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

arXiv:2610.21112v1 Announce Type: cross 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 $|\alpha_{\pm}|\sim10^{-10}$ 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 $S^{1/2}_n=1.6\times10^{-20}\,\mathrm{Hz}^{-1/2}$. 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.

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 $|\alpha_{\pm}|\sim10^{-10}$ 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 $S^{1/2}_n=1.6\times10^{-20}\,\mathrm{Hz}^{-1/2}$. 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.

General Relativity and Quantum Cosmology (gr-qc); Instrumentation and Methods for Astrophysics (astro-ph.IM); Instrumentation and Detectors (physics.ins-det); Optics (physics.optics); Quantum Physics (quant-ph)

arXiv:2610.21112 [gr-qc]

(or arXiv:2610.21112v1 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2610.21112 arXiv-issued DOI via DataCite (pending registration)

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

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