On the intensity interferometry and the second-order correlation function $g^{(2)}$ in astrophysics

Most observational techniques in astronomy can be understood as exploiting the various forms of the first-order correlation function g^(1). As however demonstrated by the Narrabri Stellar Intensity Interferometer back in the 1960’s by Hanbury Brown & Twiss, and which is the first experiment to measure the second-order correlation function g^(2), light can carry more information than simply its intensity, spectrum and polarization. Since this experiment, theoretical and laboratory studies of non-classical properties of light have become a very active field of research, namely quantum optics. Despite the variety of results in this field, astrophysics remained focused essentially on first-order coherence. In this paper, we study the possibility that quantum properties of light could be observed in cosmic sources. We provide the basic mathematical ingredients about the first and the second order correlation functions, applied to the modern context of astronomical observations. The exploitation of g^(2) is certainly richer than what a modern intensity interferometer could bring and is particularly interesting for sources of non-thermal light. We conclude by briefly presenting why microquasars in our galaxy and their extragalactic parents can represent an excellent first target in the optical/near-infrared where to observe non-thermal light, and test the use of g^(2) in astrophysical sources.

💡 Research Summary

The paper revisits the concept of intensity interferometry, originally demonstrated by Hanbury Brown and Twiss (HBT) in the 1960s, and argues that modern astronomical observations have largely remained confined to first‑order coherence (the g¹ function) despite the richer information encoded in the second‑order correlation function g². After a concise review of the theoretical foundations, the authors explain that g¹ describes the correlation of complex electric‑field amplitudes and underlies traditional tools such as interferometers, spectrographs, and polarimeters. In contrast, g² quantifies photon‑number correlations, revealing statistical phenomena such as photon bunching (g²(0)=2 for thermal light) and antibunching (g²(0)<1 for single‑photon sources). These signatures are central to quantum optics but have rarely been exploited in astrophysics because of technical limitations: the need for extremely high time resolution, large photon fluxes, and sources that deviate from pure thermal emission.

The authors identify non‑thermal astrophysical emitters—particularly synchrotron radiation from relativistic jets, inverse‑Compton scattering, and shock‑accelerated plasma—as promising candidates where g² could deviate significantly from the thermal value. They argue that measuring g² in such sources would provide direct insight into particle acceleration mechanisms, jet composition, and magnetic field geometry, complementing the spatial information obtained from conventional interferometry.

To make g² measurements feasible, the paper proposes a modern intensity‑interferometer architecture based on superconducting nanowire single‑photon detectors (SNSPDs) coupled with picosecond‑resolution time‑to‑digital converters (TDCs). Two independent telescopic apertures, separated by at least ten metres, would feed light through narrow (≤1 nm) optical bandpasses into fiber‑coupled SNSPDs. The detectors’ >90 % quantum efficiency and sub‑10 ps timing jitter enable the construction of a cross‑correlation histogram of photon arrival times, from which g²(τ) can be reconstructed after correcting for Poisson noise, background photons, and atmospheric fluctuations.

The paper highlights microquasars within our Galaxy and their extragalactic analogues (e.g., AGN jets such as M87 or 3C 273) as optimal first targets. Microquasars are relatively nearby (a few kiloparsecs), bright in the optical/near‑infrared (magnitudes 10–15), and host powerful jets that produce synchrotron emission with expected photon bunching signatures. By observing these objects with existing 8‑10 m class telescopes equipped with the proposed detector system, the authors estimate that sufficient photon counts can be accumulated to achieve statistically significant g² measurements within reasonable integration times (hours to a night).

The experimental workflow described includes: (1) selecting a narrow spectral window to isolate the non‑thermal component; (2) recording photon timestamps from both apertures; (3) computing the cross‑correlation function in real time; (4) analyzing the τ‑dependence of g² to infer source size, coherence length, and temporal variability. A g²(0) value significantly above 1 would confirm the presence of bunching, while the decay of g² with τ would provide a measure of the emitting region’s spatial extent, analogous to the classic HBT radius measurement but now applied to non‑thermal processes.

Finally, the authors discuss the broader implications of introducing quantum‑optical techniques into astronomy. Successful detection of non‑classical photon statistics would open a new observational window, allowing astronomers to probe the quantum nature of astrophysical radiation, test models of relativistic jet physics, and eventually explore more exotic phenomena such as photon entanglement over astronomical distances. The paper concludes that a focused campaign on microquasars represents a realistic and scientifically rewarding first step toward establishing g²‑based astrophysics.