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Journal of the Optical Society of America B

Optimal precision of contrast estimation between sub-Poissonian light beams

Julien Fade

Published Jun 29, 2011• 0 citations
Publisher

Abstract

Using a binomial model of sub-Poissonian light statistics, we determine and analyze the Cramer–Rao lower bound for the estimation of the contrast between two sub-Poissonian light beams. The study of this bound shows that the optimal precision of contrast estimation can be maximally improved in proportion to the Fano factor of the sub-Poissonian light sources in comparison with standard coherent light. Numerical simulations show that a simple contrast estimator can reach this bound. The general results obtained are analyzed for two practical situations involving contrast estimation between two intensity levels of a single sub-Poissonian beam.

DOI
10.1364/josab.28.001752

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Using a binomial model of sub-Poissonian light statistics, we determine and analyze the Cramer–Rao lower bound for the estimation of the contrast between two sub-Poissonian light beams. The study of this bound shows that the optimal precision of contrast estimation can be maximally improved in proportion to the Fano factor of the sub-Poissonian light sources in comparison with standard coherent light. Numerical simulations show that a simple contrast estimator can reach this bound. The general results obtained are analyzed for two practical situations involving contrast estimation between two intensity levels of a single sub-Poissonian beam.
Based on a standard binomial model of sub-Poissonian photocounting statistics, we analyze the discrimination performance between the two possibilities that light has been potentially absorbed or not. For that purpose, we study with numerical simulations the behavior of different information-theory-based measures of the contrast and show that the Chernoff measure allows one to obtain a useful contrast characterization that has simple physical interpretation and that helps in analyzing the benefit of using sub-Poissonian light to improve detection tasks.
Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here, we prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.
We study sub-Poissonian photon statistics of light in interaction of a single mode radiation, initially either in a coherent state or in a superposed coherent state with an assembly of two-level atoms using the Hamiltonian, H = ω(a+a + Sz) + g(aS+ + a+ S–) in natural units, where a+ and a are creation and annihilation operators, Sz, S ± are the collective Dicke operators, g is the coupling constant, and ω is the energy of the photons and also the separation between the two atomic levels. We study the cases of (i) a single two-level and (ii) of two two-level atoms interacting with a single mode coherent or superposed coherent radiation. We find that for large coupling time gt, Fano factor shows collapses and revival phenomena, and that the variation is large for small mean number of photons. We also find that in the case of two two-level atoms, photon statistics shows larger sub-Poissonian than the case of a single two-level atom, and that there is no definite relationship between squeezing and sub-Poissonian photon statistics of light.
States with sub-Poissonian photon-number statistics obtained by post-selection from twin beams are experimentally generated. States with Fano factors down to 0.62 and mean photon numbers around 12 are reached. Their quasi-distributions of integrated intensities attaining negative values are reconstructed. An intensified CCD camera with a quantum detection efficiency exceeding 20% is utilized both for post-selection and beam characterization. Experimental results are compared with theory that provides the optimum experimental conditions.
We analyze an intensity feedforward scheme to produce a sub-Poissonian (amplitude-squeezed) light beam from the intensity-correlated twin beams generated by a nondegenerate parametric amplifier. Photon-number measurement of the idler beam at the output of the parametric amplifier is linearly fed forward onto the output signal beam using an amplitude modulator. The minimum available Fano factor is shown to be 1/(2g-1), where g is the parametric amplifier gain, and is equal to the nonclassical intensity-noise-reduction factor of the twin beams at the output of the parametric amplifier. By changing the frequency of the input-signal beam, tunable sub-Poissonian light can be generated with this scheme for application in precision absorption spectroscopy.