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European Journal of Physics

Computer simulation for calculating the second-order correlation function of classical and quantum light

M. Facão, A Lopes, A L Silva, Pedro E. S. Silva

Published May 9, 2011• 9 citations
Publisher

Abstract

We propose an undergraduate numerical project for simulating the results of the second-order correlation function as obtained by an intensity interference experiment for two kinds of light, namely bunched light with Gaussian or Lorentzian power density spectrum and antibunched light obtained from single-photon sources. While the algorithm for bunched light was based on a previous publication, the one for antibunched light was developed by master students attending a Quantum Optics course at our University.

DOI
10.1088/0143-0807/32/4/007

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We propose an undergraduate numerical project for simulating the results of the second-order correlation function as obtained by an intensity interference experiment for two kinds of light, namely bunched light with Gaussian or Lorentzian power density spectrum and antibunched light obtained from single-photon sources. While the algorithm for bunched light was based on a previous publication, the one for antibunched light was developed by master students attending a Quantum Optics course at our University.
Abstract We report on a step-by-step-series of experiments from statistical optics with classical light to undergraduate quantum optics with single-photon states, particularly suitable to paving an introductory way to quantum phenomena. We build up a progressive process analysing temporal variations of the irradiance of light discerned by measuring the value of the non-delayed second-order correlation function g (2) ( τ = 0). We demonstrate how Poisson distributed photoelectron counts from constant irradiance ( g (2) (0) = 1) can be used to calibrate the apparatus. Measurements with harmonically modulated irradiance of Poissonian light give an introduction to g (2) (0) correlation analysis. After these introductory steps, we demonstrate photon bunching with (pseudo-) thermal light ( g (2) (0) ≈ 2), and finally show quantum antibunching of photons in Fock states ( g (2) (0) ≈ 0). All measurements are in excellent agreement with the theoretical predictions.
Since Hanbury Brown and Twiss revealed the photon bunching effect of a thermal light source in 1956, almost all studies in correlation optics have been based on light’s intensity fluctuation, regardless of fact that the polarization fluctuation is a basic attribute of natural light. In this work, we uncover the veil of the polarization fluctuation and corresponding photon correlations by proposing a new light source model, termed pseudo-natural light, embodying both intensity and polarization fluctuations. Unexpectedly, the strong antibunching and superbunching effects can be simultaneously realized in such a new source, whose second-order correlation coefficient g ( 2 ) can be continuously modulated across 1. For the symmetric Bernoulli distribution of the polarization fluctuation, particularly, g ( 2 ) can be in principle from 0 to unlimitedly large. In pseudo-natural light, while the bunching effects of both intensity and polarization fluctuations enhance the bunching to superbunching photon correlation, the antibunching correlation of the polarization fluctuation can also be extracted through the procedure of division operation in the experiment. The antibunching effect and the combination with the bunching one will arouse new applications in quantum imaging. As heuristic examples, we carry out high-quality positive or negative ghost imaging, and devise high-efficiency polarization-sensitive and edge-enhanced imaging. This work, therefore, sheds light on the development of multiple and broad correlation functions for natural light.
We describe a series of experiments used in a sophomore-level quantum physics course that are designed to provide students with a hands-on introduction to quantum mechanics. By measuring correlations, we demonstrate that a helium-neon laser produces results consistent with a classical model of light. We then demonstrate that a light source derived from a spontaneous parametric down-conversion process produces results that can only be described using a quantum theory of light, thus providing a (nearly) single-photon source. These single photons are then sent into a Mach–Zehnder interferometer, and interference fringes are observed whenever the path of the photons cannot be determined. These experiments are investigated theoretically using straightforward quantum-mechanical calculations.
Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.
Previous work on the two-time photon-number correlations of quantum non-stationary fields has focused on the demonstration of self-contradictory predictions of the photon antibunching according to different definitions. In this paper we analyse the usefulness of the conventional and generalized definitions of photon bunching in a description of classical non-stationary light. It is proved that the generalized definition applied to classical fields predicts photon bunching but never antibunching. In contrast, the two conventional definitions are shown to improperly classify certain classical non-stationary fields as being antibunched.