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arXiv:2610.21112

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

Haorong Wu, Xilong Fan, Lixiang Chen

gr-qcastro-ph.IMphysics.ins-detphysics.opticsquant-phSubmitted Oct 15, 2026• Announced Oct 16, 2026
arXivHTMLPDF

Abstract

Gravitational waves (GWs) induce quantum transitions between photon orbital-angular-momentum (OAM) states with amplitudes $α_{\pm}$. 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 $γ=0.1$, an incident light power of $P_{\mathrm{BS}}=10\,\mathrm{kW}$, a wavelength of $λ_{\mathrm{opt}}=1064\,\mathrm{nm}$, and GW amplitudes of $A=10^{-18}$, we estimate sideband transition amplitudes of $|α_{\pm}|\sim10^{-10}$ and signal powers of order $1\,\mathrm{nW}$, scaling as $P_{\mathrm{BS}}α_{\pm}\propto P_{\mathrm{BS}}ANLγ/λ_{\mathrm{opt}}$. 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.

Comments
6 pages, 4 figures, comments are welcome

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Gravitational waves (GWs) induce quantum transitions between photon orbital-angular-momentum (OAM) states with amplitudes α±α_{\pm}α±​. 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 W10^{-15}\,\mathrm{W}10−15W. We therefore introduce a stronger reference state r∣0>Pr |0>_{\mathrm{P}}r∣0>P​, with r=0.01r=0.01r=0.01, to enhance the detected signal. For an arm length of L=4 mL=4\,\mathrm{m}L=4m, N=160N=160N=160 round trips, a paraxial parameter of γ=0.1γ=0.1γ=0.1, an incident light power of PBS=10 kWP_{\mathrm{BS}}=10\,\mathrm{kW}PBS​=10kW, a wavelength of λopt=1064 nmλ_{\mathrm{opt}}=1064\,\mathrm{nm}λopt​=1064nm, and GW amplitudes of A=10−18A=10^{-18}A=10−18, we estimate sideband transition amplitudes of ∣α±∣∼10−10|α_{\pm}|\sim10^{-10}∣α±​∣∼10−10 and signal powers of order 1 nW1\,\mathrm{nW}1nW, scaling as PBSα±∝PBSANLγ/λoptP_{\mathrm{BS}}α_{\pm}\propto P_{\mathrm{BS}}ANLγ/λ_{\mathrm{opt}}PBS​α±​∝PBS​ANLγ/λopt​. The shot-noise-limited sensitivity floor is Sn1/2=1.6×10−20 Hz−1/2S^{1/2}_n=1.6\times10^{-20}\,\mathrm{Hz}^{-1/2}Sn1/2​=1.6×10−20Hz−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 0.10.10.1--10 Hz10\,\mathrm{Hz}10Hz mid-frequency gap.
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Gravitational waves manifest as a time varying straining of space: they arise from the accelerating motions of large bodies of mass and propagate across the universe at the speed of light as ripples in the fabric of space-time, a fleetingly weak effect so far eluding direct detection. The detection of gravitation waves is expected to yield a rich vein to observational astronomy, complementing existing electromagnetic surveys and revealing a hitherto unexplored range of phenomena. First generation interferometric gravitational wave detectors, notably Enhanced LIGO, achieved strain sensitivities of one part in ten to power twenty-one per square-root-Hertz at 100 Hz with an expected detection rate of 2-3 events per year. Commissioning of a new generation of Advanced LIGO interferometric detectors has concluded recently with a resultant ten-fold sensitivity improvement. Overall their potential event detection space has increased by a factor of 1000. The quantum nature of light within these detectors now limits their sensitivity over most of their frequency range. This quantum noise limit is driven by the vacuum quadrature fluctuations propagated through their open detection ports and represents a fundamental noise floor to their strain sensitivity. This thesis addresses two distinct approaches to quantum noise improvement for future upgrades to advanced detectors. The first addresses the issue of quantum noise by adopting a quantum non-demolition approach to detector readout variables, the so-called `speed-meter’ design. Such a modified instrument samples test mass momentum, a quantity for which time separated measurements commute and are therefore not bound by Heisenberg-like limits. A novel polarisation-folded sloshing cavity type speed-meter is proposed where readout fields are stored and delayed in the orthogonal polarisation of the interferometer’s arms cavities. Here frequency dependence is selected to cancel position like measurements so that only test mass momentum information remains. A quantum noise propagation model is developed and a sensitivity performance is demonstrated that beats the standard quantum limit below 100 Hz over a broad range of frequencies. A second approach to achieve quantum noise enhancement in advanced detectors involves injection of quadrature-squeezed states in the place of vacuum. This dissertation details the development of a prototype squeezed vacuum source suitable to the demanding enhancement requirements for an Advanced LIGO squeezing installation. The construction of a doubly resonant, bow-tie cavity source is presented. This employs a novel monolithic all-glass cavity construction and is vacuum compatible. This design demonstrates the viability of building a cavity using optical contacting as a construction technique for attaching mounting prisms to highly polished fused-silica breadboards. Such a design can be expected to have excellent length noise stability, provide low intrinsic phase noise and would be suitable to mount on seismic isolation stages within the LIGO vacuum envelope. Further, the travelling wave cavity design should provide excellent 50 dB intrinsic backscatter isolation. We demonstrate the first operation of such a complex non-linear device under vacuum, producing 8.6 dB of measured vacuum squeezing down to 10 Hz across the advanced LIGO ‘audio-band’ detection range.
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