The question: whenever you are dealing with quantum optics you will encounter a lot of unitary transformations very soon. A question that is in my mind for quite a long time is: Why does the discussion in a certain reference frame gives a global result that can be observed in the lab?
What I mean by that: Normaly, before starting discussing a physical system quantum physicists often happily transform the Hamiltonian with all kind of transformations until it looks simple enough to discuss it with the tools of linear algebra. Normally one uses simply the interaction picture: $ \tilde{H} = U H U^{\dagger}$ or a more sophisticated approach that conserves the Schrödinger Equation: $ \tilde{H} = U^{\dagger} H U + i \hbar \dot{U} U^{\dagger} $ for time-dependent transformations. I am aware that a unitary transformation is simply a change of reference frame which are equitable. But looking at it from a general relativity view, physics is not the same in accelerated frames. However a transformation, like the one in a rotating frame with $U = e^{i\omega |e\rangle \langle e| t}$ can be associated with transforming into an accelerated frame, can't it? So why does the physics that pops up at the end can be treated as a general result?
An example Consider the rabi oscillations happining to a two-level atom under the impact of a single mode "classical" light. We start with the dipole Hamiltonian, do some unitary transformation here and there and at the end we get a easy 2x2 matrix that describes the system and as a conclusion the rabi oscillations. But isn't that only the physics in the reference frame we transformed in?
Thanks for your hints ;) Philipp
