Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space

Ulf Leonhardt
Phys. Rev. A 48, 3265 – Published 1 October 1993
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Abstract

A lossless beam splitter (a dielectric interface, a passive interferometer, or a linear coupler) changes the quantum state of two incident modes by an SU(2) transformation. Apart from phase shifting, the argument of the quadrature wave function of the system undergoes a rotation. Quasiprobabilities are changed by the inverse mode transformation. The use of balanced beam splitting allows the simultaneous measurement of conjugate quadrature components via homodyning the emerging beams with two strong coherent reference fields that differ in their phases by π/2. The measured probability distribution is given by a generalized Q function. It depends on the state of the field entering the second beam-splitter port. For a vacuum, the Q function will be obtained. The use of unbalanced beam splitting allows the measurement of a squeezed Q function without using squeezed states. Dissipation in Gaussian reservoirs corresponds exactly to a heuristic beam-splitter model. As a mathematical tool, the Fokker-Planck equation of damping in phase-sensitive reservoirs and the corresponding quantum master equation were solved. The dissipative decay of a Schrödinger-cat state was studied as an example. The sensitivity of quantum coherence with respect to damping can be interpreted geometrically.

  • Received 6 May 1993

DOI:https://doi.org/10.1103/PhysRevA.48.3265

©1993 American Physical Society

Authors & Affiliations

Ulf Leonhardt

  • Arbeitsgruppe ‘‘Nichtklassische Strahlung’’ der Max-Planck-Gesellschaft an der Humboldt-Universität zu Berlin, Rudower Chaussee 5, 12484 Berlin, Germany

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Vol. 48, Iss. 4 — October 1993

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