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Connecting field and intensity correlations: the Siegert relation and how to test it

Ferreira, Dilleys, Romain Bachelard, William Guerin, Robin Kaiser, Mathilde Fouché

Published Jan 1, 2020• 44 citations
OpenAlex

Abstract

The Siegert relation relates the electric field and intensity correlations of light, under given assumptions. After a brief history of intensity correlations, we give a derivation of the relation. Then we present an experiment, which can be easily adapted for an undergraduate setup, and that allows measuring both field and intensity correlations at the same time, thus providing a direct test of the Siegert relation. As a conclusion, we discuss typical situations where the relation fails.

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The Siegert relation relates the electric field and intensity correlations of light, under given assumptions. After a brief history of intensity correlations, we give a derivation of the relation. Then we present an experiment, which can be easily adapted for an undergraduate setup, and that allows measuring both field and intensity correlations at the same time, thus providing a direct test of the Siegert relation. As a conclusion, we discuss typical situations where the relation fails.
The Siegert relation relates electric field and intensity correlations of light, under given assumptions. After a brief derivation of the relation, we present an experimental setup that can be implemented in a student laboratory: it allows measuring both field and intensity correlations at the same time, thus providing a direct test of the Siegert relation. Some experimental results are presented when the scattering medium corresponds to a cold atomic cloud. As a conclusion, we discuss typical situations where the relation fails.
The Siegert relation relates field and intensity temporal correlations. After a historical review of the Siegert relation and the Hanbury Brown and Twiss effect, we discuss the validity of this relation in two different domains. We first show that this relation can be used in astrophysics to determine the fundamental parameters of stars, and that it is especially important for the observation with stellar emission lines. Second, we check the validity of this relation for moving quantum scatterers illuminated by a strong driving field.
Pseudothermal light exhibits photon bunching, like thermal light, but it does not originate from randomly phased emission. As photon bunching is common in both pseudothermal and thermal light, the analysis of photon bunching is insufficient to differentiate pseudothermal light and thermal light. However, thermal light obeys the Siegert relation, which connects the interferometric visibility ∥g(1)(τ )∥ and second-order photon correlation g(2)(τ ). In this work, we present a direct test test for Siegert relation by a single-shot measurement. Using our technique, we demonstrate that laser light scattered off a rotating ground glass, violates the Siegert relation, which provides further evidence that it is a pseudothermal light source.
Light is characterized by its electric field, yet quantum optics has revealed the importance of monitoring photon-photon correlations at all orders. We here present a comparative study of two experimental setups, composed of cold and warm Rubidium atoms, respectively, which allow us to probe and compare photon correlations up to the fourth order. The former operates in the quantum regime where spontaneous emission dominates, whereas the latter exhibits a temperature-limited coherence time. While both setups present almost-chaotic light statistics, we discuss how the access to different orders of photon correlations allows one to better characterize the mechanisms responsible for deviations from those statistics.