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

only one value of J is possible from this configuration. This single ground state
term can be written compactly using Russel-Saunders notation as 5 2 S1/2. The
meaning of this term is as follows. The first number is the principle quantum
number n of the outer electron. The superscript represent 2S + 1, and here
since S = 1/2 is 2. The uppercase letter corresponds to the total orbital
angular momentum L such that S = 0, P = 1, D = 2, F = 3 . . . The subscript
represents the value of the total electronic angular momentum J.
The configuration of the first excited state of 87 Rb is [Kr]5p. Because
in this state L = 1 there are two possible values of J, 1/2 and 3/2, leading
to two possible terms 5 2 P1/2 and 5 2 P3/2. Since the value of ∆E depends on J
these two terms are split in energy giving rise to a fine-structure doublet. The
two transitions 5 2 S1/2 → 5 2 P1/2 and 5 2 S1/2 → 5 2 P3/2 are known respectively
as the D1 and D2 transitions. The D1 transition is at ≈ 795 nm while the
D2 is at ≈ 780 nm. Because these two transitions are easily resolved by many
lasers they are typically treated separately. Indeed, the work done in this
dissertation used the D2 transition exclusively.
2.2.2 Hyperfine Structure
The hyperfine splitting of atomic energy levels is due to the interaction
of the total electronic angular momentum J with the total nuclear angular
momentum I. As the name suggests this effect is even smaller than the fine
structure splitting, reduced by the factor ∼ me/MP ≈ 1/1836 which is the
electron to proton mass ratio. As in the case of the fine structure, we can form
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