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?

  • $\begingroup$ If you wanted to do it "right", then you would have to formulate it in the language of quantum field theory. If you do that, of course, then the only field that has any interest in such a description goes away. Quantum mysticism only "works" because quantum mystics don't use a self-consistent description of the world to raise an aura of mystery. $\endgroup$
    – CuriousOne
    Mar 18, 2016 at 23:25
  • $\begingroup$ @CuriousOne Thank you for your comment! Please, could you elaborate more about "the only field that has any interest in such a description goes away " ? $\endgroup$ Mar 19, 2016 at 6:49
  • $\begingroup$ I really can't tell you why some people won't accept 80 year old physics that has proven to be correct at all levels. You have to ask them about that. $\endgroup$
    – CuriousOne
    Mar 19, 2016 at 8:09
  • $\begingroup$ @CuriousOne Sorry, but I do not understand the sense of your last comment: what are you meaning? $\endgroup$ Mar 19, 2016 at 8:37
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    $\begingroup$ @CuriousOne sorry but who are these "quantum mystics"? are they people who don't accept 80 years of proven results? I just simply asked for some reference from where transmission/reflection probabilities are expressed in terms of amplitude transition probabilities $\endgroup$ Mar 19, 2016 at 8:46

1 Answer 1



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".

  • $\begingroup$ Thank you very much for your answer, which I appreciate much more than the useless comments I received earlier. That's exactly what I was looking for and I look forward for reading your tutorial. Thanks again! $\endgroup$ Feb 1, 2018 at 7:53

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