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Journal of Modern Optics

Optical state measurement by information transfer

David Thomas Pegg, Stephen Mark Barnett

Published Sep 1, 1999• 8 citations
Publisher

Abstract

Mathematically, the simplest state of light containing phase information is a superposition of the vacuum and the one-photon state and, as we show in this paper, such a state is reasonably simple to measure. We investigate how the information contained in a more complicated pure state of light, in particular the ratio of successive number-state coefficients, can be transferred selectively to fields in this two-state superposition for subsequent measurement. By this means the number-state representation of the more complicated state can be ascertained, provided there are no gaps in the number state distribution. We also discuss how to correct for the effect of non-unit efficiencies of the photodetectors involved in the transferral process.

DOI
10.1080/09500349908231363

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We suggest a method to prepare any chosen superposition a0∣0〉+a1∣1〉{a}_{0}|0〉{+a}_{1}|1〉a0​∣0〉+a1​∣1〉 of the vacuum and one-photon states. The method is based on a conditional double interferometer fed by a one-photon state and a coherent state. The scheme involves only linear optical elements and avalanche photodetectors, and therefore it should be realizable with current technology. A realistic description of the triggering photodetectors is employed, i.e., we assume that they can only check, with a certain efficiency, whether or not any photon is present. We discuss two working regimes, and show that output states with fidelity arbitrarily close to unit may be obtained, with nonvanishing conditional probability, also for low quantum efficiency at the photodetectors.
The quantization of light is the basis for quantum optics and has led to the observation of a multitude of genuine quantum effects which cannot be explained by classical physics. Yet, there exist different views when we refer to the distinct quantum character of light as opposed to classical fields. A major impact on how we describe photonic states is caused by the detection method we use for the quantum state characterization. In the theoretical modelling measuring light always means the recording of photon statistics of some kind, though the way we interpret the results is quite different and depends mainly on the intensity of actual detected light. If we use conventional photodiodes and monitor bright light, we attribute the detected statistics to quadrature measurements in a phase space representation, or—in other words—we identify the quantum state by studying its uncertainties of its field amplitude and phase properties which correspond to conjugate quantum observables. For multi-photon states with very low intensity we have to employ avalanche photodiodes (APDs) to be able to see any signal, but photon number resolution seems difficult in this regime. Recent developments allow one to ascertain information about the photon statistics from APD measurements opening up new routes for characterizing photonic states. In this article we review the different methods for modern quantum state metrology where we include theoretical aspects as well as the description of the state-of-the-art technology for measuring photon statistics.
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