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Journal of Optics B Quantum and Semiclassical Optics

Phase space complementarity in QND measurement of coherent state superposition

Radim Filip

Published Nov 27, 2001• 2 citations
Publisher

Abstract

In the proposed quantum optical experiment, the complementarity and entanglement exhibited in quantum non-demolition (QND) measurement of coherent state superposition is analysed. This problem can be considered as a continuously variable analogue of the well known exhibition of complementarity in Young's double-slit interferometer. Analysis of the relationship between distinguishability and interference in phase space, as well as quantum entanglement, is performed using directly measurable quantities obtained using homodyne detection.

DOI
10.1088/1464-4266/3/6/308

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In the proposed quantum optical experiment, the complementarity and entanglement exhibited in quantum non-demolition (QND) measurement of coherent state superposition is analysed. This problem can be considered as a continuously variable analogue of the well known exhibition of complementarity in Young's double-slit interferometer. Analysis of the relationship between distinguishability and interference in phase space, as well as quantum entanglement, is performed using directly measurable quantities obtained using homodyne detection.
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We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr\"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.
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.