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2-level Hyperfine splitting in the ground state $S_{1/2}$: $F=I-1/2$, $F=I+1/2$

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single electron

$S=1/2$

two hyperfine ground state:

$\left|J=1/2, F=I-1/2\right>$,

$\left| J=1/2, F=I+1/2 \right>$

hyperfine spliting

$S=1/2$, $L=0$ → $nS_{1/2}$

$S=1/2$, $L=1$ → $nP_{1/2}$, $nP_{3/2}$

Laser cooling: repump is required.

clock transition

$\left|F=I-1/2, m_F = 0\right>$

$\left|F=I+1/2, m_F = 0\right>$