Describing small, NRQM systems purely in terms of photons

Question

Is there a canonical way to describe an open, non-relativistic quantum system with density matrix $\rho(t)$ entirely in terms of the light that it emits and absorbs (and vice versa?) Or is it possible in general for a density matrix trajectory $\rho(t)$ to be induced by several (e.g. possibly contrived and time dependent) photon baths?

Answer 1

For Markovian systems, this is possible in a certain sense. If the quantum system is linearly coupled to the bath (which is usually the case, e.g. in light-matter interaction, in cavity-bath interaction etc.), one can write an input-output relation

$$\hat{b}_\mathrm{out}(t) = \hat{b}_\mathrm{in}(t) + i\kappa\hat{a}(t)$$

where $b$ are the bath operators, $a$ is the system operator and $\kappa$ the coupling between them.

This equation implies that if you are able to measure/specify the correlation function of the input and output operators, you are able to reconstruct the corresponding correlation function of the system operator.