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arXiv:cond-mat/0106373 · Physical Review Letters

Avalanches in a Bose-Einstein Condensate

J. Schuster, Andreas Marte, S. Amtage, B. Sang, Gerhard Rempe, Herman C. W. Beijerinck

Published Oct 8, 2001• 30 citations
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Abstract

Collisional avalanches are identified to be responsible for an 8-fold increase of the initial loss rate of a large (87)Rb condensate. We show that the collisional opacity of an ultracold gas exhibits a critical value. When exceeded, losses due to inelastic collisions are substantially enhanced. Under these circumstances, reaching the hydrodynamic regime in conventional Bose-Einstein condensation experiments is highly questionable.

DOI
10.1103/physrevlett.87.170404

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Collisional avalanches are identified to be responsible for an 8-fold increase of the initial loss rate of a large (87)Rb condensate. We show that the collisional opacity of an ultracold gas exhibits a critical value. When exceeded, losses due to inelastic collisions are substantially enhanced. Under these circumstances, reaching the hydrodynamic regime in conventional Bose-Einstein condensation experiments is highly questionable.
Summary form only given. In a Bose-Einstein condensate, due to the very low temperature, the s-wave scattering length can be used as a measure for the strength of the atom-atom interaction. Under typical experimental conditions, this interaction is weak and hence can be treated in terms of a mean field. However, when scattering length is large or the density is high, the mean field approximation breaks down. In this collisional (hydrodynamic) regime, effects of the interactions such as quantum depletion or shifts in the frequencies of the elementary excitations become large. It is therefore of great interest to study condensates close to or in the collisional regime. It has been demonstrated in recent experiments that the scattering length and thus the interactions among the atoms can be tuned by means of a Feshbach resonance (Inouye et al, 1998; Courteille et al., 1998; Vuleti et al., 1999; Cornish et al., 2000). In the vicinity of Feshbach resonances, however, the increase of the cross-section for elastic collisions is accompanied by a dramatic increase of particle losses. In this paper we report on the observation of anomalous losses from a /sup 87/Rb condensate with a high column density in the absence of an inelastic scattering resonance.
We report the realization of a Bose-Einstein condensate (BEC) in the hydrodynamic regime. The hydrodynamic regime is reached by evaporative cooling at a relatively low density suppressing the effect of avalanches. With the suppression of avalanches a BEC containing more than 108{10}^{8}108 atoms is produced. The collisional opacity can be tuned from the collisionless regime to a collisional opacity of more than 2 by compressing the trap after condensation. In the collisional opaque regime a significant heating of the cloud at time scales shorter than half of the radial trap period is measured, which is a direct proof that the BEC is hydrodynamic.
This thesis deals with elastic and inelastic collisions among ultra cold rubidium atoms. In particular, the impact of increased interaction on the stability of Bose-Einstein condensates is investigated both, experimentally and theoretically. A new decay mechanism is identified that significantly reduces the life time of condensates with respect to the expectation based on the known inelastic collision rates. Along with the interaction also the column density of the condensate is increased so that it eventually becomes impenetrable to products of exoergic collisions. These products then trigger avalanches of elastic collisions in which a significant part of the energy released in the initiatory exoergic collision is distributed among condensate atoms. Collisional avalanches are favoured by the isotropy of the differential scattering cross section in the low energy (s-wave) limit and occur as soon as the elastic collision rate exceeds a critical value. Since avalanches not only reduce the life time of the condensate but also disturb its thermodynamic equilibrium, their occurrence restricts the possibilities to explore the strongly interacting regime. A simple model is introduced to quantify the impact of avalanches on the decay and agrees well with experimental data. The thesis further contains the description and the characterisation of a new experimental apparatus which allows to create large atomic condensates with excellent reproducibility and high repetition rate complying with the requirements for the investigation of field-induced elastic scattering resonances.
We have observed a Bose-Einstein condensate in a dilute gas of 4He{}^{4}\mathrm{He}4He in the 32S1^{3}2S_{1}32S1​ metastable state. We find a critical temperature of $(4.7\ifmmode\pm\else\textpm\fi{}0.5)\ensuremath{\mu}\mathrm{K}$ and a typical number of atoms at the threshold of $8\ifmmode\times\else\texttimes\fi{}{10}^{6}$. The maximum number of atoms in our condensate is about $5\ifmmode\times\else\texttimes\fi{}{10}^{5}$. An approximate value for the scattering length $a\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(16\ifmmode\pm\else\textpm\fi{}8)\mathrm{nm}$ is measured. The mean elastic collision rate at threshold is then estimated to be about $2\ifmmode\times\else\texttimes\fi{}{10}^{4}{\mathrm{s}}^{\ensuremath{-}1}$, indicating that we are deeply in the hydrodynamic regime. The typical decay time of the condensate is 2s2\mathrm{s}2s, which places an upper bound on the rate constants for two-body and three-body inelastic collisions.
In several experiments with ultracold trapped atoms, a narrow loss feature has been observed near an atom-dimer resonance, at which there is an Efimov trimer at the atom-dimer threshold. The conventional interpretation of these loss features is that they are produced by the avalanche mechanism, in which the energetic atom and dimer from three-body recombination undergo secondary elastic collisions that produce additional atoms with sufficient energy to escape from the trapping potential. We use Monte Carlo methods to calculate the average number of atoms lost and the average heat generated by recombination events in a Bose-Einstein condensate and in a thermal gas. We improve on previous models by taking into account the energy dependence of the cross sections, the spatial structure of the atom cloud, and the elastic scattering of the atoms. We show that the avalanche mechanism cannot produce a narrow loss feature near the atom-dimer resonance. The number of atoms lost from a recombination event can be more than twice as large as the three that would be obtained in the absence of secondary collisions. However, the resulting loss feature is broad and its peak is at a scattering length that is larger than the atom-dimer resonance and depends on the trap depth.
The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, the observed rate of inelastic collisions was strongly enhanced in a sodium Bose-Einstein condensate when the scattering length was tuned to both larger or smaller values than the off-resonant value. These strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates.