Thermal noise in mirror suspension is and will be the most severe fundamental limit to the low-frequency sensitivity of interferometric gravitational wave detectors currently under construction. The technical solutions, adopted in the Virgo detector, optimize the current suspension scheme, but new materials and new designs are needed to further reduce the suspension thermal noise. Silicon fibers are promising candidates both for room temperature advanced detectors and for future cryogenic interferometric detectors

Alessandra Toncelli

F. Travasso

F. Vetrano

Fabio Marchesoni

G. Losurdo

H. Vocca

L. Bosi

Luca Gammaitoni

M. Punturo

M. Tonelli

Marina Mazzoni

P. Amico

Ruggero Stanga

English

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ARTICLE IN PRESSNuclear Instruments and Methods in Physics Research A 518 (2004) 240–243*CorrespE-mail a0168-9002/$doi:10.1016Thermal noise reduction for present and futuregravitational wave detectorsP. Amicoa,b, L. Bosia,b, L. Gammaitonia,b, G. Losurdoc, F. Marchesonia,d,M. Mazzonic,e, M. Punturoa,*, R. Stangac,e, A. Toncellif,g, M. Tonellif,g,F. Travassoa,b, F. Vetranoc,h, H. Voccaa,ba Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via Pascoli, Perugia, ItalybDipartimento di Fisica, Universit !a di Perugia, Perugia, Italyc Istituto Nazionale di Fisica Nucleare, Sezione di Firenze/Urbino, Firenze, ItalydDipartimento di Fisica, Universit !a di Camerino, Camerino, ItalyeDipartimento di Fisica, Universit !a di Firenze, Firenze, Italyf Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Pisa, ItalygDipartimento di Fisica, Universit !a di Pisa, Pisa, Italyh Istituto di Fisica, Universit !a di Urbino, Urbino, ItalyAbstractThermal noise in mirror suspension is and will be the most severe fundamental limit to the low-frequency sensitivityof interferometric gravitational wave detectors currently under construction. The technical solutions, adopted in theVirgo detector, optimize the current suspension scheme, but new materials and new designs are needed to further reducethe suspension thermal noise. Silicon fibers are promising candidates both for room temperature advanced detectorsand for future cryogenic interferometric detectors.r 2003 Elsevier B.V. All rights reserved.PACS: 43.40.Cw; 62.40.+i; 05.40.a; 04.80.NnKeywords: Gravitational wave detectors; Thermal noise; Silicon1. IntroductionThe thermal noise sources in an interferometricgravitational waves (GW) detector are mainly two:the suspension wires fluctuation and the mirrorinternal vibration. Both the phenomena aredescribed by the fluctuation–dissipation theorem[1], that relates the thermal fluctuation spectrum toonding author. Fax: +39-075-584-72-96.ddress: michele.punturo@pg.infn.it (M. Punturo).- see front matter r 2003 Elsevier B.V. All rights reserve/j.nima.2003.10.071the dissipation processes inside the observedsystem. A detailed description of the thermal noisedue to suspension wires in a GW detector can befound in Ref. [2]. The horizontal displacementpower spectrum jXhðoÞj2; neglecting any horizontalto vertical coupling in the suspension, is given byjXhðoÞj2C4kBTo5g1L2wffiffiffiffiffiffiffiffiffiffiffiEg4pnmrfðoÞCsTB ð1Þwhere Lw is the suspension wire length, E is theYoung’s modulus of the wire material, n is thed.ARTICLE IN PRESSFig. 1. Virgo sensitivity curves: (a) the expected current Virgosensitivity; (b) the thermal noise contribution (pendulum andmirror) for an upgraded version of Virgo, using monolithicfused silica suspension. The other curves represent the thermalnoise contribution in an advanced cryogenic GW detector using(c) silicon suspension fibers and calcium fluoride substrates at5 K; (d) Si suspension fibers and substrates at 123 K; (e) Sisuspension fibers and substrates at 5 K: In the cryogenicdetector simulation a Q ¼ 108 has been used as mechanicalquality factor for the mirror, neglecting the coating dissipation;the mirror thermal noise increase, due to a 6 mm thick Ta2O5coating, is reported in the figure.P. Amico et al. / Nuclear Instruments and Methods in Physics Research A 518 (2004) 240–243 241number of suspension wires (in Virgo n ¼ 4) foreach mirror of mass m and Cs is the percentage oftensile breaking stress TB at which the wire isloaded. The loss angle fðoÞ represents the sum ofall the dissipative processes that occur in thesuspension wire: fðoÞ ¼ fw þ fe þ fthðoÞ; wherefw is the loss angle due to the wire material itself,fe is the excess loss angle due to parasiticdissipation processes, like the residual clampinglosses [3] and fthðoÞ is the (linear) thermoelasticcontribution:fthðoÞ ¼ Dot1þ ðotÞ2;D ¼Ea2Tcv; t ¼cvd2w2:16 2p kð2Þwhere cv is the specific heat per volume unit, a thelinear expansion coefficient and k is the thermalconductivity of the wire material. In Virgo, thanksto the very efficient seismic noise filtering system[4], the thermal noise given by Eq. (1) dominatesfrom about 4 up to 500 Hz:2. Current solutionAlmost all the GW interferometric detectors(LIGO, TAMA and Virgo) are realized suspend-ing the mirrors, composing the optical cavities ofsuch interferometers, by metallic wires. In Virgo aspecific kind of steel (C85) has been choosen thatoptimizes [5] the ratio between brackets in Eq. (1).In this configuration the main effort, in terms ofthermal noise reduction, is devoted to the mini-mization of the excess losses, using a low dissipa-tion clamping system [3] and inserting fused silicaspacers in the wire-to-mirror contact points [6].The mirror thermal noise is optimized reducing theexcess dissipation introduced by the controlcomponents (camera targets, magnets andspacers), attaching them through the silicatebonding [2] technology. With these solutions apendulum quality factor Q and mirror Q of about106 has been obtained, reaching the expectedsensitivity curve (curve (a)) reported in Fig. 1.3. Future developments3.1. Fused silica fibersIt is well known that, using fused silica (FS)fibers to suspend the mirrors, it is possible tostrongly reduce the thermal noise on the pendulumoscillation mode; the GEO600 GW detectoralready uses a monolithic design, but, because ofseveral technical issues, with different and morerelaxed specifications with respect to the Virgorequirements. FS fibers show an intrinsic loss angleof about two orders of magnitude lower thanmetallic wires [5]. The thermo-elastic dissipation inFS fibers is suppressed by the fact that the thermalexpansion coefficient a is about 0:5 106 K1 atroom temperature. The tensile strength of a FSfiber is about TbC4 GPa [2], dominated by thecracks and defects present in the fiber surface(low Cs). In the Perugia labs, the development of aFS suspension for Virgo has successfully com-pleted the research phase and, now, it is in theARTICLE IN PRESSP. Amico et al. / Nuclear Instruments and Methods in Physics Research A 518 (2004) 240–243242engineering phase. A full scale prototype will besoon realized in the Virgo site. The maindifficulties in the realization of this suspensionare due to the fact that Virgo has the largest andheaviest mirrors available in the current GWdetectors and the seismic attenuation system iscurrently the most complex one realized for aGW detector. The sensitivity of Virgo, withmonolithic FS suspension should improve asreported in Fig. 1 (curve (b)).3.2. Crystalline fibersFS fibers are not a good candidate to realize acryogenic suspension for a future interferometer;in fact, the dissipation angle of FS shows a(Debye) peak at low temperature and the lowthermal conducibility of FS reduces the extractionof the heat deposited by the laser in the mirror.Other materials must be investigated. In additionto the constraints imposed by Eq. (1) (low lossangle f; high tensile strength TB and highreliability Cs), a material, good to realize thesuspension of an advanced cryogenic interferom-eter, must show a high thermal conductivity and,possibly, a low thermal expansion coefficient. Thelatter characteristics reduce also the thermoelasticcontribution (see Eq. (2)) to the thermal noise.Several materials have been investigated, modelingtheir linear thermoelastic noise at room tempera-ture (see Fig. 2). Crystalline silicon is a goodFig. 2. Thermoelastic loss angles computed for differentmaterials at room temperature.candidate thanks to its high thermal conductivity(kð300 KÞ ¼ 1:48 102 W m1 K1) that pushesthe thermoelastic peak at higher frequency, wherethe pendulum thermal noise is not dominant.Silicon becomes a perfect candidate when it isstudied for a cryogenic interferometer; the largethermal conductivity (Fig. 3) at low temperaturepermits to extract a large fraction of energy fromthe interferometer mirror. The expansion coeffi-cient a is null (Fig. 3) at about 17 and 123 K; inthese conditions the contribution to the thermalnoise due to the linear thermoelastic effect is null.Furthermore, the intrinsic loss angle of Silicon isexpected to be very good ðfð300 KÞC2:8 108;fð77 KÞC5 109 and fð4:2 KÞC6 1010Þ [8]and the breaking strength of a Si fiber is largerthan steel (about 7 GPa; but still dominated bysurface effects that decrease that value down toabout 1 GPa). For all these reasons crystallinesilicon is a very good candidate to realize thesuspensions of a future cryogenic interferometer.A fiber production facility, using the mPull-Downtechnique, is under development, in the Pisa labs,to realize crystalline fibers to be tested in acryogenic environment. If a new generation oflasers at wavelength longer than 1:3 mm; withcharacteristics compatible with the requirementsof a GW detector, will be developed, crystallinesilicon it is also interesting to realize the substratesof a cryogenic interferometric GW detector. Infact, the low thermal expansion coefficient, atcryogenic temperature, reduces the thermodyna-mical noise [9], that is the main substrate thermalFig. 3. Thermal properties of silicon [7]: expansion coefficient(continuous line), conductivity (dashed line).ARTICLE IN PRESSP. Amico et al. / Nuclear Instruments and Methods in Physics Research A 518 (2004) 240–243 243noise source in other material candidates (sap-phire, calcium fluoride) for cryogenic GW inter-ferometer. The expected sensitivity of a futuredetector with silicon suspension fibers and sub-strates is reported in Fig. 1 (curves (c), (d) and (e)).3.2.1. Optical coolingIn the thermoelastic dissipation formula (2), theparameter T is the temperature of the flexuralpoint of the suspension wire. To reduce this noisecontribution, it is enough to cool down only alimited region around these flexural points. It isunder investigation the possibility to cool down alimited section of a crystalline fiber through atechnology based on the anti-Stokes luminescence[10]. In a rare-earth-doped fiber, the fundamentaland first excited energy atomic levels are split inmultiplets by Stark effect. The Stark splitting istypically small (ESC0:02 eVÞ; while the energy gapbetween the fundamental and excited levels isabout 1:2 eV ðlgC1 mmÞ: An incident laser (op-tical pump) of wavelength lg can excite the ions byabsorption; by interacting with the phonon energy,the emission can occur at a slight higher energy(DECES). Hence, this process can be used to cooldown a small sample. In effect, the energyextraction with this technology shows a lowefficiency (few percent), ulteriorly decreasing withthe overall temperature [10]. The cooling efficiencycan be increased by multiple interaction of theincident laser light with the crystalline medium. Ina fiber this could be implemented thanks to thecylindrical geometry of the sample. The possibilityto work with cryogenic GW interferometers atintermediate temperature, as suggested in thesilicon fiber case, permits to use this opticalcooling technique to cool down or to control thetemperature of the suspension fibers or, maybe,mirrors.AcknowledgementsThis work has been supported by the IstitutoNazionale di Fisica Nucleare, under the Virgoproject.References[1] H.B. Callen, T.A. Welton, Phys. Rev. 83 (1951) 34;H.B. Callen, R.F. Greene, Phys. Rev. 86 (1952) 702.[2] P. Amico, et al., Rev. Sci. Instrum. 73 (2002) 3318.[3] G. Cagnoli, et al., Phys. Lett. A 213 (1996) 245.[4] G. Ballardin, et al., Rev. Sci. Instrum. 72 (2001) 3643.[5] G. Cagnoli, et al., Phys. Lett. A 255 (1999) 230.[6] G. Cagnoli, et al., Rev. Sci. Instrum. 71 (2000) 2206.[7] C.A. Swenson, J. Phys. Chem. Ref. Data 12 (1983) 179.[8] J. Ferreirinho, in: D.G. Blair (Ed.), The Detectionof Gravitational Waves, Cambridge University Press,Cambridge, 1991.[9] V.B. Braginsky, et al., Phys. Lett. A 264 (1999) 1.[10] M.T Murtagh, et al., J. Non-Cryst. Solids 253 (1999) 50.

Thermal noise reduction for present and future gravitational wave detectors

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Thermal noise reduction for present and future gravitational wave detectors

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