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Conference on Lasers and Electro-Optics

Kinetic evolution of trapped Bose gas in evaporative cooling

Makoto Yamashita, Masato Koashi, N. Imoto

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.The successful demonstrations of Bose-Einstein condensation (BEG) with alkali atoms in a magnetic trap have opened up a new field of quantum physics. The evaporative cooling that enables six-order increase of phase space density is the essential technique for achieving the BEC transition in these experiments. However, at low temperatures, this cooling method is strongly affected by Bose statistics of alkali atoms, since evaporation occurs through the scattering process between trapped atoms. The quantum kinetics of nonequilibrium gas has been the subject of considerable interest for classic gas on the basis of truncated Boltzman distribution. We extend this method to treat the quantum statistics.

DOI
10.1109/iqec.1998.680321

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Summary form only given.The successful demonstrations of Bose-Einstein condensation (BEG) with alkali atoms in a magnetic trap have opened up a new field of quantum physics. The evaporative cooling that enables six-order increase of phase space density is the essential technique for achieving the BEC transition in these experiments. However, at low temperatures, this cooling method is strongly affected by Bose statistics of alkali atoms, since evaporation occurs through the scattering process between trapped atoms. The quantum kinetics of nonequilibrium gas has been the subject of considerable interest for classic gas on the basis of truncated Boltzman distribution. We extend this method to treat the quantum statistics.
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.
Bose-Einstein condensation (BEC) in a gas has now been achieved. Alkali atoms (87Rb^{87}Rb87Rb, 23Na^{23}Na23Na and 7Li^{7}Li7Li) have been cooled to the point of condensation (temperature of 100 nK) using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. This important experimental result has also renewed the interest on theoretical studies of BEC. In this contribution we discuss the statistical mechanics of the trapped BEC at zero temperature. In particular, we study the stability of the condensate by using a variational method with local and non-local interaction between the particles.
We discuss the kinetic theory for evaporative cooling of a dilute collisional gas in a trap. The analysis in O. J. Luiten et al., Phys. Rev. A 53, 381 (1996) is extended to incorporate a time-dependent trap strength and truncation energy. We employ the equations obtained to predict the efficiency of evaporative cooling of sodium atoms in a Ioffe trap and realize that a time-dependent trap strength can be crucial for the cooling. The calculations are classical in the sense that no effects of quantum statistics are taken into account: nevertheless the results of the calculations are useful in order to reveal experimental routes towards a Bose-Einstein condensate of sodium atoms.
The dynamics of evaporative cooling of magnetically trapped 87 Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. The theoretical optimization of the cooling trajectory clarifies that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against serious three-body recombination loss. The number of condensed atoms is expected to be largely enhanced by the optimization as compared with the typical value produced by the conventional evaporative cooling, where the frequency of the radio-frequency magnetic field is swept exponentially. Next, we precisely examine how the growth of a condensate depends on the experimental parameters of evaporative cooling in this inefficient exponential-sweep cooling. We find that, due to large nonlinear three-body loss, the number of condensed atoms finally becomes insensitive to the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. This result opens up the experimental possibility that the final number of condensed atoms can be well stabilized against the shot-to-shot fluctuations of experimental conditions in evaporative cooling.
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.