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Optics and Spectroscopy

Decoherence of the field in quantum nondemolition photon number measurement using the Kerr nonlinearity

A. V. Kozlovskiĭ

Published Nov 1, 2004• 0 citations
Publisher

Abstract

The role of decoherence of an electromagnetic field in the process of quantum nondemolition measurement of the number of photons using a nonlinear Mach-Zehnder interferometer is investigated. This decoherence is caused by distributed losses in a Kerr medium. A long interaction time between the field and the medium is required to achieve a high accuracy in the photon number measurement. The losses in the Kerr medium accompanying the resonance four-wave interaction between the measured and the probe fields lead to a measurement error close to unity at γτ ≫1 (γ is the rate of losses in the medium, and τ is the time of interaction between the field and the medium); consequently, nondemolition quantum measurement turns out to be impossible in the scheme considered. Under these conditions, an increase in the intensity of the probe field does not result in achievement of the required measurement accuracy.

DOI
10.1134/1.1828626

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The role of decoherence of an electromagnetic field in the process of quantum nondemolition measurement of the number of photons using a nonlinear Mach-Zehnder interferometer is investigated. This decoherence is caused by distributed losses in a Kerr medium. A long interaction time between the field and the medium is required to achieve a high accuracy in the photon number measurement. The losses in the Kerr medium accompanying the resonance four-wave interaction between the measured and the probe fields lead to a measurement error close to unity at γτ ≫1 (γ is the rate of losses in the medium, and τ is the time of interaction between the field and the medium); consequently, nondemolition quantum measurement turns out to be impossible in the scheme considered. Under these conditions, an increase in the intensity of the probe field does not result in achievement of the required measurement accuracy.
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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.
This paper intends to clarify some issues in the theory of quantum measurement by taking advantage of the self-consistent quantum formulation of nonlinear optics. A quantum-nondemolition measurement of the photon number of an optical pulse can be performed with a nonlinear Mach-Zehnder interferometer followed by a balanced detector. The full quantum-mechanical treatment shows that the shortcut in the description of the quantum-mechanical measurement, the so-called ``collapse of the wave function,'' is not needed for a self-consistent interpretation of the measurement process. Coherence in the density matrix of the signal to be measured is progressively reduced with increasing accuracy of the photon-number determination. The quantum-nondemolition measurement is incorporated in the double-slit experiment and the contrast ratio of the fringes is found to decrease systematically with increasing information on the photon number in one of the two paths. The ``gain'' in the measurement can be made arbitrarily large so that postprocessing of the information can proceed classically.
The parity of photonic number states is known to be an important observable for quantized electromagnetic fields with applications to quantum information processing and to Heisenberg-limited measurement of phase shifts in quantum interferometry performed with maximally entangled states and with twin number states. In this paper we describe an approach to the quantum nondemolition measurement of parity for quantized optical fields. The method proposed involves the use of a cross-Kerr interaction where we assume a large Kerr nonlinearity is available through the techniques of electromagnetically induced transparency. Our proposed method does not require the measurement of photon number but rather measures parity directly. The method not only allows for the quantum nondemolition measurement of parity but also allows for the von Neumann projection of parity eigenstates from an arbitrary field state. The generation and detection of higher-order parity eigenstates is also discussed. Losses from dissipation and the effects of detector efficiency are considered.