Complementarity in a quantum nondemolition measurement

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Abstract
We present an analysis of a quantum nondemolition (QND) measurement, which determines which of the two possible paths a photon follows through a Mach-Zehnder interferometer. The measurement is effected by the nonlinear Kerr effect. If a photon traverses the arm of the interferometer containing the Kerr medium, it shifts the phase of a probe beam and then continues through to the interferometer output. The measurement does not destroy the photon but does disturb its phase. Using various probe states, we show how such phase disturbances reduce fringe visibility and enforce a principle of complementarity; the more accurately the QND measurement determines the path of the photon, the lower is the fringe visibility. We determine the appropriate parameters to optimize the observation of the two complementary quantities.