The LASER beam is producing linearly polarized light which can be thought of as to be produced by equal number of R state photons and L state photons.Therefore,the Hg+ ion has equal probability of interacting with +h spin photons or -h spin photons[Hecht,p-330:discussion on angular momentum picture of photon].Therefore, as a whole,the LASER light cannot possibly impart angular momentum to any of the ions and flip its spin.Hence,the probability of (resonant) scattering is small.This makes the experiment a succession of individual photon collisions by one OR the other of the two ions---ONE AT A TIME.The observed scattering is non-resonant scattering.
If the ions were point scatterers,they would have scattered the light (may be their unique P state would have changed---but as far as interference is concerned,state of polarization does not matter).Light scattered from the trap material would not interfere for lack of coherence. Whereas,scattered light from the two scondary point sources will maintain constant phase relationship and will interfere.This way it is equivalent to Young's double slit experiment.
Even though we started with linearly polarized light,it's not ideal.A few trace of elliptically polarized light will invole unequal count of R and L state.As a ressult,net angular momentum CAN BE imparted on the Hg+ ions (though probability is extremely small).This corresponds to resonant scattering where spin-flip occurs.More generally,where there is no spin-flip,non-resonant scattering occurs and scattered wave produce interference patterns.
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