The U(1,1) and U(2) transformations realized by three-mode interaction in the respective parametric approximations are studied in conditional measurement, and the corresponding non-unitary transformation operators are derived. As an application, the preparation of single-mode quantum states using an optical feedback loop is discussed, with special emphasis of Fock state preparation. For that example, the influence of non-perfect detection and feedback is also considered.
@article{arxiv.quant-ph/0007050,
title = {Conditional quantum state engineering in repeated 2-photon down conversion},
author = {J. Clausen and H. Hansen and L. Knoll and J. Mlynek and D. -G. Welsch},
journal= {arXiv preprint arXiv:quant-ph/0007050},
year = {2016}
}