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arXiv:gr-qc/0008026 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics

Harry J. Kimble, Yuri Levin, Andrey B. Matsko, Kip S. Thorne, Sergey P. Vyatchanin

Published Dec 26, 2001• 669 citations
arXivHTMLPDF

Abstract

The LIGO-II gravitational-wave interferometers (ca. 2006--2008) are designed to have sensitivities near the standard quantum limit (SQL) in the vicinity of 100 Hz. This paper describes and analyzes possible designs for subsequent LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a squeezed-input interferometer (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is injected into the interferometer's dark port; (ii) a variational-output interferometer (conceived in a different form by Vyatchanin, Matsko and Zubova), in which homodyne detection with FD homodyne phase is performed on the output light; and (iii) a squeezed-variational interferometer with squeezed input and FD-homodyne output. It is shown that the FD squeezed-input light can be produced by sending ordinary squeezed light through two successive Fabry-P\'erot filter cavities before injection into the interferometer, and FD-homodyne detection can be achieved by sending the output light through two filter cavities before ordinary homodyne detection. With anticipated technology (power squeeze factor ${e}^{\ensuremath{-}2R}=0.1$ for input squeezed vacuum and net fractional loss of signal power in arm cavities and output optical train ${\ensuremath{\epsilon}}_{*}=0.01)$ and using an input laser power ${I}_{o}$ in units of that required to reach the SQL (the planned LIGO-II power, ${I}_{\mathrm{SQL}}),$ the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts $\ensuremath{\mu}\ensuremath{\equiv}\sqrt{{S}_{h}}/\sqrt{{S}_{h}^{\mathrm{SQL}}}$ and with the following corresponding increase $\mathcal{V}=1/{\ensuremath{\mu}}^{3}$ in the volume of the universe that can be searched for a given noncosmological source: $\mathrm{Squeezed}\mathrm{input}---\ensuremath{\mu}\ensuremath{\simeq}\sqrt{{e}^{\ensuremath{-}2R}}\ensuremath{\simeq}0.3$ and $\mathcal{V}\ensuremath{\simeq}{1/0.3}^{3}\ensuremath{\simeq}30$ using ${I}_{o}{/I}_{\mathrm{SQL}}=1.$ $Variational\ensuremath{-}output---\ensuremath{\mu}\ensuremath{\simeq}{\ensuremath{\epsilon}}_{*}^{1/4}\ensuremath{\simeq}0.3$ and $\mathcal{V}\ensuremath{\simeq}30$ but only if the optics can handle a ten times larger power: ${I}_{o}{/I}_{\mathrm{SQL}}\ensuremath{\simeq}1/\sqrt{{\ensuremath{\epsilon}}_{*}}=10.$ $\mathrm{Squeezed}\mathrm{varational}---\ensuremath{\mu}{=1.3(e}^{\ensuremath{-}2R}{\ensuremath{\epsilon}}_{*}{)}^{1/4}\ensuremath{\simeq}0.24$ and $\mathcal{V}\ensuremath{\simeq}80$ using ${I}_{o}{/I}_{\mathrm{SQL}}=1;$ and $\ensuremath{\mu}\ensuremath{\simeq}{(e}^{\ensuremath{-}2R}{\ensuremath{\epsilon}}_{*}{)}^{1/4}\ensuremath{\simeq}0.18$ and $\mathcal{V}\ensuremath{\simeq}180$ using ${I}_{o}{/I}_{\mathrm{SQL}}=\sqrt{{e}^{\ensuremath{-}2R}/{\ensuremath{\epsilon}}_{*}}\ensuremath{\simeq}3.2.$

DOI
10.1103/physrevd.65.022002

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In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g., LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. A previous paper analyzed a straightforward but impractical design for a speed-meter interferometer that accomplishes this. This paper describes some practical variants of speed-meter interferometers. Like the original interferometric speed meter, these designs in principle can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies. These variants essentially consist of a Michelson interferometer plus an extra ``sloshing'' cavity that sends the signal back into the interferometer with opposite phase shift, thereby cancelling the position information and leaving a net phase shift proportional to the relative velocity. In practice, the sensitivity of these variants will be limited by the maximum light power Wcirc{W}_{\mathrm{circ}}Wcirc​ circulating in the arm cavities that the mirrors can support and by the leakage of vacuum into the optical train at dissipation points. In the absence of dissipation and with squeezed vacuum (power squeeze factor ${e}^{\ensuremath{-}2R}\ensuremath{\simeq}0.1)$ inserted into the output port so as to keep the circulating power down, the SQL can be beat by ${h/h}_{\mathrm{SQL}}\ensuremath{\sim}\sqrt{{W}_{\mathrm{circ}}^{\mathrm{SQL}}{e}^{\ensuremath{-}2R}{/W}_{\mathrm{circ}}}$ at all frequencies below some chosen ${f}_{\mathrm{opt}}\ensuremath{\simeq}100\mathrm{Hz}.$ Here ${W}_{\mathrm{circ}}^{\mathrm{SQL}}\ensuremath{\simeq}800\mathrm{kW}{(f}_{\mathrm{opt}}/100\mathrm{}\mathrm{Hz}{)}^{3}$ is the power required to reach the SQL in the absence of squeezing. (However, as the power increases in this expression, the speed meter becomes more narrow band; additional power and reoptimization of some parameters are required to maintain the wide band. See Sec. III B.) Estimates are given of the amount by which vacuum leakage at dissipation points will debilitate this sensitivity (see Fig. 12); these losses are 10% or less over most of the frequency range of interest $(f\ensuremath{\gtrsim}10\mathrm{Hz}).$ The sensitivity can be improved, particularly at high freqencies, by using frequency-dependent homodyne detection, which unfortunately requires two 4-km-long filter cavities (see Fig. 4).
The quantum noise of the light field is a fundamental noise source in interferometric gravitational wave detectors. Injected squeezed light is capable of reducing the quantum noise contribution to the detector noise floor to values that surpass the so-called Standard-Quantum-Limit (SQL). In particular, squeezed light is useful for the detection of gravitational waves at high frequencies where interferometers are typically shot-noise limited, although the SQL might not be beaten in this case. We theoretically analyze the quantum noise of the signal-recycled laser interferometric gravitational-wave detector GEO600 with additional input and output optics, namely frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We focus on the frequency range between 1 kHz and 10 kHz, where, although signal recycled, the detector is still shot-noise limited. It is found that the GEO600 detector with present design parameters will benefit from frequency dependent squeezed light. Assuming a squeezing strength of -6 dB in quantum noise variance, the interferometer will become thermal noise limited up to 4 kHz without further reduction of bandwidth. At higher frequencies the linear noise spectral density of GEO600 will still be dominated by shot-noise and improved by a factor of 10^{6dB/20dB}~2 according to the squeezing strength assumed. The interferometer might reach a strain sensitivity of 6x10^{-23} above 1 kHz (tunable) with a bandwidth of around 350 Hz. We propose a scheme to implement the desired frequency dependent squeezing by introducing an additional optical component to GEO600s signal-recycling cavity.
The ability to directly detect gravitational waves will open a completely new branch of astronomy to view the Universe, one that is inaccessible to electromagnetic-based astronomy. First generation ground-based interferometric gravitational-wave detectors have achieved strain sensitivities of order one part in ten to the twenty-one, at 100 Hz detection frequency. A new generation of detectors are under construction, designed to improve on the sensitivity of the first-generation detectors by a factor of 10. The quantum nature of light will broadly limit the sensitivity of these new instruments. This quantum noise will originate from the quantum vacuum fluctuations that enter the unused port of the interferometer. One of the most promising options for reducing the quantum noise impact and further increasing the sensitivity is applying quantum squeezed vacuum states. These squeezed states have lower noise in one quadrature than the vacuum state. By replacing the quantum vacuum fluctuations entering the interferometer with squeezed vacuum states, the quantum noise impact is reduced. This thesis firstly details the development of a squeezed light source that produces squeezed states applicable for enhancing interferometric gravitational-wave detectors. A doubly-resonant, travelling-wave bow-tie cavity squeezed light source is presented. For the first time, greater than 10 dB of quantum noise suppression across the gravitational-wave detection band is directly observed, and 11.6 dB of quantum noise suppression is observed above 200 Hz. This squeezing cavity design also has benefits with intrinsic isolation to backscattered light. Experiments that quantify this isolation are reported. The properties affecting squeezing magnitude and low-frequency squeezing measurement are discussed. In addition, a modified squeezing-ellipse-phase control technique for squeezed vacuum states is presented. This thesis secondly presents results from the LIGO Squeezed Light Injection Experiment, undertaken to test squeezed light injection into a 4 km interferometric gravitational-wave detector. The results of the experiment show the first measurement of squeezing-enhancement in a 4 km gravitational-wave detector, with 2.15 dB measured above 250 Hz. This represents the best sensitivity to gravitational waves yet achieved at these frequencies by any single gravitational-wave detector to date. An unknown area was whether the addition of a squeezer would introduce noise couplings that degrade the crucial low frequency sensitivity. The results demonstrate that injected squeezed states are compatible with low frequency gravitational-wave measurement. The characterisation of squeezing-injection optical losses and fluctuations of the squeezing angle are also reported. The knowledge and processes gained, from both the squeezed light source development work and the LIGO Squeezed Light Injection Experiment, will inform the design, planning and implementation of squeezed states in future gravitational-wave detectors.
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
In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g. LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors rather than monitoring their relative position. This paper describes and analyzes the most straightforward design for a speed meter interferometer that accomplishes this---a design (due to Braginsky, Gorodetsky, Khalili and Thorne) that is analogous to a microwave-cavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and is used to show [in accord with the speed being a quantum nondemolition observable] that in principle the interferometric speed meter can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies, and can do so without the use of squeezed vacuum or any auxiliary filter cavities at the interferometer's input or output. However, in practice, to reach or beat the SQL, this specific speed meter requires exorbitantly high input light power. The physical reason for this is explored, along with other issues such as constraints on performance due to optical dissipation. This analysis forms a foundation for ongoing attempts to develop a more practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising LIGO-III/EURO interferometer design that entails low laser power.
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, [Delta]X1 [Delta]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.