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arXiv:cond-mat/0507580 · Physical Review A

Dissociation of Feshbach molecules into different partial waves

Stephan Dürr, Thomas Volz, Niels Syassen, Gerhard Rempe, Eric van Kempen, S. J. J. M. F. Kokkelmans, BOUDEWIJN J. VERHAAR, Harald Friedrich

Published Nov 10, 2005• 25 citations

Abstract

Ultracold molecules can be associated from ultracold atoms by ramping the magnetic field through a Feshbach resonance. A reverse ramp dissociates the molecules. Under suitable conditions, more than one outgoing partial wave can be populated. A theoretical model for this process is discussed here in detail. The model reveals the connection between the dissociation and the theory of multichannel scattering resonances. In particular, the decay rate, the branching ratio, and the relative phase between the partial waves can be predicted from theory or extracted from experiment. The results are applicable to our recent experiment in $^{87}\mathrm{Rb}$, which has a $d$-wave shape resonance.

DOI: 10.1103/physreva.72.052707

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•Jan 1, 2007•0 citations

Ultracold molecules can be associated from ultracold atoms by ramping the magnetic field through a Feshbach resonance. A reverse ramp dissociates the molecules. Under suitable conditions, more than one outgoing partial wave can be populated. A theoretical model for this process is discussed here in detail. The model reveals the connection between the dissociation and the theory of multichannel scattering resonances. In particular, the decay rate, the branching ratio, and the relative phase between the partial waves can be predicted from theory or extracted from experiment. The results are applicable to our recent experiment in

^{87}\mathrm{Rb}

, which has a

d

-wave shape resonance.

Ultracold molecules are associated from an atomic Bose-Einstein condensate by ramping a magnetic field across a Feshbach resonance. The reverse ramp dissociates the molecules. The kinetic energy released in the dissociation process is used to measure the widths of four Feshbach resonances in

^{87}\mathrm{Rb}

. This method to determine the width works remarkably well for narrow resonances even in the presence of significant magnetic-field noise. In addition, a quasimonoenergetic atomic wave is created by jumping the magnetic field across the Feshbach resonance.

The dissociation of ultracold molecules was studied by ramping an external magnetic field through a Feshbach resonance. The observed dissociation energies directly yielded the strength of the atom-molecule coupling. They showed nonlinear dependence on the ramp speed. This was explained by a Wigner threshold law which predicts that the decay rate of the molecules above threshold increases with the density of states. In addition, inelastic molecule-molecule and molecule-atom collisions were characterized.

The effect of random magnetic fields on the dissociation of ultracold molecules with Feshbach resonances is studied analytically. The dissociation spectrum and the evolution of the molecule fraction are obtained for a general form of the magnetic-field ramp and different noise properties relevant to standard experimental conditions. The results uncover the robustness against noise of some characteristics of the dissociation process, in particular, of the dependence of the mean atomic kinetic energy on the system parameters. Implications for the applicability of a method proposed to determine the width of the Feshbach resonances from the measurement of the dissociation spectrum are analyzed. Moreover, we discuss how the presence of fluctuations can affect the use of particular ramp shapes to tailor the properties of the generated atomic distribution.

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.

This thesis describes experiments with ultracold diatomic molecules associated from ultracold 87Rb atoms using magnetically-induced scattering resonances (Feshbach resonances). The association method is based on a slow magnetic-field ramp across a Feshbach resonance which converts an atom pair into a bound molecule. The reaction is reversible and coherent and no latent heat is released. A Bose-Einstein condensate serves as a source of ultracold atoms. In one of the experiments reported here, the association technique is used to create a quantum state with exactly one molecule at each site of a three-dimensional optical lattice. This state opens up interesting possibilities with respect to quantum simulations and quantum information processing.