Conditional quantum state engineering in repeated 2-photon down conversion

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.Comment: 17 pages, 4 figures, using a4.st

Efficient optical quantum state engineering

We discuss a novel method of efficiently producing multi-photon states using repeated spontaneous parametric downconversion. Specifically, by attempting downconversion several times, we can pseudo-deterministically add photons to a mode, producing various several-photon states. We discuss both expected performance and experimental limitations.Comment: 4 pages, 4 figure

Conditional quantum-state transformation at a beam splitter

Using conditional measurement on a beam splitter, we study the transformation of the quantum state of the signal mode within the concept of two-port non-unitary transformation. Allowing for arbitrary quantum states of both the input reference mode and the output reference mode on which the measurement is performed, we show that the non-unitary transformation operator can be given as an $s$-ordered operator product, where the value of $s$ is entirely determined by the absolute value of the beam splitter reflectance (or transmittance). The formalism generalizes previously obtained results that can be recovered by simple specification of the non-unitary transformation operator. As an application, we consider the generation of Schr\"odinger-cat-like states. An extension to mixed states and imperfect detection is outlined.Comment: 7 Postscript figures, using Late

Quantum state conversion by cross-Kerr interaction

A generalized Mach-Zehnder-type interferometer equipped with cross-Kerr elements is proposed to convert N-photon truncated single-mode quantum states into (N+1)-mode single-photon states, which are suitable for further state manipulation by means of beam splitter arrays and ON/OFF-detections, and vice versa. Applications to the realization of unitary and non-unitary transformations, quantum state reconstruction, and quantum telemanipulation are studied.Comment: 22 pages, 4 figures, using a4.st