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I'm referring to this question: Natural linewidth of hyperfine levels?

Let's take Rubidium-85 for example. It's written everywhere that the D2 line has a linewidth of around 6 MHz. But the D2 "line", a transition between fine structure levels, is basically just a composition of the underlying hyperfine lines, which are shifted in frequency by tens of MHz relative to the D2 line.

How can the D2 line have a linewidth of 6 MHz if the underlying hyperfine lines are shifted by way more than 6 MHz? My only explanation would be that the 6 MHz already refers to the hyperfine lines. But this would mean that they all have the same linewidth?

What's the truth here?

Emilio Pisanty
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Philipp
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1 Answers1

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Well, after asking some smart people and reading some papers, I can hopefully provide a satisfying explanation:

All hyperfine sub-levels from a certain fine structure level share the same lifetime / linewidth to a certain accuracy. They are not identical, but the differences are neglectable for most applications. Therefore, people say the D2 line has a linewidth of 6 MHz.

The rate of a certain dipole transitions is, to first order, determined by the dipole matrix element between the corresponding electronic total angular momentums $J$. $$ \Gamma_{J\rightarrow J'} \propto \frac{\left<J|r|J'\right>}{2J'+1} $$ The D2 line's hyperfine transitions share the same change in J, namely $3/2 \rightarrow 1/2$. The only difference between the hyperfine sub-levels with different $F$ from a certain fine structure level is the orientation of the electron spin (up or down), but nevertheless, they share the same $J$ and therefore the same rate / lifetime / linewidth.

Philipp
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