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International Journal of Quantum Information

HIGH-ORDER PHOTON-NUMBER CORRELATIONS: A RESOURCE FOR CHARACTERIZATION AND APPLICATIONS OF QUANTUM STATES

Alessia Allevi, Stefano Olivares, Maria Bondani

Published Dec 1, 2012• 34 citations
Publisher

Abstract

We measure high-order correlation functions of detected-photon numbers in the mesoscopic regime by means of hybrid photodetectors. The analytical expressions for correlations are evaluated in terms of quantities that can be experimentally accessed by a selfconsistent analysis of the detectors' outputs. We demonstrate that high-order correlations can be used to characterize the nature of the optical states, for instance by better discriminating between classical and quantum behavior even in critical situations, such as multimode twin-beam state. The results are in very good agreement with the theory, both for classical states and quantum states.

DOI
10.1142/s0219749912410031

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We measure high-order correlation functions of detected-photon numbers in the mesoscopic regime by means of hybrid photodetectors. The analytical expressions for correlations are evaluated in terms of quantities that can be experimentally accessed by a selfconsistent analysis of the detectors' outputs. We demonstrate that high-order correlations can be used to characterize the nature of the optical states, for instance by better discriminating between classical and quantum behavior even in critical situations, such as multimode twin-beam state. The results are in very good agreement with the theory, both for classical states and quantum states.
We implement a direct detection scheme based on hybrid photodetectors to experimentally investigate high-order correlations for detected photons by means of experimentally accessible quantities. The scheme is self-consistent, allowing the estimation of all the involved parameters (quantum efficiency, number of modes, and average energy). In particular, we show how high-order correlation functions can be exploited to fully characterize bipartite multimode states in regimes realistic for quantum technology, that is, in the mesoscopic photon-number domain and with limited quantum efficiency. Furthermore, we introduce a nonclassicality criterion based on a simple linear combination of high-order correlation functions.
We demonstrate that by using a pair of hybrid photodetectors, it is possible to quantify the photon-number correlation coefficient between the components of a classical state described by non-trivial statistics and by a non-Gaussian Wigner function. The measurements, performed in the quite unexplored mesoscopic domain (up to 100 photons incident onto the detector), are in good agreement with the theoretical predictions, and thus open the possibility of performing further tests on this exotic state for its application in the field of quantum information.
Abstract The calculation of autocorrelation functions represents a routinely used tool to characterise quantum states of light. In this paper, we evaluate the g(2) function for detected photons in the case of mesoscopic multi-mode twin-beam states in order to fully investigate their statistical properties starting from measurable quantities. Moreover, we show that the second-order autocorrelation function is also useful to estimate the spurious effects affecting the employed Silicon-photomultiplier detectors.
We demonstrate that by using pairs of photodetectors endowed with internal gain we are able to quantify the photon-number correlation coefficient between the two components of a pulsed bipartite state in the "mesoscopic" intensity regime (less than 100 mean photons). We compare the performances of hybrid photoemissive detectors to those of multipixel silicon photon counters and demonstrate that the absence of significant noise allows the evaluation of the variance of the distribution of the differences in photon numbers, and hence of the shot-noise level, without any correction.
Harnessing entanglement as a resource is the main workhorse of many quantum protocols, and establishing the degree of quantum correlations of quantum states is an important certification process that has to take place prior to any implementations of these quantum protocols. The emergence of photodetectors known as photon-number-resolving detectors (PNRDs) that allow for accounting of photon numbers simultaneously arriving at the detectors has led to the need for modeling accurately and applying them for use in the certification process. Here we study the variance of difference of photocounts (VDP) of two PNRDs, which is one measure of quantum correlations, under the effects of loss and saturation. We found that it would be possible to distinguish between the classical correlation of a two-mode coherent state and the quantum correlation of a twin-beam state within some photo count regime of the detector. We compare the behavior of two such PNRDs. The first for which the photocount statistics follow a binomial distribution accounting for losses, and the second is that of Agarwal, Vogel, and Sperling for which the incident beam is first split and then separately measured by ON/OFF detectors. In our calculations, analytical expressions are derived for the variance of difference where possible. In these cases, Gauss' hypergeometric function appears regularly, giving an insight to the type of quantum statistics the photon counting gives in these PNRDs. The different mechanisms of the two types of PNRDs leads to quantitative differences in their VDP.