Thanks. In that case I don’t think there is a contradiction with what I said, if there is no wave function corresponding to the atom (alone). I understood the original comment as saying that the quantum state of the atom during the transition between energy levels was a superposition of the corresponding pure states (i.e. a pure state) and I was objecting to that.
Yeah I mean that’s still fine. The entanglement between system and field never persists since the field is taken to be measured immediately. The systems are only non-separable as long as they’re entangled. See the notes by Steck on the derivation of the SME and SSE.
I agree that if the field is taken to be a degree of freedom entangled with the system under measurement, things are funnier. This experiment isn’t really like spontaneous or stimulated emission... where yeah, DURING the process, the photon pooped out is entangled with your subsystem. In the case of the present experiment there’s a much more subtle thing going on with a three level system where the bright-zero manifold is used as a witness to the dark-zero manifold, where the presence or lack thereof of fast jumps in the bright-zero manifold betray information about the dark-zero manifold, necessarily.
I've been reading a bit about quantum state diffusion, continuous measurements and quantum trajectories. My superficial understanding of the subject is the following. Let's say that you have an open system described by a reduced density operator evolving according to some master equation. The system will be in general described by a mixed state.
You can have an alternative representation with the quantum state changing in a non-deterministic way according to a stochastic equation. In this representation the quantum state remains pure for one "trajectory" but to describe the system you need to consider the ensemble of realizations. So you still have a mixture and the same density matrix as before.
I think it's a bit more subtle than this. Taking ensemble averages is itself a gesture of throwing information away, so yes, you do now have classical uncertainty that now may be represented by a density matrix. I think what I take issue with is "to describe the system." The master equations are deep down, kalman filters. They take some inputs and through bayes rule produce their best estimate of what state the system is in. Given perfect information, in this situation, they'll produce, somewhat miraculously, a complete description of the state of the system. If you had a person that was being bombarded by soccer balls from random directions you wouldn't say that an average of their muscle movements described the human-soccerball system. You'd wind up with something not particularly informative. Yes, you do need to take averages at some point... but you might want to average over a solid angle of impinging soccer balls... then you get somewhat deterministic, informative behavior.
I want to get across that this experiment is in some sense probing the way a quantum system processes quantum fluctuations. An ensemble average of traces therefore throws away/averages out the very thing that the system is responding to.
> Given perfect information, in this situation, they'll produce, somewhat miraculously, a complete description of the state of the system.
I don't think that the complete description of the system when the atom is going from a pure excited state to a pure ground state will include pure states of the atom which are superpositions of the excited state and the ground state. If we have a complete description of the system, the atom may be part of a larger system which is in a pure state and in that case the quantum state of the atom may be an improper mixture of the excited state and the ground state. The atom may also be in a pure state on its own, but then it will be either in the excited state or in the ground state.
That's all I said. I may be wrong but I fail to see in your comments a reason to think so.
Edit: By the way, I know an atom can in principle be in a state which is a superposition of states with different energies (I said so in my first comment). It's just that I don't think that happens during the spontaneous transition from one state to another. If it does happen, I would be glad to learn about it.
Edit2: Looking again at some quantum optics papers I see people argue that stochastic equations have a physical meaning and are not just a calculation device. Anyway, those interaction models are quite complex and full of approximations so it's not clear what "pure" means anymore...
