​When I started to think about the dynamics of electrons excited by light, that is the time-dependence of spectroscopic processes, I got interested in non-perturbative theoretical treatments (because at resonance there are some tricky issues with perturbation theory). This line of thought leads quickly to the Rabi model – a system with only 2 electronic quantum states interacting with light treated as a classical time-dependent external field. The exact solution to this model can be found analytically; it exhibits interesting dynamical phenomena that are absent in perturbation theory. There aren’t too many non-trivial problems for which this is possible. Then, when I began to learn more about quantum optics, I was delighted to find that that the full quantum electrodynamics version of this model – two electron states interacting with a quantised electromagnetic field (ie photons) – is also analytically soluble. This is the Jaynes-Cummings model. These notes describe how this solution works and what can be done with it. There’s lots that can be learned from this, especially useful theoretical techniques for handling problems of this kind, things like the mapping of any 2-state system on to a spin ½ system. Nowadays 2-state models are quite widespread. They are called qubits.

Excitations in 2-state Systems.pdf