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arXiv:cond-mat/0311558 · Physical Review Letters

Dissociation and Decay of Ultracold Sodium Molecules

Takashi Mukaiyama, J. R. Abo-Shaeer, K. Xu, J. K. Chin, Wolfgang Ketterle

Published May 4, 2004• 139 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.92.180402

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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.
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 87Rb^{87}\mathrm{Rb}87Rb. 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.
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 87Rb^{87}\mathrm{Rb}87Rb, which has a ddd-wave shape resonance.
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.
The variation of a magnetic field in the vicinity of a zero-energy resonance allows highly vibrationally excited molecules (‘Feshbach molecules’) to be produced from an ultracold atomic gas. In this thesis, we study the dynamics of this process. We begin by studying the dissociation of Feshbach molecules, showing that in the limit of a sudden jump the shape of the spectrum of dissociated atoms can act as a probe of the zero-energy resonance. For some resonances, such jumps are within reach of current experiments. We also study the intermediate region between sudden jumps and asymptotically wide, linear ramps. It is shown from a precise derivation how the latter limit leads to a universal spectrum with a shape independent of the implementation of the two-body physics, provided that the near-resonant scattering properties are correctly modelled. We then turn to the dynamics of Feshbach molecule production from thermal and condensed gases. Our microscopic quantum dynamics approach includes the exact twobody evolution as an input to the many-body calculations. We show that in the long-time limit, and the Markov limit for the interactions, the non-Markovian Boltzmann equation (NMBE) we derive for the one-body density matrix reduces to the normal Boltzmann equation. In the limit of short times and small depletion of the atomic gas, the molecule production efficiency can be calculated by thermally averaging the two-body transition probability density. This thermal averaging technique is applied to studies of the formation of Feshbach molecules using a magnetic field modulation that is near-resonant with the molecular bound state energy. The continuum is shown to have a significant effect on both the dynamics and efficiency of this process. We examine the dependence of the molecule production efficiency on the duration, amplitude and frequency of the modulation, as well as the temperature and density of the gas. This method of producing molecules is effective for a wide range of bound state energies, but requires sufficient variation of the two-body energy levels with magnetic field. Lastly, we implement the NMBE for the case of a fast linear ramp across a Feshbach resonance. The solution of this equation is made feasible by including a large part of the required computation in the kernel, which is calculated in advance. The NMBE allows predictions of the molecule production efficiency which go beyond the thermal averaging technique by accounting for the depletion and rethermalisation of the continuum. In the limit of small depletions, the two approaches give the same results. As the depletion increases, the two approaches differ due to many-body effects limiting the maximum possible molecule production efficiency. We have observed this in our simulations by considering higher-density gases. We have therefore shown the suitability and practicability of this beyond mean-field approach for application to further problems in the production of Feshbach molecules from ultracold gases.
Ultracold sodium molecules were produced from an atomic Bose-Einstein condensate by ramping an applied magnetic field across a Feshbach resonance. More than 10(5) molecules were generated with a conversion efficiency of approximately 4%. Using laser light resonant with an atomic transition, the remaining atoms could be selectively removed, preventing fast collisional relaxation of the molecules. Time-of-flight analysis of the pure molecular sample yielded an instantaneous phase-space density greater than 20.