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arXiv:cond-mat/0410765 · Physical Review A

Production of three-body Efimov molecules in an optical lattice

Martin Stoll, Thorsten Köhler

Published Aug 17, 2005• 43 citations
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Abstract

We study the possibility of associating metastable Efimov trimers from three free Bose atoms in a tight trap realized, for instance, via an optical lattice site or a microchip. The suggested scheme for the production of these molecules is based on magnetically tunable Feshbach resonances and takes advantage of the Efimov effect in three-body energy spectra. Our predictions of the energy levels and wave functions of three pairwise interacting $^{85}\mathrm{Rb}$ atoms rely upon exact solutions of the Faddeev equations and include the tightly confining potential of an isotropic harmonic atom trap. The magnetic field dependence of these energy levels indicates that it is the lowest-energetic Efimov trimer state that can be associated in an adiabatic sweep of the field strength. We show that the binding energies and spatial extents of the trimer molecules produced are comparable, in their magnitudes, to those of the associated diatomic Feshbach molecule. The three-body molecular state follows Efimov's scenario when the pairwise attraction of the atoms is strengthened by tuning the magnetic field strength.

DOI
10.1103/physreva.72.022714

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We study the possibility of associating metastable Efimov trimers from three free Bose atoms in a tight trap realized, for instance, via an optical lattice site or a microchip. The suggested scheme for the production of these molecules is based on magnetically tunable Feshbach resonances and takes advantage of the Efimov effect in three-body energy spectra. Our predictions of the energy levels and wave functions of three pairwise interacting 85Rb^{85}\mathrm{Rb}85Rb atoms rely upon exact solutions of the Faddeev equations and include the tightly confining potential of an isotropic harmonic atom trap. The magnetic field dependence of these energy levels indicates that it is the lowest-energetic Efimov trimer state that can be associated in an adiabatic sweep of the field strength. We show that the binding energies and spatial extents of the trimer molecules produced are comparable, in their magnitudes, to those of the associated diatomic Feshbach molecule. The three-body molecular state follows Efimov's scenario when the pairwise attraction of the atoms is strengthened by tuning the magnetic field strength.
We consider in detail the situation of applying a time-dependent external magnetic field to a 87 Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Köhler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87 Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.
Recent experiments with Bose-Einstein condensates of 85Rb atoms near a Feshbach resonance have produced evidence for a condensate of diatomic molecules coexisting with the atom condensate. It should also be possible to create condensates of the triatomic molecules predicted by Efimov coexisting with the atom and dimer condensates. The smoking gun for the trimer condensate would be oscillatory dependence of observables on the binding energy of the trimer. It may also be possible to deduce the existence of the trimer condensate from the spectra of the bursts of atoms and dimers created in the disappearance of the trimers.
We show that, for ultracold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pairwise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van der Waals potentials and near Fano-Feshbach resonances. For van der Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pairwise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr^{88}\mathrm{Sr}88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.
This thesis presents experiments exploring Feshbach molecules and Efimov trimers in an ultracold Bose-Fermi atomic gas mixture of 40K and 87Rb. These bound states are accessed via scattering resonances, called Fano-Feshbach resonances, which arise as a consequence of a bound state being tuned through degeneracy with the threshold energy of colliding atoms. In addition to allowing the tunability of interactions, the Fano-Feshbach resonance allows for a weakly bound molecule state, called the Feshbach molecule state, to be populated. The efficiency of conversion to the Feshbach molecule state depends upon the rate with which the bound state energy is swept through degeneracy with atomic threshold energy. In regions of large scattering lengths, three-body bound states, called Efimov states, also influence inelastic Bose-Bose-Fermi collisions and boson+molecule collisions in our system. The work presented in this thesis utilizes a magnetically tunable Fano-Feshbach resonance to study Feshbach molecule creation in the perturbative limit (the limit of fast magnetic-field sweeps) and the saturated limit (the limit of slow sweeps), where a phenomenological model is applied to understand the conversion efficiency as well as the quantum degeneracy of the molecules. In addition, I present a study of boson+molecule collision rates and Bose-Bose-Fermi collision rates in order to observe signatures of Efimov states and compare against results in the gas mixture 41K-87Rb to address the question of universality of the three-body parameter in heteronuclear gas mixtures.
Ultracold ground-state dipolar 40K^{40}\mathrm{K}40K87Rb^{87}\mathrm{Rb}87Rb molecules recently have been produced in a loose harmonic trap by employing a magnetic field sweep across a Feshbach resonance followed by stimulated Raman adiabatic passage [K.-K. Ni et al., Science 322, 231 (2008)]. The overall experimental efficiency for molecule formation was around 2020%20. We show that the efficiency can be increased to nearly 100100%100 if one first loads the atomic gases into an optical lattice of the appropriate depth and tunes the interspecies attraction to have exactly one atom of each species at an occupied lattice site. Our proposed scheme provides a large enhancement to the dipolar molecule density, even at relatively high temperatures, and avoids three-body recombination loss by preventing lattice sites from being triply occupied.
Under certain circumstances, three or more interacting particles may form bound states. Although the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of 11 precisely determined three- and four-body features are found in the inelastic-loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, whereas a systematic deviation from universality is found when comparing features across the resonance.