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arXiv:2209.06480 · The European Physical Journal D

Field and intensity correlations: the Siegert relation from stars to quantum emitters

Pierre Lassègues, Mateus Antônio Fernandes Biscassi, Martial Morisse, A. Cidrim, Nolan Matthews, G. Labeyrie, Jean‐Pierre Rivet, F. Vakili, Robin Kaiser, William Guerin, Romain Bachelard, Mathilde Hugbart

Published Dec 1, 2022• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1140/epjd/s10053-022-00558-5

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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.
Intensity-interferometry based on Hanbury-Brown and Twiss's seminal experiment for determining the radius of the star Sirius formed the basis for developing the quantum theory of light. To date, the principle of this experiment is used in various forms across different fields of quantum optics, imaging and astronomy. Though, the technique is powerful, it has not been generalized for objects at different temperatures. Here, we address this problem using a generating functional formalism by employing the P-function representation of quantum-thermal light. Specifically, we investigate the photon coincidences of a system of two extended objects at different temperature using this theoretical framework. We show two unique aspects in the second-order quantum coherence function - interference oscillations and a long-baseline asymptotic value that depends on the observation frequency, temperatures and size of both objects. We apply our approach to the case of binary stars and discuss the advantages of measuring these two features in an experiment. In addition to the estimation of the radii of each star and the distance between them, we also show that the present approach is suitable for the estimation of temperatures as well. To this end, we apply it to the practical case of binary stars Luhman 16 and Spica ααα Vir. We find that for currently available telescopes, an experimental demonstration is feasible in the near term. Our work contributes to the fundamental understanding of intensity interferometry of quantum-thermal light and can be used as a tool for studying two-body thermal emitters - from binary stars to extended objects.
Intensity interferometry based on Hanbury Brown and Twiss's seminal experiment for determining the radius of the star Sirius formed the basis for developing the quantum theory of light. To date, the principle of this experiment is used in various forms across different fields of quantum optics, imaging, and astronomy. Although the technique is powerful, it has not been generalized for objects at different temperatures. Here, we address this problem using a generating functional formalism by employing the PPP-function representation of quantum-thermal light. Specifically, we investigate the photon coincidences of a system of two extended objects at different temperatures using this theoretical framework. We show two unique aspects in the second-order quantum coherence function: interference oscillations and a long-baseline asymptotic value that depends on the observation frequency, temperatures, and size of both objects. We apply our approach to the case of binary stars and discuss the advantages of measuring these two features in an experiment. In addition to the estimation of the radii of each star and the distance between them, we also show that the present approach is suitable for the estimation of temperatures as well. To this end, we apply it to the practical case of binary stars Luhman 16 and Spica $\ensuremath{\alpha}$ Vir. We find that for currently available telescopes, an experimental demonstration is feasible in the near term. Our work contributes to the fundamental understanding of intensity interferometry of quantum-thermal light and can be used as a tool for studying two-body thermal emitters, from binary stars to extended objects.
Optical interferometry was at the heart of the revolution which ushered in the new era of twentieth century physics. For example, the Michelson interferometer was used to show that there is no detectable motion relative to the ‘ether’; a key experiment in support of special relativity. It is a wonderful tribute to Michelson that the same interferometer concept is central to the gravity-wave detectors which promise to provide new insights into general relativity and astrophysics in the twenty-first century. Similar tales can be told about the Sagnac and Mach–Zehnder interferometers as discussed in this chapter. We further note that the intensity correlation stellar interferometer of Hanbury- Brown and Twiss was a driving force in ushering in the modern era of quantum optics. We are thus motivated to develop the theory of field (amplitude) and photon (intensity) correlation interferometry. In doing so we will find that the subject provides us with an exquisite probe of the micro and macrocosmos, i.e., quantum mechanics and general relativity. With these thoughts in mind we here develop a framework to study the quantum statistical correlations of light. We will motivate the quantum correlation functions of the field operators from the standpoint of photodetection theory. Many experimentally observed quantities, such as photoelectron statistics and the spectral distribution of the field, can be related to the appropriate field correlation functions. These correlation functions are essential in the description of Young's double-slit experiment and the notion of the power spectrum of light.
In this paper we investigate the close relationship between Dicke superradiance, originally predicted for an ensemble of two-level atoms in entangled states, and the Hanbury Brown and Twiss effect, initially established in astronomy to determine the dimensions of classical light sources such as stars. By studying the state evolution of the fields produced by classical sources---defined by a positive Glauber-Sudarshan PPP function---when recording intensity correlations of higher order in a generalized Hanbury Brown and Twiss setup we find that the angular distribution of the last detected photon, apart from an offset, is identical to the superradiant emission pattern generated by an ensemble of two-level atoms in entangled symmetric Dicke states. We show that the phenomenon derives from projective measurements induced by the measurement of photons in the far field of the sources and the permutative superposition of quantum paths identical to those leading to superradiance in the case of single photon emitters. We thus point out an important similarity between classical sources and quantum emitters upon detection of photons if the particular photon source remains unknown. We finally present a compact result for the characteristic functional which generates intensity correlations of arbitrary order for any kind of light source.
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.
Spatiotemporal coupling is present when the electric fields of any pulsed beams fail to separate into a product of purely spatial and temporal factors, and it affects ultimately on the propagation of the light. Here we study the effect of spatiotemporal coupling on the Hanbury Brown and Twiss (HBT) effect for the first time, with the help of our recent developed method [ Opt. Express 28 , 32077 ( 2020 ) 10.1364/OE.405726 ], by assuming the Gaussian statistics of partially coherent spatiotemporal pulsed sources containing the intensity and correlation coupling effect between the spatial and temporal domain. The generalized results for the spatiotemporal coupling HBT effect are investigated and through a nontrivial two-dimensional case, we numerically illustrate the influence of the spatiotemporal coupling on the HBT effect. It observes that even a very tiny coupling effect will strongly change the HBT effect at longer distances. This work will be potentially useful for the study of the HBT effect (intensity-intensity correlations) with dynamic sources having spatiotemporal coupling in both optics and other branches of physics.