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?

Wolpertinger · Answer

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
$$hat{b}_mathrm{out}(t) = hat{b}_mathrm{in}(t) + ikappahat{a}(t)$$
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.

Describing small, NRQM systems purely in terms of photons

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