Conditional quantum-state engineering in repeated 2-photon down-conversion

Abstract.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 on Fock-state preparation. For that example, the influence of non-perfect detection and feedback is alsoconsidered.