Comparison of squashing and self-consistent input-output models of quantum feedback

We re-approach the comparison of two models related to the same scheme. The first one admits that in the feedback loop between the photon annihilation and creation operators, unusual commutation relations hold. As a consequence, in the feedback loop, squashing of the light occurs. In the second one, the description arrives at the feedback loop via unitary transformations. But it is obvious that the unitary transformation which describes the modulator changes even the annihilation operator of the mode which passes by the modulator which is not natural. The first model could be called “squashing model” and the second one could be named “self-consistent model”. Although the predictions of the two models differ only a little and both the ways of analysis have their advantages, they have also their drawbacks and further investigation is possible.