Photon counting readout for detection and inference of gravitational waves from neutron star merger remnants

TL;DR

The paper investigates photon counting as a quantum‑readout alternative for next‑generation GW detectors in the high‑frequency, quantum‑noise–dominated band ($>1\ \text{kHz}$). By formulating a per‑frequency temporal‑mode basis and a photon‑counting likelihood, it demonstrates that even rare photon detections from subthreshold post‑merger signals can provide informative constraints, and that hierarchical population analyses can substantially improve neutron‑star radius constraints compared with standard homodyne readout, especially when classical noise is suppressed or squeezing is applied. Across single‑event and population analyses, photon counting outperforms conventional readouts in the regime where quantum noise dominates and classical noise is small, potentially enabling the detection of ~1 in 100 post‑merger signals with $\text{SNR}\sim0.2$ and improving $R_{1.6}$ measurements by up to a factor of a few under CE design sensitivity. The findings motivate further development of hardware capable of hardware‑level matched filtering in a photon‑counting framework and invite exploration of high‑frequency stochastic GW detection with this readout approach.

Abstract

Gravitational waves emitted after neutron star binary coalescences and the information they carry about dense matter are a high-priority target for next-generation detectors. Even though such detectors are expected to observe millions of signals, detectable post-merger emission will remain rare. In this work, we explore post-merger detectability and inference through an alternative detector readout scheme for data dominated by quantum-noise, which is the case above $1$\,kHz: photon-counting. In such a readout, signals and noise become quantized into discrete distributions corresponding to the detection of single photons measured in a chosen basis of modes. Through simulated data, we demonstrate that photon counting can be efficient even for weak signals. We find ${\sim}1$ in 100 signals with a post-merger signal-to-noise ratio of 0.2 can result in a single photon and thus be detected. Furthermore, after $2\times10^4$ signals -- equivalent to $10^{-2}$ to $1.5$ years of observation -- photon counting results in a twofold improvement in the measurement of the radius of a $1.6\,M_\odot$ neutron star. Constraints can be further tightened if the detector classical noise is reduced. Photon counting offers a promising alternative to traditional homodyne readout techniques for extracting information from low signal-to-noise ratio post-merger signals.

Figures (7)

• Figure 1: Demonstration of the detection of a BNS post-merger signal with a damped-sinusoid temporal mode basis. In the upper panel, we show the strain (left vertical axis) and basis filter (right vertical axis) spectral amplitudes as a function of frequency. The basis modes are colored according to their expected number of signal photons. While each basis mode is initially constructed according to Eq. \ref{['eq:basis']}, orthonormalization leads to more complex basis filter structure. In the lower panel, we present the 200 basis filters in terms of their time, frequency, and phase (sine on the left half circle and cosine of the right), again colored by the expected number of signal photons.
• Figure 2: Marginal posterior distribution for the damped-sinusoid parameters obtained with the homodyne (orange) and photon counting (blue) readouts for a signal with SNR 5. The true values are shown with grey lines. Contours correspond to the 50% and 90% credible levels. Overall, homodyne constraints are more stringent in this relatively high-SNR regime --- to be expected. The time and phase posterior distributions are bimodal with the photon counting readout due to two different temporal mode filters, $\{d_k\}$, generating photons.
• Figure 3: Same as Fig. \ref{['fig:corner_super']} but for a signal with SNR 1. Such a low SNR signal is not detected by the homodyne readout. In the case of photon counting, $\bar{N}_\textrm{sig} = 0.125$, and so there is a $11.8\%$ chance that at least one photon is generated. If a photon is recorded, the signal is detected and its parameters are constrained.
• Figure 4: Impact of the noise backgrounds for the homodyne (upper; orange) and photon counting (lower; blue) readouts. The left panel shows the post-merger signal spectrum, as well as $S_\textrm{HD}(f)$ for the homodyne and $S_n(f)$ for the photon counting at different levels. The relevant statistic for the homodyne readout is SNR $\sim 1/S_\textrm{HD}(f)$, while the relevant statistic for the photon counting is $\bar{N}_\textrm{sig}/\bar{N}_\textrm{cl} \sim |h(f)|^2/S_n(f)$; both are denoted in the colormap. The thicker lines correspond to the expected results with CE's design squeezing level (10 dB; for the homodyne), or classical noise realization (for the photon counting), and the white lines on the colorbars indicate their corresponding values. In the right panel, we show the marginal posterior for the peak frequency for each corresponding noise level.
• Figure 5: Marginal posterior (90% credible levels) for simulated post-merger signals with varying photon counts. As the photon count increases, constraints narrow in a manner similar to homodyne readout. Each case corresponds to a specific realization of a simulated signal resulting in the indicated numbers of photons for illustration. For the SNRs anticipated for next-generation detectors, $N_\textrm{sig} > 1$ will be rare.