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Optoelectronics Instrumentation and Data Processing

Study of photon statistics using a compound Poisson distribution and quadrature measurements

Yu. I. Bogdanov, Nadezhda A. Bogdanova, Konstantin G. Katamadze, G. V. Avosopiants, Vladimir F. Lukichev

Published Sep 1, 2016• 17 citations
Publisher

Abstract

This paper describes the model of a compound Poisson distribution for photon statistics with regard to their bunching in Fock states, thermal states, and others. The method of generating functions is used to calculate the probability distributions, moments, and correlation functions. The parameters of conditional states arising from the subtraction of photons by splitting the beam are determined. The problem of state reconstruction with regard to quadrature quantum measurements is considered. The study is aimed at developing high-precision methods for generating and controlling optical quantum states.

DOI
10.3103/s8756699016050095

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This paper describes the model of a compound Poisson distribution for photon statistics with regard to their bunching in Fock states, thermal states, and others. The method of generating functions is used to calculate the probability distributions, moments, and correlation functions. The parameters of conditional states arising from the subtraction of photons by splitting the beam are determined. The problem of state reconstruction with regard to quadrature quantum measurements is considered. The study is aimed at developing high-precision methods for generating and controlling optical quantum states.
The estimation of high order correlation function values is an important problem in the field of quantum computation. We show that the problem can be reduced to preparation and measurement of optical quantum states resulting after annihilation of a set number of quanta from the original beam. We apply this approach to explore various photon bunching regimes in optical states with gamma-compounded Poisson photon number statistics. We prepare and perform measurement of the thermal quantum state as well as states produced by subtracting one to ten photons from it. Maximum likelihood estimation is employed for parameter estimation. The goal of this research is the development of highly accurate procedures for generation and quality control of optical quantum states.
The statistical distribution for the number of bosons in a specified subsystem of a finite-dimensional multilevel system is obtained and investigated under conditions for which the total number of particles is a random variable characterized by the Poisson distribution. The resulting hyper-Poisson distribution is determined by the confluent hypergeometric function and contains as its particular limiting cases the Poisson distribution, as well as the single-mode and multimode thermal distributions. The developed model can be efficiently used to describe the thermal characteristics of bounded quantum systems, as well as in the problems of statistical reconstruction of optical quantum states, processes, and detectors.
We present a study of optical quantum states generated by subtraction of photons from the thermal state. Some aspects of their photon number and quadrature distributions are discussed and checked experimentally. We demonstrate an original method of up to ten photon subtracted state preparation with use of just one single-photon detector. All the states were measured with use of a balanced homodyne technique and the corresponding density matrices were reconstructed. The fidelity between desired and reconstructed states exceeds 9999%99. Combined with homodyne detection it can also be used for precise measurement of high-order autocorrelation functions.