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arXiv:cond-mat/0007179 · Physical Review A

Dynamics of evaporative cooling in magnetically trapped atomic hydrogen

Makoto Yamashita, Masato Koashi, T. Mukai, Masaharu Mitsunaga, Nobuyuki Imoto

Published Aug 9, 2000• 13 citations
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Abstract

We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to $9\ifmmode\times\else\texttimes\fi{}{10}^{8}$ and the corresponding condensate fraction to a small value of 4% as observed experimentally.

DOI
10.1103/physreva.62.033602

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The dynamics of evaporative cooling of magnetically trapped 87Rb{}^{87}\mathrm{Rb}87Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. We carried out the quantitative calculations of the time evolution of conventional evaporative cooling where the frequency of the radio-frequency magnetic field is swept exponentially. This ``exponential-sweep cooling'' is known to become inefficient at the final stage of the cooling process due to a serious three-body recombination loss. We precisely examine how the growth of a Bose-Einstein condensate depends on the experimental parameters of evaporative cooling, such as the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. It is shown that three-body recombination drastically depletes the trapped 87Rb{}^{87}\mathrm{Rb}87Rb atoms as the system approaches the quantum degenerate region and the number of condensed atoms finally becomes insensitive to these experimental parameters. This result indicates that the final number of condensed atoms is well stabilized by a large nonlinear three-body loss against the fluctuations of experimental conditions in evaporative cooling.
We report experiments on evaporative cooling of spin-polarized atomic hydrogen gas confined in a cryogenic magnetic trap, and present a model of the trapped gas based on a generalized truncated Boltzmann approximation for the phase-space distribution function. The model takes into account the dimension of the evaporation [three-dimensional (3D) or 1D] and the time dependence of both the depth and the shape of the confining potential. Our observations are consistent with 1D evaporative cooling. To attain maximal phase-space density, we used the model assuming 1D evaporative cooling to optimize the evaporation procedure. With this work, the low dimension of evaporation was identified as the bottleneck thus far preventing us from achieving Bose-Einstein condensation in trapped atomic hydrogen.
Evaporative cooling of trapped atoms is studied based on the quantum kinetic theory. We extend the classical analysis of Luiten et al. [Phys. Rev. A 53, 381 (1996)] to treat Bose statistics of alkali-metal atoms. Dynamics in evaporative cooling process is described by a kinetic equation for the truncated Bose-Einstein distribution function under the assumption that the system is close to the thermal equilibrium. This approach is applicable to the ``slow'' evaporative cooling normally adopted in most experiments for the efficient production of Bose-Einstein condensates. Time-evolution calculations explain the current experiment well with sodium atoms using a slow evaporative cooling and demonstrate a rapid growth of condensate in the cooling process.
A study is made of the quantum mechanics of a gas of spin-polarized (b-state) atomic hydrogen confined in a three-dimensional dynamic (ac) magnetic trap. A previous classical treatment indicated that evaporative cooling from such a trap could be used to attain conditions for Bose-Einstein condensation (BEC). An approximate solution is developed for the quantum mechanics of a single atom in an ac trap. This solution is then used to treat the statistical mechanics of the BEC in an ac trap. The ideal-gas limit is briefly considered, and this is compared with the more realistic approximation of a nonideal gas described by the finite-temperature Hartree-Fock equations with an s-wave scattering-length interaction. The threshold temperature for BEC differs only slightly from the value for an ideal gas. However, the nature of the condensate is strongly dependent on the scattering length.
We study the optimization of evaporative cooling in trapped bosonic atoms on the basis of quantum kinetic theory of a Bose gas. The optimized cooling trajectory for 87Rb{}^{87}\mathrm{Rb}87Rb atoms indicates that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against loss of trapped atoms caused by three-body recombination. The number of condensed atoms is largely enhanced by the optimization, more than two orders of magnitude in our present calculation using relevant experimental parameters, as compared with the typical value given by the conventional evaporative cooling where the frequency of radio-frequency magnetic field is swept exponentially. In addition to this optimized cooling, it is also shown that highly efficient evaporative cooling can be achieved by an initial exponential and then a rapid linear sweep of frequency.