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Physical Review A

Multiple coincidences and the quantum state reconstruction problem

Henryk Paul, Päivi Törmä, T. Kiss, Igor Jex

Published Nov 1, 1997• 12 citations
Publisher

Abstract

We analyze the recently proposed method [H. Paul et al., Phys. Rev. Lett. 76, 2464 (1996)] for reconstructing the quantum state of a light field from multiple coincidences measured at the outputs of a passive multiport. We show that applying a large multiport the reconstruction of a pure state becomes possible using avalanche photodiode-type detectors. The presented simulations show that the photon chopping scheme is appropriate for the indirect measurement of the photon statistics of a weak nonclassical signal.

DOI
10.1103/physreva.56.4076

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We analyze the recently proposed method [H. Paul et al., Phys. Rev. Lett. 76, 2464 (1996)] for reconstructing the quantum state of a light field from multiple coincidences measured at the outputs of a passive multiport. We show that applying a large multiport the reconstruction of a pure state becomes possible using avalanche photodiode-type detectors. The presented simulations show that the photon chopping scheme is appropriate for the indirect measurement of the photon statistics of a weak nonclassical signal.
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Reconstruction of photon statistics of optical states provides fundamental information on the nature of any optical field and finds various relevant applications. Nevertheless, no detector that can accurately discriminate the number of incident photons is available, whereas reconstruction by quantum tomography is not an easily implementable technique suited for a diffuse use. Even if on/off detectors, as usual avalanche photodiodes operating in Geiger mode, seem useless as photocounters, recently it was shown that reconstruction of photon statistics is possible by considering variable quantum efficiency. We have experimentally demonstrated the potential of this technique by reconstructing photon statistics for various optical fields both in the cw and pulsed regime ranging from heralded photon states to multi-thermal and coherent ones. In this paper, after having introduced the method, a review of the results obtained for the mono-partite case is given and the extension to bi-partite case is presented in detail.
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.
Reconstruction of photon statistics of optical states provides fundamental information on the nature of any optical field and helps with various relevant applications. Nevertheless, no detector that can reliably discriminate the number of incident photons is available. On the other hand, the alternative of reconstructing the density matrix by quantum tomography leads to various technical difficulties that are particularly severe in the pulsed regime (where mode matching between a signal and local oscillator is very challenging). Even if on/off detectors, as usual avalanche photodiodes operating in Geiger mode, seem useless as photo-counters, it was recently shown how reconstruction of photon statistics is possible by considering a variable quantum efficiency. Here we present experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams in a scheme based on on/off avalanche photodetection assisted by maximum-likelihood estimation. Reconstructions of the distribution for both semiclassical and quantum states of light (as single photon, coherent, pseudothermal, and multithermal states) are reported for single-mode and multimode beams. The stability and good accuracy obtained in the reconstruction of these states clearly demonstrate the interesting potentialities of this simple technique.
We propose a design for a photon-counting detector that is capable of resolving multiphoton events. The basic element of the setup is a fiber loop, which traps the input field with the help of a fast electro-optic switch. A single weakly coupled avalanche photodiode is used to detect small portions of the signal field extracted from the loop. We analyze the response of the loop detector to an arbitrary input field and discuss both the reconstruction of the photon-number distribution of an unknown field from the count statistics measured in the setup and the application of the detector in conditional-state preparation.