Feshbach spectroscopy of a shape resonance

We present a spectroscopy technique for studying cold-collision properties. The technique is based on the association and dissociation of ultracold molecules using a magnetically tunable Feshbach resonance. The energy and lifetime of a shape resonance are determined from a measurement of the dissociation rate. Additional spectroscopic information is obtained from the observation of a spatial interference pattern between an outgoing $s$ wave and $d$ wave. The experimental data agree well with the results from a model, in which the dissociation process is connected to a scattering gedanken experiment, which is analyzed using a coupled-channel calculation.

Figure 1

Molecule dissociation rate $\Gamma$ as a function of magnetic field $B$ with respect to the position of the Feshbach resonance $B_{\mathit{res}}$. The experimental data for the total rate (circles) clearly show the effect of the shape resonance near $1.3\mathrm{G}$. The solid line is a Lorentzian fit to the data. The dashed (dotted) line shows the prediction for the total ($s$-wave) dissociation rate from a coupled-channel calculation. The $s$-wave dissociation is not affected by the shape resonance.

Figure 2

(Color online) Time-of-flight images of unbound atoms obtained in the molecule dissociation. The images were taken at different values of $B-B_{\mathit{res}}$. The magnetic field is vertical in the images. The interference between the $s$ and $d$ partial waves undergoes a change in relative phase and amplitude. At $0.1\mathrm{G}$, the dissociation is mostly $s$ wave, producing a circle. For higher magnetic fields, both partial waves are populated. From $0.2\text{to}0.6\mathrm{G}$, the interference suppresses atom emission along $B$, whereas the opposite relative phase in the interference between 1.0 and $1.4\mathrm{G}$ suppresses emission perpendicular to $B$. At 0.7 and $0.9\mathrm{G}$, the relative phase is such that neither component is strongly suppressed. The typical radius reached by the atoms during the constant time of flight increases for increasing $B$, thus indicating an increase of the kinetic energy released in the dissociation.

Figure 3

Parameters extracted from the spatial interference patterns. (a) Branching ratio for decay into the $d$ wave. Again, the $d$-wave shape resonance is clearly visible. (b) Partial-wave phases and relative phase. The solid, dashed, and dotted lines show the theoretical prediction for the relative phase ${\delta }_{\mathit{rel}}={\delta }_2^{bg}-{\delta }_0^{bg}$, the $s$-wave phase ${\delta }_0^{bg}$, and the $d$-wave phase ${\delta }_2^{bg}$, respectively. Experimental data (circles) agree well with the theory (solid line) in (a) and (b).