In 1956, two radio telescopes at Jodrell Bank stared at Sirius, capturing not an image but the trembling of intensity. The Hanbury Brown and Twiss (HBT) experiment revealed a surprising thing: correlations of arriving photons can tell us about the statistics of the source — whether it's chaotic, like a thermal lamp, or coherent, like a laser. It was like deducing the character of a dancer from the rhythm of their steps. Today we know that the Universe itself performs a quantum dance: relic gravitons — quantized vibrations of spacetime, stretched by inflation (predicted by Alan Guth) in the first fraction of a second after the Big Bang. These gravitons are not just waves; they are entangled and squeezed, like partners bound by invisible threads. Their dance is super-Poissonian — with bunching more turbulent than ordinary light. The temptation arose: couldn't we, like HBT, 'photograph' this performance, capturing its shadow in photon light?
In the arsenal of quantum optics there is a powerful formalism, developed by Serge Haroche for cavity electrodynamics. Theorists applied it to an ideal Fabry–Pérot cavity — two mirrors with a single photon mode trapped between them. Through this cavity, a background gravitational noise is passed, described as tensor perturbations in an expanding universe obeying Hubble's law — the discovery of Edwin Hubble. The interaction is minimal and dictated by curvature. Constructing the full Hamiltonian of the system in the rotating wave approximation, the problem was reduced to three modes: one photonic and two gravitonic with opposite momenta. The time evolution was computed using displacement and squeezing operators — mathematical transformations that, roughly speaking, 'stretch' and 'squeeze' quantum fluctuations.
The main result of the calculations turned out to be disarmingly simple. The photon number operator commutes with the full Hamiltonian. In the language of physics, this means: the amount of light in the resonator remains unchanged, no matter what the gravitons do. Consequently, any correlation function measuring photon coincidence counts factorizes — it depends only on the initial state of the field, not on the gravitational statistics. For the second-order coherence degree g(2) — the very HBT signal — an expression emerges in which there is no trace of gravitons. If the resonator is excited in a coherent state, g(2)=1; for chaotic light, g(2)=2; for a Fock state, g(2)<1. And the gravitons themselves exhibit a g(2) value up to 3 in the limit of large squeezing. Their dance remains shadowless: intensity correlations of photons fundamentally cannot 'see' the quantum nature of the gravitational background.
This stark conclusion closes one of the attractive pathways in quantum gravity. Even a flawless resonator cannot play the role of an intermediary between us and the quantum world of gravity. Yet the search is not over. Future theoretical models may bypass the prohibition by introducing nonlinear couplings — for example, via dark photons or axion fields. Experimentalists, in turn, are turning their gaze to the polarization of the cosmic microwave background and to progress in optomechanics, where ultrasensitive interferometers may eventually catch individual gravitons at high frequencies. The dance of gravitons continues, and although its shadows do not fall on ordinary light, scientists are seeking new stages where the quantum choreography might finally reveal itself.
The HBT method was originally proposed for measuring the angular sizes of stars, not at all for quantum research. It was only later that Roy Glauber and George Sudarshan realized its deep connection with photon statistics.
In Carl Sagan's novel 'Contact', the characters analyze pulse statistics to reveal the artificial origin of a signal. Here, we try to capture a natural quantum signature in the noise of the Universe, but it eludes us — like shadows from invisible dancers.