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arXiv:quant-ph/0310066 · Physical Review A

High-efficiency quantum-nondemolition single-photon-number-resolving detector

William J. Munro, Kae Nemoto, Raymond G. Beausoleil, Timothy P. Spiller

Published Mar 31, 2005• 223 citations
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Abstract

We discuss an approach to the problem of creating a photon-number-resolving detector using the giant Kerr nonlinearities available in electromagnetically induced transparency. Our scheme can implement a photon-number quantum-nondemolition measurement with high efficiency $(\ensuremath{\sim}99%)$ using fewer than 1600 atoms embedded in a dielectric waveguide.

DOI
10.1103/physreva.71.033819

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We discuss an approach to the problem of creating a photon-number-resolving detector using the giant Kerr nonlinearities available in electromagnetically induced transparency. Our scheme can implement a photon-number quantum-nondemolition measurement with high efficiency (\ensuremath∼99(\ensuremath{\sim}99%)(\ensuremath∼99 using fewer than 1600 atoms embedded in a dielectric waveguide.
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.
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.
We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.