Understanding Atomic Decay Pathways

[Higgy]

I've drawn up a simple system to help with my question.

Suppose we prepare an atom in an excited state (| 4 \rangle in the figure), and it can spontaneously decay to the ground state (| 1 \rangle) through either of two intermediate states (| 2 \rangle or | 3 \rangle).

Is the probability that it decays along a particular pathway dependent only on the transition dipole matrix elements connecting the relevant states of that pathway?

Is there a way (even for a similar, but different system) that I could "force" the atom to decay one way and not the other?

I'm trying to dream up an exhaustive list of possibilities (which might end up being a short list). One thought I had was to apply a electric field to Stark shift the states out of resonance (but the system becomes complicated, due to mixing...). Similarly with a magnetic field, if I had specified magnetic sublevels.

Just thought I'd put the question out there to see if there are any interesting related phenomena that people know of.

 

[DrClaude]

The two paths may not be equivalent. For instance, one may be related to a dipole forbidden transition, meaning the other path will dominate.

In general, it is not possible to change the relative natural decay rate of the two paths. However, if the states are degenerate, it could be in some cases possible to use that degeneracy to affect the decay, if that decay is not the same for all sub-states.

 

[Dr_Nate]

What you are trying to do is to change the overlap integrals. An electric or magnetic field will change the shape of the wave function of those states, so yes it is possible, but any calculations needed will not be trivial.