Thesis (pdf) - Swinburne University of Technology

Chapter 2: Theoretical Background
During each scattering event, both energy and momentum have to be con-
served. The force that an atom experiences in a light field is the product of
the scattering rate and the momentum that is transferred to the atom in each
scattering process.
�F = ¯h Γ
2
s0
1 + s0 + (2∆/Γ) 2 · � k (2.33)
To cool an atom, we need to reduce the thermal motion. This can be
done by the force of the spontaneous scattering. Each spatial direction can be
cooled by one pair of beams if we use light with a negative detuning ∆ < 0 and
irradiate the atom with a pair of counterpropagating beams of same intensity
and detuning.
Consider an atom moving with a velocity �v due to the thermal motion. The
Doppler effect will shift the frequency of the light of the counterpropagating
beam to a different, smaller detuning than the rest frame detuning ∆, so
the effective detuning the atom experiences is ∆ − �v · � k. Under the same
conditions the atom sees a higher detuning from the light propagating in the
same direction. The probability to absorb a photon is different for each beam:
it is higher for the counter propagating beam. After each absorption, a photon
will be emitted by the atom. This is done isotropically and after many cycles
the momentum change due to the emissions averages out. The atom will have
experienced a net momentum transfer that is directed against its propagation
and slowing it in this direction. As this is done in every spatial direction,
the undirected thermal motion is reduced and thus the atom is cooled. This
procedure has been termed “optical molasses”, as in the linear approximation
of equation (2.33) the force is linear in the velocity of the atom like viscous
damping in mechanics.
Involved with the re-emission of the photons is a heating process; so the
lowest possible temperatures that can be reached this way is the equilibrium
between the cooling and the heating process. It can be shown that the lowest
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