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arXiv:cond-mat/0209100 · Physical Review A

Microscopic theory of atom-molecule oscillations in a Bose-Einstein condensate

Thorsten Köhler, Thomas Gasenzer, Keith R. Burnett

Published Jan 7, 2003• 98 citations
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Abstract

In a recent experiment at JILA [E. A. Donley et al., Nature (London) 417, 529 (2002)] an initially pure condensate of ${}^{85}\mathrm{Rb}$ atoms was exposed to a specially designed time-dependent magnetic-field pulse in the vicinity of a Feshbach resonance. The production of additional components of the gas as well as their oscillatory behavior have been reported. We apply a microscopic theory of the gas to identify these components and determine their physical properties. Our time-dependent studies allow us to explain the observed dynamic evolution of all fractions, and to identify the physical relevance of the pulse shape. Based on ab initio predictions, our theory strongly supports the view that the experiments have produced a molecular condensate.

DOI
10.1103/physreva.67.013601

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An initially stable 85 Rb Bose-Einstein condensate (BEC) was subjected to a carefully controlled magnetic field pulse in the vicinity of a Feshbach resonance.This pulse probed the strongly interacting regime for the condensate, with calculated values for the diluteness parameter (na 3 ) ranging from 0.01 to 0.5.The field pulse was observed to cause loss of atoms from the condensate on remarkably short time scales (≥10 µs).The dependence of this loss on magnetic field pulse shape and amplitude was measured.For triangular pulses shorter than 1 ms, decreasing the pulse length actually increased the loss, until extremely short time scales (a few tens of microseconds) were reached.Such time scales and dependencies are very different from those expected in traditional condensate inelastic loss processes, suggesting the presence of new microscopic BEC physics.
We study Feshbach resonance scattering in a time-dependent magnetic field. We explain the extremely rapid decay observed in a recent experiment investigating Feshbach resonances in a Na Bose-Einstein condensate. In our picture, the decay is stimulated by the formation of a molecular condensate of quasibound atom pairs. Another essential element is the concept of a global and a local resonance lifetime. The predicted decay rates are large, about 5 orders of magnitude larger than typical dipole decay rates, and 1 order larger than typical exchange decay rates. We point out the possible role of a Josephson-like oscillation between the atomic condensate and a long-range molecular condensate.
With help of a Feshbach scattering resonance it is possible to change the effective two-body interaction of ultra-cold atoms from repulsive to attractive, from weak to strong. Regular field theory for the description of Bose-Einstein condensates is based on a single interaction parameter only, the scattering length. Such a description, however, is not valid anymore for the resonance regime. We formulated a field-theory that incorporated the microscopic energy-dependent two-body interactions, that also takes pair correlations into account. This theory allowed us to explain an experiment at JILA where Ramsey fringes were observed in a ^85Rb Bose-Einstein condensate by making use of a Feshbach resonance. The theory and experiment show that coherent molecules are created, a first step in the direction of molecular BEC. For non-resonant interactions, the self-energy corresponding to the atom-atom interactions is proportional to the scattering length. Close to resonance, however, this relationship no longer applies, and the energy will level off to a finite value on resonance. We investigate this resonance self-energy, and compare it with experimental results from strongly interacting Fermi systems.
We perform numerical simulations based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. [Nature (London) 412, 295 (2001)] on the dynamics of collapsing and exploding Bose-Einstein condensates of 85Rb{}^{85}\mathrm{Rb}85Rb atoms. These authors manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one, and vice versa. In the actual experiment they suddenly changed the scattering length of atomic interaction from a positive to a large negative value on a preformed condensate in an axially symmetric trap. Consequently, the condensate collapsed and ejected atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates.
We discuss the long-range nature of the molecules produced in recent experiments on molecular Bose-Einstein condensation. The properties of these molecules depend on the full two-body Hamiltonian and not just on the states of the system in the absence of interchannel couplings. The very long-range nature of the state is crucial to the efficiency of production in the experiments. Our many-body treatment of the gas accounts for the full binary physics and describes properly how these molecular condensates can be directly probed.