Beam Splitter: looking for a "not-typical" second quantization but full-quantum description In all the books of Quantum Optics I read, the theory of beam-splitter (BS) is presented in more or less the same way, e.g. introduction of the transmission-reflection matrix, case study of the single photon and vacuum at the BS inputs, or example with the coherent states, or Hong-Ou-Mandel effect.
However, I'm looking for a quantum description of the BS in terms of the interaction between the photons and the atoms, e.g. with the Fermi Golden rule. 
Please, can someone point me to some paper and/or book where I could find such description?
 A: @TrulyIgnorant 
I personally think this is a great question, and surprisingly one that has not yet been fully answered to my knowledge! There are two works that come very close to putting together a first-principles derivation that is fully quantum-mechanical, i.e. by quantizing the modes of a beam-splitter, showing their connection to a Hamiltonian and taking a limit that reproduces the unitary transformation you're referring to.
The papers are:
"Quasi mode theory of the beam splitter-a quantum scattering theory approach" by B. J. Dalton, Stephen M. Barnett & P. L. Knight
combined with
"A quantum scattering theory approach to quantum-optical measurements" B. J. Dalton, Stephen M. Barnett & P. L. Knight
In my advisor's group we're currently working on a tutorial that will go through this quantization and derivation to make it hopefully more clear - I'll try to post back here after we're done. A related question is how precisely to quantize a cavity coupled to the world - Sergio Dutra worked on this problem and distilled it very nicely in his book "Cavity Quantum Electrodynamics".
