonance in atom-dimer mixtures; see Sec. 4. The width of this region reflects the uncertainty of the resonance's center position.