Displacement-noise-free gravitational-wave detector using quantum tomography of photon orbital angular momentum states

Abstract

Gravitational waves (GWs) induce quantum transitions between photon orbital-angular-momentum (OAM) states with amplitudes ${\alpha }_{\pm }$. Exploiting this effect, we present a displacement-noise-free detection framework that extracts GW information from the OAM Hilbert space. Parametrized quantum state tomography of the GW-induced OAM sidebands enables a single V-shaped detector to resolve all seven wave parameters: the frequency, propagation direction, two polarization amplitudes, and initial phase of each polarization. Direct detection of the sidebands yields a weak signal of approximately $10^{-15}\mathrm{W}$. We therefore introduce a stronger reference state $r|0{>}_{\mathrm{P}}$, with $r=0.01$, to enhance the detected signal. For an arm length of $L=4\mathrm{m}$, $N=160$ round trips, a paraxial parameter of $\gamma =0.1$, an incident light power of $P_{\mathrm{BS}}=10\mathrm{kW}$, a wavelength of ${\lambda }_{\mathrm{opt}}=1064\mathrm{nm}$, and GW amplitudes of $A=10^{-18}$, we estimate sideband transition amplitudes of $|{\alpha }_{\pm }|\sim 10^{-10}$ and signal powers of order $1\mathrm{nW}$, scaling as $P_{\mathrm{BS}}{\alpha }_{\pm }\propto P_{\mathrm{BS}}ANL\gamma /{\lambda }_{\mathrm{opt}}$. The shot-noise-limited sensitivity floor is $S_n^{1/2}=1.6\times 10^{-20}{\mathrm{Hz}}^{-1/2}$. Because the scheme measures OAM transition amplitudes rather than differential arm lengths, it is intrinsically free from displacement noise and provides a broadband probe of GWs, specifically bridging the $0.1$--$10\mathrm{Hz}$ mid-frequency gap.

arXiv comment6 pages, 4 figures, comments are welcome