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European Journal of Physics

Monte Carlo simulation of photonic state tomography: a virtual Hanbury Brown and Twiss correlator

Eoin Murray, G. Juška, E. Pelucchi

Published Mar 15, 2016• 1 citation
Publisher

Abstract

Abstract This paper provides a theoretical background for the simulations of particular quantum optics experiments, namely, photon intensity correlation measurements. A practical example, adapted to polarisation-entangled photon pairs emitted from a quantum dot, is presented. The tool, a virtual Hanbury Brown and Twiss correlator, simulates polarisation-resolved the second-order correlation functions, which then can be used in a photonic state tomography procedure—a full description of a light source’s polarisation state. This educational tool is meant to improve general understanding of such quantum optics experiments.

DOI
10.1088/0143-0807/37/3/034002

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Abstract This paper provides a theoretical background for the simulations of particular quantum optics experiments, namely, photon intensity correlation measurements. A practical example, adapted to polarisation-entangled photon pairs emitted from a quantum dot, is presented. The tool, a virtual Hanbury Brown and Twiss correlator, simulates polarisation-resolved the second-order correlation functions, which then can be used in a photonic state tomography procedure—a full description of a light source’s polarisation state. This educational tool is meant to improve general understanding of such quantum optics experiments.
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The Hanbury Brown–Twiss (HBT) interferometer, which is used to measure the correlation of two photons or two light beams, has played a crucial role in quantum optics and quantum information. We propose a generalized HBT interferometer, which is able to measure the correlation of photons or light beams up to eight in a single experimental run. With an improved time correlated single-photon counting (TCSPC) algorithm, two-, three-, and four-photon coincidence counts, and the degree of fifth-order coherence of pseudothermal light are measured with a data collection time of 60 s. The generalized HBT interferometer can be used to measure the correlation of two multi-photon detection events by simulating photon number resolving detectors with multiple single-photon detectors. The generalized HBT interferometer and improved TCSPC algorithm provide a versatile framework for studying multi-photon correlations and interference, which is helpful to understand the physics of multi-photon interference and may find applications in fluorescence lifetime imaging and other techniques using TCSPC.
I briefly review second order or two-photon correlations starting from the Hanbury Brown-Twiss correlations to its modern versions in quantum optics studies. With this background, I address some foundational issues in the physics of quantum correlations and quantum entanglement and argue in favour of the validity of Einstein locality, to settle a long-standing debate. Understanding entanglement from this perspective has applications in quantum information theory, especially in gaining intuition about the relation between different measures of entanglement and its time evolution. Some examples are highlighted. I discuss how ideas on photon correlations applied to squeezing fluctuations in coherent light have become important in metrology, and perhaps crucial, in the successful operation of high sensitivity gravitational wave detectors.
Abstract Complementarity theory is the essence of the Copenhagen interpretation in quantum mechanics. Since the Hanbury Brown and Twiss experiments, the particle nature of photons has been intensively studied for various quantum phenomena such as anticorrelation and Bell inequality violation over the last several decades. Regarding the quantum features based on the particle nature of photons, however, no clear answer exists for how to generate such an entangled photon pair or what causes the maximum correlation between them. Here, we experimentally demonstrate the physics of quantumness on anticorrelation using well defined and nearly sub-Poisson distributed coherent photons, where a particular photon number is post-selected using a photon resolving coincidence measurement technique. As a results, unprecedented wavelength dependent first-order intensity correlation has been observed in the two-photon second-order intensity correlation with 99.9 % visibility, where this result demonstrates the anticorrelation theory in Scientific Reports 10, 7309 (2020) and opens the door to the on-demand quantum correlation control.
Typically, optical microscopy uses the wavelike properties of light to image a scene. However, photon arrival times provide more information about emitter properties than the classical intensity alone. Here we show that the Hanbury Brown and Twiss experiment (second-order correlation function) measures the relative brightness of two single-photon emitters. By combining the total number of detected photons with the zero-lag value of the correlation function, the positions and relative brightness of two emitters in two dimensions can be resolved from only three measurement positions: trilateration. This result is impossible to achieve on the basis of classical intensity measurements alone and represents a minimal demonstration of the advantage gained using quantum measurements over conventional classical microscopy. The effective point-spread function for imaging scales approximately as the inverse square root of the acquisition time.