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.
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