Quantum State Characterization of Gravitational Waves via Graviton Counting Statistics

TL;DR

This work addresses how to extract the quantum statistics and full Gaussian-state description of gravitational waves using single-graviton detectors. It develops a quadratic GW–detector interaction and shows that Gaussian states remain Gaussian under evolution, with detector moments evolving linearly and enabling direct access to graviton counting statistics and the second-order coherence $g^{(2)}(0)$. By mapping $g^{(2)}(0)$ from the GW to the detector and employing phase-sensitive homodyne-style measurements, the authors propose a practical tomography scheme for Gaussian gravitational waves, including explicit formulas based on generating functions and loop Hafnians. The results demonstrate that graviton counting can distinguish coherent, squeezed, and thermal GW states and, in principle, allow full quantum-state tomography, highlighting a bridge between quantum optics and gravitational-wave physics with potential experimental realizations in macroscopic quantum sensors.

Abstract

Although gravitational waves are now routinely observed, the detection of individual gravitons has long been regarded as impossible. Recent work, however, has demonstrated that single-graviton detection can be achieved and may be feasible in the near future. Here we show that beyond mere particle detection, these detectors provide access to the quantum state and particle statistics of gravitational waves. We show that graviton detection probabilities enable the discrimination between squeezed, coherent, and thermal radiation. We further demonstrate that the full quantum statistics contained in the second-order correlation function of the passing wave can be directly measured at the detector, independent of the weak gravitational interaction strength. Building on recent quantum-optical techniques, this capability opens the way to full quantum state tomography of Gaussian states. Our results demonstrate that single-graviton detection is not only of foundational significance but also of practical value, allowing for the characterization of quantum statistics and the states of the gravitational radiation field, which remain currently unknown.

Figures (3)

• Figure 1: A gravitational wave (GW) from an astrophysical source is detected with a bulk acoustic resonator. The GW leaves an imprint in the form of resonant graviton-to-phonon conversion. (a) and (b) represent different detection schemes. (a) Measurement of single phononic excitations. Different GW states result in different detection probabilities, opening the possibility for distinguishing different quantum states of the gravitational radiation. (b) Measurement of the second-order coherence. Detection of the phonon second-order correlation function in the bar detector gives direct information about the graviton statistics of the GW, which can be used to perform GW state tomography as the phononic initial state $\ket{\beta}$ is varied.
• Figure 2: Graviton absorption depends on the state of the passing gravitational wave. Here, we assume a passing GW with strain amplitude $h=10^{-22}$ and show the fractional graviton absorption probability difference between a purely coherent and general Gaussian gravitational wave state. $n_\text{q}/n_\text{grav}$ is the fraction of squeezed and thermal gravitons to the total intensity, as given by Eq. \ref{['eq:average_graviton_count']}. The curves in (a) and (b) show the first three excitation probabilities for a detector coupling strength of $n_\text{grav} (\gamma_\text{g} t)^2 \approx1$ and $n_\text{grav} (\gamma_\text{g} t)^2 \approx2$, respectively. (c) and (d) are contour plots of the fractional difference in single-graviton absorption $\Delta\mathbb{P}_1(\bar{n},r)/\mathbb{P}_{1,\text{c}}$ for the mostly thermal $n_\text{q} \approx \bar{n}$ limit (c), and the mostly squeezed $n_\text{q} \approx \sinh^2(r)$ limit (d), respectively, with the interaction strength as in (a).
• Figure 3: The $\text{g}^{(2)}$-function of the GW is directly mapped on the detector, allowing for the characterization of the quantum statistics and state of the radiation. The figure shows contour plots of $\text{g}^{(2)}_\text{grav}(0)-1$ for gravitational wave signals with strain $h=10^{-22}$, $\theta=0$, with the total number of gravitons given by Eq. \ref{['eq:average_graviton_count']} with $n_\text{q} \lesssim n_\text{grav}$. Fig. (a) corresponds to the limit $\bar{n}\approx n_\text{q}$, and Fig. (b) corresponds to $\sinh^2r\approx n_\text{q}$. In both panels, the yellow dashed curve corresponds to $g_\text{grav}^{(2)}(0)=2$ as for an exactly thermal state. For Gaussian signals, this value is exceeded through squeezing in the gravitational wave.