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

and Claude Cohen-Tannoudji discovered that cooling beyond the Doppler limit
was due to an interaction between the optical field and the atom’s magnetic
sublevels [12].
The effect responsible for the additional cooling can be understood by
considering an atom with a ground state total electronic angular momentum
J = 1/2 and an excited state total electronic angular momentum J ′ = 3/2
moving through a standing wave formed by two counter-propagating beams
with orthogonal linear polarization.
As indicated in Fig. 2.9(a) the relative strength of the transitions de-
pend on the value of mJ in the lower (J = 1/2) and upper (J ′ = 3/2) state.
For example, for σ + polarized light, which by definition drives transitions with
∆mJ = +1, the coupling of the|J = 1/2,mJ = 1/2〉 → |J = 3/2,mJ = 3/2〉
transition is three times stronger than the coupling of the |J = 1/2,mJ =
−1/2〉 → |J = 3/2,mJ = 1/2〉 transition. On the contrary, for σ − polar-
ized light, which drives transitions with ∆mJ = −1, the coupling of the |J =
1/2,mJ = −1/2〉 → |J = 3/2,mJ = −3/2〉 transition is three times stronger
than the coupling of the |J = 1/2,mJ = 1/2〉 → |J = 3/2,mJ = −1/2〉 transi-
tion. The relative strength of all allowed electric dipole transition are given as
integer values in this figure and can be calculated using the formalism outlined
in Sec. 2.6.
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