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Physical Review Letters

High Power Interferometric Phase Measurement Limited by Quantum Noise and Application to Detection of Gravitational Waves

Peter K Fritschel, Gabriela I. González, Brian T. Lantz, P. Saha, Michael E. Zucker

Published Apr 13, 1998• 40 citations
Publisher

Abstract

Interferometric detection of gravitational waves at levels of astrophysical interest is expected to require measurement of optical phase differences of $\ensuremath{\le}{10}^{\ensuremath{-}10}$ rad. To achieve this sensitivity the measurement must be made at the quantum (shot noise) limit. We have built a laboratory-scale interferometer to investigate limits to sensing the phase at this level, and obtained, with 70 W of circulating power, a phase sensitivity limited by shot noise of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0ex}{0ex}}\mathrm{rad}/\sqrt{\mathrm{Hz}}$ at frequencies above 1.5 kHz. We describe the experiment and discuss the implications for the Laser Interferometer Gravitational-Wave Observatory (LIGO).

DOI
10.1103/physrevlett.80.3181

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Interferometric detection of gravitational waves at levels of astrophysical interest is expected to require measurement of optical phase differences of \ensuremath≤10\ensuremath−10\ensuremath{\le}{10}^{\ensuremath{-}10}\ensuremath≤10\ensuremath−10 rad. To achieve this sensitivity the measurement must be made at the quantum (shot noise) limit. We have built a laboratory-scale interferometer to investigate limits to sensing the phase at this level, and obtained, with 70 W of circulating power, a phase sensitivity limited by shot noise of 3\ifmmode×\else\texttimes\fi10\ensuremath−10rad/Hz3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0ex}{0ex}}\mathrm{rad}/\sqrt{\mathrm{Hz}}3\ifmmode×\else\texttimes\fi10\ensuremath−10rad/Hz​ at frequencies above 1.5 kHz. We describe the experiment and discuss the implications for the Laser Interferometer Gravitational-Wave Observatory (LIGO).
Interferometric detection of gravitational waves at a level of astrophysical interest is expected to require measurement of optical phase differences of < or = 10(-10) rad. A fundamental limit to the phase sensing is the statistics of photon detection--Poisson statistics for light in a coherent state. We have built a laboratory-scale interferometer to achieve and investigate the phase detection sensitivity required for the Laser Interferometer Gravitational-Wave Observatory. With 70 W of circulating power, we have obtained a phase sensitivity of 1.28 x 10(-10) rad/square root(Hz) at frequencies above 600 Hz, limited by quantum noise. Below 600 Hz, excess noise above the quantum limit is seen, and we present our investigations into the sources of this excess. Compared with the results of previous such experiments, the phase sensitivity over the full 100-Hz-10-kHz band of interest has been improved by factors of up to 100, with a factor-of-2.5 improvement in the quantum-limited level.
Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational-wave detectors, such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer.
Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources—photon shot noise and quantum radiation pressure noise—which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’.
Direct detection of gravitational waves will require earth based detectors to measure strains of the order 10−21, at frequencies of 100 Hz, a sensitivity that has been accomplished with the initial generation of LIGO interferometric gravitational wave detectors. A new generation of detectors currently under construction is designed improve on the sensitivity of the initial detectors by about a factor of 10. The quantum nature of light will limit the sensitivity of these Advanced LIGO interferometers at most frequencies; new approaches to reducing the quantum noise will be needed to improve the sensitivity further. This quantum noise originates from the vacuum fluctuations that enter the unused port of the interferometer and interfere with the laser light. Vacuum fluctuations have the minimum noise allowed by Heisenberg’s uncertainty principle, ∆X1∆X2 ≥ 1, where the two quadratures X1 and X2 are non-commuting observables responsible for the two forms of quantum noise, shot noise and radiation pressure noise. By replacing the vacuum fluctuations entering the interferometer with squeezed states, which have lower noise in one quadrature than the vacuum state, we have reduced the shot noise of a LIGO interferometer. The sensitivity to gravitational waves measured during this experiment represents the best sensitivity achieved to date at frequencies above 200 Hz, and possibly the first time that squeezing has been measured in an interferometer at frequencies below 700 Hz. The possibility that injection of squeezed states could introduce environmental noise couplings that would degrade the crucial but fragile low frequency sensitivity of a LIGO interferometer has been a major concern in planning to implement squeezing as part of baseline interferometer operations. These results demonstrate that squeezing is compatible with the low frequency sensitivity of a full scale gravitational wave interferometer. We also investigated the limits to the level of squeezing observed, including optical losses and fluctuations of the squeezing angle. The lessons learned should allow for responsible planning to implement squeezing in Advanced LIGO, either as an alternative to high power operation or an early upgrade to improve the sensitivity. This thesis is available at DSpace@MIT and has LIGO document number P1300006. Thesis Supervisor: Nergis Mavalvala Title: Professor of Physics
Nearly a century after Einstein first predicted the existence of gravitational waves, a global network of Earth-based gravitational wave observatories 1-4 is seeking to directly detect this faint radiation using precision laser interferometry. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometre-level sensitivity of the kilometre-scale Michelson interferometers deployed for this task. Here, we inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz, critically important for several astrophysical sources, with no deterioration of performance observed at any frequency. With the injection of squeezed states, this LIGO detector demonstrated the best broadband sensitivity to gravitational waves ever achieved, with important implications for observing the gravitational-wave Universe with unprecedented sensitivity.
A fundamental noise source limiting the measurement sensitivity of interferometric gravitational wave (GW) observatories is the light's quantum noise. While the sensitivity of the first observatory generation was limited by the shot noise at Fourier frequencies above several hundred hertz, the future observatory generations are expected to be limited by quantum noise also in their low-frequency detection band. Squeezed states of the light field allow for improving the sensitivity at all quantum-noise-limited frequencies. Recently, a squeezing-reduced shot noise of the GW observatory GEO 600 was demonstrated. Based on this success, the Einstein Telescope design study proposes squeezed-light injection to reduce shot noise as well as quantum radiation pressure noise by a factor of ten in power, i.e. by 10 dB. This contribution summarizes the current state of the art in the field of squeezed-light generation for gravitational wave astronomy and the prospects for the intermediate future.