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Consider we want coupling between two hyperfine levels both in the ground state of 87Rb atom. Is the dipole transition rules still valid if we use RF or microwave?

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The selection rules concern the conservation of angular momentum when considering the photon + atom system. Thus, the selection rules are the same for RF and microwave illumination. However, RF and microwave photons have orders of magnitude different frequencies and this is very relevant for using them to drive atomic transitions.

The two hyperfine levels in Rb are separated by 6.8 GHz. This is a frequency which is squarely in the realm of microwave, not RF. I consider anything between 1 MHz and a few hundred MHz to be definitely RF. outside of that range it may also be RF but it gets hazier. In any case, if you try to drive a hyperfine transition using RF illumination at a few hundred MHz it will not work because you are too far off resonance. Thus, the reason you can't drive hyperfine transitions isn't because it is forbidden by selection rules, but rather because it is highly suppressed spectroscopically.

RF is rather used to drive transitions between different sublevels within either the $F=1$ or $F=2$ hyperfine manifolds.

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  • $\begingroup$ Thank you! Yes I know RF is usually applied to drive between Zeeman sublevels. $\endgroup$ – Jason Tao Sep 22 '18 at 16:02

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