Quadrature-witness readout for backscatter mitigation in gravitational-wave detectors limited by back-action

TL;DR

This work addresses back-scatter noise in gravitational-wave detectors by introducing a quadrature-witness readout that is compatible with frequency-dependent squeezing. By splitting the output to two balanced homodyne detectors and injecting a second squeezed state through the readout port, the method preserves quantum enhancement for the signal quadrature while obtaining a witness for back-scatter in the orthogonal quadrature. The results show that, for realistic loss budgets, loud back-scatter events can be partially subtracted using the witness, with subtraction fractions rising as the witness-SNR threshold decreases, albeit at a small high-frequency penalty that can be mitigated through optimization. The approach offers a practical augmentation to current detectors, potentially improving robustness and sensitivity to non-stationary disturbances and other orthogonal-noise sources without major hardware redesign.

Abstract

Disturbances in gravitational wave (GW) observational data are often caused by non-stationary noise in the detector itself, such as back-scattering of laser stray light into the signal field. Unlike GW signals, non-stationary noise can appear in both the GW-signal quadrature and the orthogonal quadrature, which is usually not measured. Simultaneous sensing of this orthogonal quadrature provides a witness channel that can be used to reconstruct the disturbance in the signal quadrature enabling a subtraction of non-stationary noise. Here, we present the concept of quadrature witness that is compatible with frequency-dependent squeezing, which is already used to simultaneously reduce photon shot noise and photon radiation pressure noise. We demonstrate that implementing this approach in a GW detector could reduce noise caused by loud back-scatter events, thereby improving the overall sensitivity and robustness of GW observatories.

Figures (7)

• Figure 1: Conceptual setup of our approach in a GW detector. The walls of the vacuum tanks are excited by microseims and anthropogenic sources. Dual readout is implemented by the readout beamsplitter and two balanced homodyne detectors (BHD) in the output of the interferometer. One BHD measures the signal quadrature while the other one measures the witness quadrature. A second squeezed state in injected through the open port of the readout beamsplitter. Frequency-dependent squeezing is realized by a filter cavity and injected into the detector through a Faraday isolator (FI).
• Figure 2: Strain sensitivity of the signal quadrature (top) demonstrates that frequency-dependent squeezing is compatible with dual readout. Quadrature-witness with readout squeezing (solid blue) maintains quantum enhancement at all frequencies compared to the case without squeezing (dashed grey), only suffering a 3 dB penalty for dual readout at high frequency. Readout squeezing allows to restore a significant portion of sensitivity compared to the dual readout without readout squeezing (orange dashed). The witness quadrature sensitivity (bottom) is sufficient to allow effective back-scatter subtraction. The detector parameters are chosen such that we achieve optimal frequency-dependent squeezing and reach approximately the same signal quadrature sensitivity as A+ for single readout (see Table \ref{['tab:parameters:Aplus:sym']}).
• Figure 3: Optimized signal (top) and witness (bottom) quadrature sensitivities. The baseline curves show the sensitivities for a detector with readout losses of $2\%$ after the readout beam-splitter and $15\,\text{dB}$ of readout squeezing. The solid curves show the sensitivities for the optimized readout beamsplitter power reflectivity of $69\%$ and amount of readout squeezing of $9.5\,\text{dB}$. For comparison, we plotted the sensitivity of the dual readout without readout squeezing for the same reflectivity.
• Figure 4: Scattering signal from a fast scattering event. a) Normalized projections in the signal $\text{p}_{\text{sc}}$ and witness quadrature $\text{a}_{\text{sc}}$ of a scattering signal in time domain. b) Amplitude spectral density of the same scattering signal compared to the signal and witness quadrature sensitivities. Here, we can see the characteristic scatter shoulder produced by a fast scattering event.
• Figure 5: Histograms of our set of of random scattering events. a) Histogram of signal-to-noise ratios for the signal quadrature. b) Histogram of signal-to-noise ratios for the witness quadrature.