Single-Photon Atomic Cooling - Raizen Lab - The University of ...

D2 transition in 87 Rb has a natural linewidth of 6 MHz due to the process of
radiative damping [70]. Doppler broadening smears this line out increasing its
observed width to ∼ 0.5 GHz at room temperature. The source of this broad-
ening can be understood by considering the relationship between the angular
frequency ω of radiation in the laboratory frame of reference and the angular
frequency ω ′ seen in a frame of reference moving at velocity v
ω ′ = ω − k · v, (2.96)
where k is the wavevector of the radiation and has a magnitude k = ω/c. This
equation is correct to first order in v/c and suffices in most situations, however
higher order Doppler effects must be considered in extremely precise spectro-
scopic measurements. As indicated by the dot product, it is the component of
velocity along the direction of ˆ k which is responsible for this shift. Therefore
to simplify this notation we assume a 1-D geometry so that k ·v = kv. Figure
2.13 illustrates these ideas for a single atom moving with velocity v to the
right. This atom sees radiation traveling to the right at a decreased frequency
and radiation traveling to the left at an increased frequency.
Consider now an ensemble which consists of atoms which absorb ra-
diation at frequency ω0 in their rest frame, i.e. when ω ′ = ω0. Atoms with
velocity v will absorb radiation when the Doppler effect shifts the frequency
into resonance
ω − ω0 = kv. (2.97)
If we assume that the ensemble is in thermal equilibrium then the
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