Dynamics of Cold Atoms Leading to Bose-Einstein Condensation

Makoto Yamashita, Masato Koashi, Nobuyuki Imoto,
Tetsuya Mukai, and Masaharu Mitsunaga
Physical Science Laboratory

Extremely low temperatures of submicrokelvin order have been achieved by laser cooling of neutral atomic gases. At such low temperatures, atoms show a wave-like character that obeys quantum mechanics. For bosonic atoms, Bose-Einstein condensation (BEC) occurs when a macroscopic number of atoms occupy the single lowest energy level. Bose-Einstein condensation in cold atoms was demonstrated quite recently for alkali-metal atoms (Rb, Na, and Li) and atomic hydrogen. An atomic wave with macroscopic coherence is formed as a result of condensation and the BEC has "atom laser" properties. In all BEC experiments, evaporative cooling is used at the final stage of cooling to reach temperatures low enough for the BEC transition to occur. As shown in Fig. 1, atomic gas is trapped in the magnetic potential and cooled by slow evaporation, which selectively removes the energetic atoms produced by interatomic elastic collisions. Below the critical temperature of BEC, quantum statistical effects in the atomic scattering process strongly affect evaporative cooling.
We have analyzed the dynamics of evaporative cooling on the basis of the quantum kinetic theory for a Bose gas and clarified the formation process of BEC. Our analytical approach provided a quantitative explanation of recent experimental results, and can be used over the whole temperature region of evaporative cooling and for alkali-metal and hydrogen atoms. The theory can be extended to optimize the experimental conditions so that larger amounts of BEC can be produced. Figure 2 shows the time evolution of the peak density of Na gas in the evaporative cooling process. The gas density rapidly increases after the BEC transition indicated by the arrow, which accounts for the rapid formation of BEC in the experiments. This density increase is caused by the fact that the stimulated scattering in elastic collision process strongly enhances the transition rate of cold atoms into the condensed state. The result clarifies that bosonic stimulation occurs during the formation process of BEC, which is considered to be an analog of stimulated emission of photons in the optical lasers.
[1] M. Yamashita, M. Koashi, and N. Imoto, Phys. Rev. A 59 (1999) 2243.

Fig. 1. Schematic diagram of evaporative cooling.

Fig. 2. Time evolution of peak density. The arrow indicates the point at which the BEC transition occurs.