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arXiv:gr-qc/9703005 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum nondemolition and higher order effects for a nonlinear meter in an interferometric gravitational wave antenna

Yu. Levin

Published Feb 15, 1998• 1 citation
arXivHTMLPDF

Abstract

A new optical topology and signal readout strategy for a laser interferometer gravitational wave detector were proposed recently by Braginsky and Khalili. Their method is based on using a nonlinear medium inside a microwave oscillator to detect the gravitational-wave-induced spatial shift of the interferometer's standing optical wave. This paper proposes a quantum nondemolition scheme that could be realistically used for such a readout device and discusses a ``fundamental'' sensitivity limit imposed by a higher order optical effect.

DOI
10.1103/physrevd.57.2069

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A new optical topology and signal readout strategy for a laser interferometer gravitational wave detector were proposed recently by Braginsky and Khalili. Their method is based on using a nonlinear medium inside a microwave oscillator to detect the gravitational-wave-induced spatial shift of the interferometer's standing optical wave. This paper proposes a quantum nondemolition scheme that could be realistically used for such a readout device and discusses a ``fundamental'' sensitivity limit imposed by a higher order optical effect.
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.
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Quantum fluctuation of light limits the sensitivity of advanced laser interferometric gravitational-wave detectors. It is one of the principal obstacles on the way towards the next-generation gravitational-wave observatories. The envisioned significant improvement of the detector sensitivity requires using quantum non-demolition measurement and back-action evasion techniques, which allow us to circumvent the sensitivity limit imposed by the Heisenberg uncertainty principle. In our previous review article (Danilishin and Khalili in Living Rev Relativ 15:5, 2012 ), we laid down the basic principles of quantum measurement theory and provided the framework for analysing the quantum noise of interferometers. The scope of this paper is to review novel techniques for quantum noise suppression proposed in the recent years and put them in the same framework. Our delineation of interferometry schemes and topologies is intended as an aid in the process of selecting the design for the next-generation gravitational-wave observatories.
A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.
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).