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

ω ω ω ω
Figure 2.13: The Doppler effect shifts the observed frequency of radiation
due to the atoms velocity. The atom travels to the right and sees radiation
traveling to the right at a decreased frequency and radiation traveling to the
left at an increased frequency.
velocity distribution is given by the 1-D Maxwell-Boltzmann distribution
f(v)dv = 1
u √ v2
e− u
π 2 , (2.98)
where u = 2kBT/m is the most probable speed for atoms. The absorption
profile g(ω) of this ensemble can be found by relating the velocity of the atoms
with their corresponding absorption frequency using Eq. 2.97, the result being
g(ω) =
c
√ e
uω0 π
c2
−
u2 ( ω−ω0 ) ω0 2
. (2.99)
This Doppler broadened profile has a Gaussian shape and a full width at half
maximum (FWHM) ∆ωD of
∆ωD = 2ω0
√ u
ln2 , (2.100)
c
which for 87 Rb is 1.4 × 10 −6 , limiting the resolution of spectroscopic mea-
surements to approximately 1 part in 10 6 . Because we use a laser frequency
locking scheme which is referenced to 87 Rb transition lines, the resolution with
which we resolve these transitions places a limit on our ability to control the
frequency of the lasers. The needed resolution is 1 part in 10 8 so we must use
a spectroscopic technique which suppresses the effect of Doppler broadening.
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