Quantum-state transformation by dispersive and absorbing four-port devices

The recently derived input-output relations for radiation at a dispersive a nd absorbing four-port device [T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1661 (1996)] are used to derive the unitary transformation that relates th e output quantum state to the input quantum state, including radiation and matter and without placing frequency restrictions. It is shown that for eac h frequency component the transformation can be regarded as a U(4) group tr ansformation, which can directly be calculated from the underlying complex refractive-index profile of the device without additional postulates. If fo r narrow-bandwidth radiation far from the medium resonances the absorption matrix of the four-port device can be disregarded, the well-known U(2) grou p transformation for a lossless device is recognized. Explicit formulas for the transformation of Fock states, coherent states, and phase-space functi ons are given. [S1050-2947(99)03406-X].