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European Quantum Electronics Conference (EQEC)

How to distinguish among several photons

Jaroslav Řeháček, Z. Hradil, Jan Peřina, Ondřej Haderka

Published Jan 1, 2003• 0 citations
Publisher

Abstract

The paper describes on the possibility of detecting photons using the proposed setup. Different channels of the setup are adjustable by means of a variable ratio coupler. Photon number distribution may be estimated using the maximum likelihood method. The information obtained may then quantified using the Fisher information. Equivalent efficiency of an ideal photodetector that can be associated with realistic detection is defined.

DOI
10.1109/eqec.2003.1314201

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The paper describes on the possibility of detecting photons using the proposed setup. Different channels of the setup are adjustable by means of a variable ratio coupler. Photon number distribution may be estimated using the maximum likelihood method. The information obtained may then quantified using the Fisher information. Equivalent efficiency of an ideal photodetector that can be associated with realistic detection is defined.
We give a detailed analysis of an indirect method used to obtain the photon distribution of a single-mode field using only on/off avalanche photodetectors. The method is based on measuring the field at different quantum efficiencies and then inferring the photon distribution by maximum-likelihood estimation. We address the case when only a limited range of quantum efficiency is available and when these values are not precisely known. The convergence of the method and its robustness against fluctuations are illustrated by means of numerically simulated experiments.
In optical quantum information processing, two of the most basic elements are the sources of quantum mechanical states of light, and the devices that can detect these states. In this chapter, we narrow this down to photon sources and photodetectors. We will describe first how detectors work, starting from abstract ideal detectors, via a complete description of realistic detectors in terms of POVMS, to a brief overview of current photodetectors. Subsequently, we will define what is a single-photon source, and how we can determine experimentally whether a source produces single photons or something else. Having laid down the ground rules, we will survey some of the most popular ways photons are produced in the laboratory. Finally, we take a look at the production of entangled photon sources and quantum non-demolition measurements of photons. A mathematical model of photodetectors Photodetectors are devices that produce a macroscopic signal when triggered by one or more photons. In the ideal situation, every photon that hits the detector contributes to the macroscopic signal, and there are no ‘ghost’ signals, or so-called dark counts. In this situation we can define two types of detector, namely the ‘photon-number detector’, and ‘detectors without number resolution’. First, the photon number detector is a (largely hypothetical) device that tells us how many photons there are in a given optical mode that is properly localized in space and time. This property is called ‘photon-number resolution’.
We study the problem of estimating the magnitude of a Gaussian beam displacement using a two-pixel or ``split'' detector. We calculate the maximum likelihood estimator and compute its asymptotic mean-squared error via the Fisher information. Although the signal-to-noise ratio is known to be simply related to the Fisher information under idealized detection, we find the two measures of precision differ markedly for a split detector. We show that a greater signal-to-noise ratio ``before'' the detector leads to a greater information penalty, unless adaptive realignment is used. We find that with an initially balanced split detector, tuning the normalized difference in counts to 0.884753...0.884753...0.884753... gives the highest posterior Fisher information, which provides an improvement by at least a factor of about 2.5 over operating in the usual linear regime. We discuss the implications for weak-value amplification, a popular probabilistic signal amplification technique.