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arXiv:0810.3911

Gravitational Waves detection and spectroscopy with a Double-slit Quantum Eraser

Clovis Jacinto de Matos, Fabrizio Tamburini, Josep Maria Perdigués Armengol, C. N. Colacino

Published Oct 21, 2008• 0 citations
arXivHTMLPDF

Abstract

We propose the use of heralded photons to detect Gravitational Waves (GWs). Heralded photons are those photons that, produced during a parametric downconversion process, are "labelled" by the detection and counting of coincidences of their correlated or entangled twins and therefore can be discriminated from the background noise, independently of the type of correlation/entanglement used in the setup. Without losing any generality, we illustrate our proposal with a gedankenexperiment, in which the presence of a gravitational wave causes a relative rotation of the reference frames associated to the double-slit and the test polarizer, respectively, of a Walborn's quantum eraser \cite{wal02}. In this thought experiment, the GW is revealed by the detection of heralded photons in the dark fringes of the recovered interference pattern by the quantum eraser. Other types of entanglement, such as momentum-space or energy-time, could be used to obtain heralded photons to be used in the future with high-frequency GW interferometric detectors when enough bright sources of correlated photons will be available.

DOI
10.48550/arxiv.0810.3911

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We propose the use of heralded photons to detect Gravitational Waves (GWs). Heralded photons are those photons that, produced during a parametric downconversion process, are "labelled" by the detection and counting of coincidences of their correlated or entangled twins and therefore can be discriminated from the background noise, independently of the type of correlation/entanglement used in the setup. Without losing any generality, we illustrate our proposal with a gedankenexperiment, in which the presence of a gravitational wave causes a relative rotation of the reference frames associated to the double-slit and the test polarizer, respectively, of a Walborn's quantum eraser \cite{wal02}. In this thought experiment, the GW is revealed by the detection of heralded photons in the dark fringes of the recovered interference pattern by the quantum eraser. Other types of entanglement, such as momentum-space or energy-time, could be used to obtain heralded photons to be used in the future with high-frequency GW interferometric detectors when enough bright sources of correlated photons will be available.
We propose a thought technique for detecting gravitational waves (GWs) using Einstein-Podolsky-Rosen photon entangled states. GWs decohere the entangled photon pairs, introduce a relative rotation, and desynchronize Alice's and Bob's reference frames, thus reducing the measured nonlocality of correlated quanta described by Bell's inequalities. Gravitational waves, distorting quantum encryption key statistics away from a pure white noise, act then as shadow eavesdroppers. The deviation from the intrinsic white-noise randomness of a quantum key distribution process can reveal the presence of a gravitational wave by analysis of the emerging color distortions in the key. Photon entangled states provide the key advantage of revealing the polarization rotation introduced by GWs without the need of previously fixed reference frames.
We propose a "thought technique" for detecting Gravitational Waves using Einstein-Podolski-Rosen photon Entangled States. GWs decohere the entangled photon pairs, introduce a relative rotation and de-synchronize Alice and Bob's reference frames thus reducing the measured non-locality of correlated quanta described by Bell's inequalities. Gravitational Waves, distorting quantum encryption key statistics away from a pure white noise, act then as shadow eavesdroppers. The deviation from the intrinsic white-noise randomness of a Quantum Key Distribution process can reveal the presence of a gravitational wave by analyzing the emerging color distortions in the key. Photon entangled states provide the key advantage of revealing the polarization rotation introduced by GWs without the need of previously fixed reference frames
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.
We report a quantum eraser experiment which actually uses a Young double slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert, and Walther [Nature (London) 351, 111 (1991)]. One photon of an entangled pair is incident on a Young double slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the interference pattern. To recover interference, we measure the polarization of the other entangled photon. In addition, we perform the experiment under ``delayed erasure'' circumstances.
Quantum noise is one of the limiting factors in laser-interferometric gravitational-wave (GW) detectors. The application of squeezed states in these interferometers allows the reduction of quantum noise in one quadrature. Due to opto-mechanical coupling in a GW detector the squeezed quadrature needs to be rotated within the spectrum to achieve a broadband noise reduction. So far, the implementation of additional filter cavities is considered that allow for the optimal, frequency-dependent rotation of the squeezed quadrature. However, these cavities need to have low loss, a length in the order of \unit[100]{m} and must be situated in the vacuum system, making them cost-intensive. In 2017, Ma and coworkers proposed a scheme for the broadband quantum-noise reduction without the need of additional filter cavities. It was shown by Brown et al. that a similar scheme can be used to broadband-enhance interferometers with a detuned signal-recycling cavity. Here, we performed a proof-of-principle experiment of the proposal on a table-top-scale. Squeezed states were produced detuned to the carrier field of a \unit[2.5]{m}-linear cavity and read out in a bichromatic homodyne detection. The frequencies of the lower and upper local oscillator were at entangled sidebands of the squeezed field. Depending on the relations between the involved frequencies, we can address both variants of the proposal. We show, that the frequency-dependences of the resulting noise spectra fit to a theoretical model we derived from the theory used by Ma et al. With this work we set the path towards an implementation of these schemes in a GW-detector prototype, where the compatibility of the approach with a low-frequency suspended interferometer can be tested. Moreover, we used the same setup to show nonclassical interferometer enhancement at low frequencies by high-frequency squeezed states. Here, a heterodyne readout scheme was implemented to avoid limiting noises at low frequencies. The application of squeezed states centered around the local oscillator frequency yielded an improvement in signal-to-noise ratio of $\unit[3.4]{dB}\pm\unit[0.3]{dB}$. Additionally, I designed, built and characterized a compact source of squeezed vacuum-states at \unit[1064]{nm} with a footprint of just $\unit[0.8]{m^2}$. I show measurements of squeezed states from this source with a reduction of quantum noise of $\unit[10.7]{dB}\pm\unit[0.2]{dB}$ below the vacuum noise and present a noise reduction in the frequency range from \unit[70]{kHz} to \unit[65]{MHz}.