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

Using this relation and introducing the on-resonance damping rate Γ ≡ Γω0 =
(ω0/ω) 2 ΓL allows the polarizability to be written as [68]
Γ/ω 2 0
α = 6πǫ0c 3
ω2 0 − ω2 − i(ω3 /ω3 . (2.51)
0)Γ
Interestingly, the semi-classical approach which treats the atom as a
two-level quantum system interacting with a classical field yields the same
result in the low-saturation limit with one notable exception. The damping
rate must be found from the dipole matrix element between the ground and
excited state.
Γ = ω3 0
|〈e|µ|g〉|2
3πǫ0c3 (2.52)
But for the D lines in alkali atoms, including 87 Rb, which are strongly allowed
dipole transitions the classical estimation agrees with the true decay rate to
within a few percent [68].
Using the classical estimation for α in the equation for the dipole po-
tential (Eq. 2.46) yields a very useful result, valid in the limit of large detuning
and negligible saturation
Udip(r) = 3πc2
2ω 3 0
Γ
I(r). (2.53)
∆
Here ∆ ≡ ω − ω0 is the optical detuning from resonance. Udip is inversely
proportional to the optical detuning which can take on both positive and neg-
ative values. When ω > ω0, so-called blue-detuning, the potential is positive,
and atoms experience a repulsive force pushing them away from local intensity
maxima. When ω < ω0, so-called red-detuning, atoms are pulled into local
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