Detectability of an orbital-angular-momentum-based gravitational wave detector

Abstract

The orbital angular momentum (OAM) of light provides a new approach to probing gravitational waves (GWs) through transitions between OAM states. Here, we assess the detectability of an OAM-based GW detector by developing a readout scheme and evaluating its noise budget over the frequency range from $1~\mathrm{mHz}$ to $100~\mathrm{Hz}$, including laser-intensity noise, laser-phase noise, mode-impurity noise, and shot noise. For a symmetric superposition OAM state, the GW-induced transition amplitudes satisfy $α_+=-α_-^*$, whereas the noise-induced mode-crosstalk coefficients obey $n_+=n_-^*$. Hence, the GW-induced signal forms a differential-mode contribution, while laser-intensity and mode-impurity noises enter as common-mode contributions, enabling their suppression by the balanced detection. Under a fixed beam-waist constraint, a shorter arm permits a larger paraxial parameter, reducing the equivalent angular-noise strain sensitivity. We adopt an arm length of $L=4\,\mathrm{m}$, $N=160$ round trips, a paraxial parameter of $γ=0.1$, a laser power incident on the beam splitter of $P_{\mathrm{BS}}=10\,\mathrm{kW}$, and a wavelength of $λ_{\mathrm{opt}}=1064\,\mathrm{nm}$. Using representative noise spectra, we find that, for GWs from an equal-mass binary black hole with source-frame component masses of $M_{\mathrm{src}}=10^{4}\,M_{\odot}$ at redshift $z=1$, balanced detection yields an SNR of $24.7$ for an imbalance parameter of $ε=10^{-3}$ and $239$ for $ε=10^{-5}$, with the sensitivity approaching the shot-noise limit in the latter case. These results highlight the importance of a compact optical configuration and strong common-mode rejection for realizing an OAM-based GW detector.