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arXiv:cond-mat/0605143 · Physical Review A

Classification of zero-energy resonances by dissociation of Feshbach molecules

Thomas M. Hanna, Krzysztof Góral, Emilia Witkowska, Thorsten Köhler

Published Aug 23, 2006• 7 citations
arXivHTMLPDF

Abstract

We study the dissociation of Feshbach molecules by a magnetic field sweep across a zero-energy resonance. In the limit of an instantaneous magnetic field change, the distribution of atomic kinetic energy can have a peak indicating dominance of the molecular closed-channel spin configuration over the entrance channel. The extent of this dominance influences physical properties such as stability with respect to collisions, and so the readily measurable presence or absence of the corresponding peak provides a practical method of classifying zero-energy resonances. Currently achievable ramp speeds, e.g., those demonstrated by D\"urr et al. [Phys. Rev. A 70, 031601 (2005)], are fast enough to provide magnetic field changes that may be interpreted as instantaneous. We study the transition from sudden magnetic field changes to asymptotically wide, linear ramps. In the latter limit, the predicted form of the atomic kinetic energy distribution is independent of the specific implementation of the two-body physics, provided that the near-resonant scattering properties are properly accounted for.

DOI
10.1103/physreva.74.023618

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Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.

•May 3, 1998•0 citations
We study the dissociation of Feshbach molecules by a magnetic field sweep across a zero-energy resonance. In the limit of an instantaneous magnetic field change, the distribution of atomic kinetic energy can have a peak indicating dominance of the molecular closed-channel spin configuration over the entrance channel. The extent of this dominance influences physical properties such as stability with respect to collisions, and so the readily measurable presence or absence of the corresponding peak provides a practical method of classifying zero-energy resonances. Currently achievable ramp speeds, e.g., those demonstrated by D"urr et al. [Phys. Rev. A 70, 031601 (2005)], are fast enough to provide magnetic field changes that may be interpreted as instantaneous. We study the transition from sudden magnetic field changes to asymptotically wide, linear ramps. In the latter limit, the predicted form of the atomic kinetic energy distribution is independent of the specific implementation of the two-body physics, provided that the near-resonant scattering properties are properly accounted for.
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.
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.
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.
Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose and two-spin-component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled-channels theory provides a rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, and the classification in terms of entrance- and closed-channel-dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic-field sweeps in cold Bose and Fermi gases and pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean-field, as well as beyond mean-field approaches are reviewed in detail, including the associated ranges of validity.
We have generalized the BOUND and MOLSCAT packages to allow calculations in basis sets where the monomer Hamiltonians are off diagonal and used this capability to carry out bound-state and scattering calculations on $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ and $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ as a function of magnetic field. Following the bound-state energies to the point where they cross thresholds gives very precise predictions of the magnetic fields at which zero-energy Feshbach resonances occur. We have used this to locate and characterize two very narrow Feshbach resonances in $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$. Such resonances can be used to tune elastic and inelastic collision cross sections, and sweeping the magnetic field across them will allow a form of quantum control in which separated atoms and molecules are associated to form complexes. For the first resonance, where only elastic scattering is possible, the scattering length shows a pole as a function of magnetic field and there is a very large peak in the elastic cross section. For the second resonance, however, inelastic scattering is also possible. In this case the pole in the scattering length is dramatically suppressed and the cross sections show relatively small peaks. The peak suppression is expected to be even larger in systems with stronger inelasticity. The results suggest that calculations on ultracold molecular inelastic collisions may be much less sensitive to details of the potential energy surface than has been believed.
Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.