Arm-length stabilisation for interferometric gravitational-wave detectors using frequency-doubled auxiliary lasers
Adam J. Mullavey, Bram J. J. Slagmolen, John Miller, Matthew Evans, Peter Fritschel, Daniel Sigg, Sam J. Waldman, Daniel A. Shaddock, David E. McClelland
aa r X i v : . [ phy s i c s . i n s - d e t ] D ec Arm-length stabilisation forinterferometric gravitational-wavedetectors using frequency-doubledauxiliary lasers
Adam J. Mullavey, Bram J. J. Slagmolen, John Miller, , ∗ Matthew Evans, Peter Fritschel, Daniel Sigg, Sam J. Waldman, Daniel A. Shaddock, and David E. M c Clelland Centre for Gravitational Physics, The Australian National University,Canberra, ACT, 0200, AUSTRALIA LIGO Laboratory, Massachusetts Institute of Technology,185 Albany St, Cambridge, MA 02139, USA LIGO Hanford Observatory, PO Box 159, Richland, WA 99352, USA*[email protected]
Abstract:
Residual motion of the arm cavity mirrors is expected toprove one of the principal impediments to systematic lock acquisitionin advanced gravitational-wave interferometers. We present a techniquewhich overcomes this problem by employing auxiliary lasers at twicethe fundamental measurement frequency to pre-stabilise the arm cavities’lengths. Applying this approach, we reduce the apparent length noise of a1.3 m long, independently suspended Fabry-Perot cavity to 30 pm rms andsuccessfully transfer longitudinal control of the system from the auxiliarylaser to the measurement laser. © 2018 Optical Society of America
OCIS codes: (120.2230) Fabry-Perot; (120.3180) Interferometry.
References and links
1. C. Cutler and K. S. Thorne, “An overview of gravitational wave sources”, in
General Relativity and Grav-itation,
N. T. Bishop and S. D. Maharaj, eds. (World Scientific Publishing Company, 2002), pp. 72–112. http://arxiv.org/abs/gr-qc/0204090 .2. H. L¨uck, C. Affeldt, J. Degallaix, A. Freise, H. Grote, M. Hewitson, S. Hild, J. Leong, M. Prijatelj, K. A. Strain,B. Willke, H. Wittel, and K. Danzmann, “The upgrade of GEO 600,” JPCS , 012012 (2010).3. K. Kuroda and the LCGT Collaboration, “Status of LCGT,” Classical Quant. Grav. , 084004 (2010).4. G. M. Harry and the LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wavedetectors,” Classical Quant. Grav. , 084006 (2010).5. The VIRGO Collaboration, “Status of the Virgo project,” Classical Quant. Grav. , 114002 (2011).6. The LIGO Scientific Collaboration and the VIRGO Collaboration, “TOPICAL REVIEW: Predictions for therates of compact binary coalescences observable by ground-based gravitational-wave detectors,” Classical Quant.Grav. , 173001 (2010).7. O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov,S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “LockAcquisition Scheme For The Advanced LIGO Optical configuration,” JPCS , 265–269 (2006).8. R. L. Ward, “Length Sensing and Control of a Prototype Advanced Interferometric Gravitational Wave Detector,”Ph.D. thesis, California Institute of Technology (2010).9. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase andfrequency stabilization using an optical resonator,” Appl. Phys. B , 97–105 (1983).0. N. A. Robertson, B. Abbott, R. Abbott, R. Adhikari, G. S. Allen, H. Armandula, S. M. Aston, A. Baglino,M. Barton, B. Bland, R. Bork, J. Bogenstahl, G. Cagnoli, C. Campbell, C. A. Cantley, K. Carter, D. Cook,D. Coyne, D. R. Crooks, E. J. Daw, D. B. DeBra, E. Elliffe, J. Faludi, P. Fritschel, A. Ganguli, J. A. Gi-aime, S. Gossler, A. Grant, J. Greenhalgh, M. Hammond, J. Hanson, C. Hardham, G. M. Harry, A. Heptonstall,J. Heefner, J. Hough, D. Hoyland, W. Hua, L. Jones, R. Jones, J. E. Kern, J. LaCour, B. T. Lantz, K. Lilienkamp,N. Lockerbie, H. L¨uck, M. MacInnis, K. Mailand, K. Mason, R. Mittleman, S. A. Nayfeh, J. Nichol, D. J. Ott-away, H. Overmier, M. Perreur-Lloyd, J. Phinney, M. V. Plissi, W. Rankin, D. I. Robertson, J. Romie, S. Rowan,R. Scheffler, D. H. Shoemaker, P. Sarin, P. H. Sneddon, C. C. Speake, O. Spjeld, G. Stapfer, K. A. Strain, C. I.Torrie, G. Traylor, J. van Niekerk, A. Vecchio, S. Wen, P. Willems, I. Wilmut, H. Ward, M. Zucker, and L. Zuo,“Seismic isolation and suspension systems for Advanced LIGO,” in Gravitational Wave and Particle AstrophysicsDetectors , J. Hough and G. H. Sanders, eds., Proc. SPIE , 81-91 (2004).11. J. Miller, M. Evans, L. Barsotti, P. Fritschel, M. MacInnis, R. Mittleman, B. Shapiro, J. Soto, and C. Torrie,“Damping parametric instabilities in future gravitational wave detectors by means of electrostatic actuators,”Phys. Lett. A , 788 – 794 (2011).12. D. A. Shaddock, “Digitally enhanced heterodyne interferometry,” Opt. Lett. , 3355–3357 (2007).13. R. W. P. Drever and S. J. Augst, “Extension of gravity-wave interferometer operation to low frequencies,” Clas-sical Quant. Grav. , 2005–2011 (2002).14. M. Principe, “Noise Modeling and Reduction in Gravitational Wave Detection Experiments,” Ph.D. thesis, Uni-versity of Sannio, Benevento (2010).15. A. Villar, E. Black, G. Ogin, T. Chelermsongsak, R. DeSalvo, I. Pinto, and M. Principe, “Loss angles from thedirect measurement of Brownian noise in coatings,” presented at the LSC-Virgo meeting, Krakow, Poland, 20-24Sept. 2010.16. D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIPConf. Proc. , 654–660 (2006).17. L.-S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate can-cellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. , 1777–1779(1994).18. A. J. Mullavey, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, “Stable transfer of an optical frequencystandard via a 4.6 km optical fiber,” Opt. Exp. , 5213–5220 (2010).19. B. J. J. Slagmolen, P. Fritschel, D. Sigg, J. Miller, A. J. Mullavey, S. J. Waldman, M. Evans, K. Arai, A. F. Brooks,D. Yeaton-Massey, L. Barsotti, R. Adhikari, and D. E. McClelland, “Arm-Length Stabilisation for AdvancedLIGO lock acquisition,” In preparation (2011).20. B. J. J. Slagmolen, A. J. Mullavey, J. Miller, D. E. McClelland, and P. Fritschel, “Tip-Tilt mirror suspension:Beam steering for Advanced LIGO sensing and control signals,” Submitted to: Rev. Sci. Instrum. (2011).
1. Introduction
Direct detection of gravitational radiation, predicted by Einstein’s general theory of relativity,remains one of the most exciting challenges in experimental physics. Due to their relativelyweak interaction with matter, gravitational waves promise to allow exploration of hitherto in-accessible processes and epochs [1]. Unfortunately, this weak coupling also hinders detectionwith strain amplitudes at the Earth estimated to be . − . Nevertheless, the network of ad-vanced gravitational wave detectors currently under construction [2–5] is widely expected tooperate with sufficient sensitivity to observe several events per year (see e.g. [6]).Modern gravitational-wave detectors are Michelson-style interferometers, enhanced by theaddition of resonant cavities at their inputs, outputs and, generally, in each of their arms (seeFig. 1). When all of these cavities are held within their respective linewidths by interferometercontrol systems we say that the interferometer is locked . When the interferometer is not lockedno meaningful scientific data can be recorded. Due to interactions between the optical cavities,lock acquisition is a non-trivial problem.The second generation of interferometric gravitational-wave detectors will employ higherfinesse (narrower linewidth) arm cavities. Recent investigations indicate that it is these armcavities which will pose the greatest challenges during the lock acquisition process [7,8]. In thiswork we develop a tool, an arm-length stabilisation system or ALS , to address these challenges. Y L X l Y l SR l X l PR MICH = l X - l Y PRCL = l PR +( l X + l Y )/2SRCL = l SR +( l X + l Y )/2DARM = L X - L Y CARM = ( L X + L Y )/2InputLaser DetectionPhotodiode Fig. 1. (Colour online) Schematic of a contemporary gravitational-wave interferometer in-dicating primary length degrees of freedom. In this work MICH, PRCL and SRCL aredescribed as central degrees of freedom. The arms have lengths L X , Y of order 1 km; theother cavities, PRCL and SRCL, are significantly shorter ( .
50 m).
2. Arm-length stabilisation
The length degrees of freedom of all gravitational-wave interferometers are controlled using anextension of the Pound-Drever-Hall (PDH) technique [9] – radio-frequency phase-modulationsidebands are impressed upon the input laser light at multiple frequencies and the circulatingfield is detected and demodulated at selected interferometer output ports [7, 8].The resonant state of the modulation sidebands, the demodulation frequencies and phases,and the macroscopic cavity lengths are all carefully chosen to provide low-noise sensing sig-nals for each of the degrees of freedom when the interferometer is locked. In particular, themodulation frequencies are chosen such that the control sidebands do not resonate inside thearm cavities.Due to the optical couplings between the various cavities, these detection schemes do notalways provide reliable sensing signals during lock acquisition. In this respect, the arm cavitiesare singularly troublesome.Advanced gravitational-wave interferometers utilise multi-stage seismic isolation systemswhich offer excellent performance above ∼ ∼ µ m rms, 1000 times greaterthan a typical arm cavity’s linewidth ( ∼ ∼
40 kg). As a result of thesechoices, the test mass actuators will often lack sufficient authority to gain control over the armcavities when they are freely swinging.Although it is possible to acquire lock under these conditions, this acquisition cannot berealised in a repeatable, systematic manner. The goals of the arm-length stabilisation systemare therefore twofold:a) Maintain both arm cavities at a fixed offset from resonance so that the central degrees offreedom may be locked without obstruction.b) Reduce rms cavity motion to within one linewidth ( ∼
3. Technique
We now describe the approach adopted to achieve the above goals, providing a general descrip-tion of the strategy applied followed by explanatory details concerning one possible practicalimplementation. Compared to other techniques considered for arm-length stabilisation, this ap-proach relies on proven technologies, offers greater sensitivity [12] and is less invasive [13].
An additional auxiliary laser is placed behind each end test mass. These lasers are indepen-dently locked to their respective arm cavities by actuating on the lasers’ frequencies, circum-venting the weak test mass actuators.By comparing the frequencies of the auxiliary lasers to the frequency of the main interfer-ometer’s pre-stabilised laser (PSL), one can construct ALS signals describing the offset of thePSL from resonance in the arms. Outside of the cavity linewidth, conventional length sensingsignals are often non-linear and cannot be used to effect closed-loop control. In contrast, theseALS signals remain valid even when the PSL is far removed from resonance; hence they canbe used to actively stabilise and adjust the detunings of the arms during lock acquisition byactuating on the end test masses.To avoid cross-coupling between main interferometer and arm-length stabilisation signals,the auxiliary lasers operate at 532 nm. This wavelength was chosen for its harmonic relationshipto the wavelength of the PSL (1064 nm). The use of two distinct wavelengths demands that thearm cavity mirror coatings be dichroic. The choice of cavity finesse (i.e. mirror reflectivities) at532 nm is relatively free. Low values ease auxiliary laser lock acquisition whilst higher valuesprovide improved mode filtering and noise performance. A finesse of around 100 represents areasonable compromise. Dichroic mirrors compatible with this specification are not expectedto increase the observed mirror thermal noise significantly [14, 15].
We now proceed through our realisation of this arm-length stabilisation strategy sequentially(see Fig. 2). For clarity, we consider only a single resonant cavity, representing one arm of anadvanced interferometer.1. The 532 nm output of a dual-wavelength (1064 nm and 532 nm) auxiliary laser is lockedto the arm cavity using the PDH technique. This wide-bandwidth ( >
10 kHz) control loopprovides the reference measurement of the arm’s resonant frequency. The auxiliary laserremains tightly locked to the arm cavity at all times whilst the ALS system is active. . PDH2. Digitalphasemeter 4. Frequencyoffset 5. PDH3. PLLservo PSLAuxiliaryLaser 532 nmElectrical1064 nm/
Fig. 2. (Colour online) Schematic of the arm-length stabilisation system. The numberingindicates the flow of the lock acquisition process and corresponds to the enumerated listbelow.
2. The frequency of the auxiliary laser is subsequently compared to that of the PSL bymeasuring the frequency of their heterodyne beat note using a LISA-like digital phaseme-ter [16]. This comparison is made at 1064 nm using the auxiliary laser’s second output(which has a constant phase relationship with the 532 nm beam). The beat-note frequencyindicates how far the PSL beam is from resonating in the arm cavity. The extensive linearrange of this heterodyne measurement, compared to conventional PDH-based sensors, is thekey feature of the ALS system.In an operational gravitational-wave detector this measurement necessitates the transfer of afrequency reference through ∼
4. Experimental test
In order to validate the fundamental approach discussed above, a laboratory-scale proof-of-principle experiment was carried out at The Australian National University’s Centre for Gravi-tational Physics. To concentrate on the novel aspects of the arm-length stabilisation system, weagain examined only a single optical resonator.Our 1.3 m long cavity was formed from two single-stage piano-wire suspension systemsknown as ‘Tip-Tilts’ [20]; it had a g-factor of 0.46 and measured finesses of 300 at 1064 nm and100 at 532 nm. (For comparison, the Advanced LIGO detectors are expected to have finessesof approximately 450 and 100.) The dichroic cavity mirrors were controlled by coil-magnetactuators via an Advanced LIGO digital control system. The role of the PSL was played by astandard diode-pumped solid-state laser (JDSU NPRO 126); the auxiliary laser was an InnolightPrometheus. N o r m a li s e d PS L P o w e r −101 PS L P DH [ a . u . ] N o r m a li s e d A ux . P o w e r −20 Fig. 3. (Colour online) Systematic cavity detuning over more than one free spectral rangeusing the arm-length stabilisation system. Top – Normalised cavity transmission at thewavelength of the measurement laser (1064 nm); Middle – Pound-Drever-Hall signal gen-erated from the measurement laser alone; Bottom – Normalised cavity transmission at thewavelength of the auxiliary laser (532 nm). n Fig. 3 we conclusively demonstrate the technique’s capacity to explore the full range ofarm cavity detunings. With the ALS system active, the offset frequency of the phase-lockedloop (item 4 in Fig. 2) was swept linearly over more than one free spectral range. Since theauxiliary laser is securely locked to the arm cavity, this offset frequency directly controls thedetuning of the PSL from resonance.In a gravitational-wave interferometer this capability would permit us to maintain a specifieddetuning, away from any undesirable resonances, allowing the central degrees of freedom tobe easily locked, thus meeting the first ALS goal. The extent to which the specified detuning is‘fixed’ will be explored below.Complete command over arm cavity detuning also allows us to satisfy the implicit goal ofmanoeuvring the cavity system from a stable off-resonance state to a position where acquisitionsignals become meaningful. A typical handover from ALS to PSL control signals is shown inFig. 4. N o r m a li s e d PS L po w e r R e l a ti v e l oop g a i n N o r m a li s e d A ux . po w e r (i) (ii) (iii) (iv) Fig. 4. (Colour online) Transfer of arm cavity length control from the arm-length stabil-isation system to signals derived solely from the measurement laser. Top – Normalisedcavity transmission at the wavelength of the measurement laser (1064 nm); Middle – Rela-tive gain of arm-length stabilisation (blue dashed) and measurement laser (grey) controlsignals; Bottom – Normalised cavity transmission at the wavelength of the auxiliary laser(532 nm). The division of the axes into four regions is discussed in the main text. Thetimescale of this handover does not represent the limit of system performance.
The axes are divided into four shaded regions, representing different stages of the transfer:(i) The cavity is initially stabilised at a point far from resonance. The detuning is reduced inan orderly fashion by adjusting the offset frequency of the phase-locked loop.(ii) The cavity approaches resonance, circulating power begins to increase and PSL-basedcontrol signals become viable.(iii) Control over the cavity length is transferred to the PSL. As both PSL and ALS systemsactuate on the cavity’s end test mass, this handover is realised simply by tuning the rela-tive gain of the two feedback loops.(iv) The cavity is under the control of PSL signals alone. −1 −15 −14 −13 −12 −11 −10 −9 Frequency [Hz] D i s p l ace m e n t no i s e m√Hz RequirementRMS
Fig. 5. (Colour online) Residual cavity displacement noise relative to the measurementlaser with arm-length stabilisation system active. The integrated rms noise (dashed line)is within one full-width-half-maximum cavity linewidth (solid horizontal line) as required.Data shown in this figure were taken with our optical table’s pneumatic vibration isolatorsactivated. The prominent features around 1 Hz are due to the mechanical resonances of thissystem. All other presented data were recorded with this isolation system turned off.
Recall that the second goal of the arm-length stabilisation system is to reduce the rms dis-placement noise of the arm cavity, relative to the PSL, to within one linewidth. The full-width-half-maximum-power cavity linewidth is given by D FWHM = (cid:26) l / ( F ) [m] c / ( L F ) [Hz] , (1)where l is the laser wavelength, F is the cavity finesse, c is the speed of light and L is thecavity length. For our parameters the cavity linewidth is approximately 1.8 nm, comparable tothe Advanced LIGO value of 1.2 nm.This specification was tested by tuning the cavity onto resonance using the arm-length stabil-isation system and employing the PSL PDH measurement as an out-of-loop sensor. The result-ing amplitude spectral density is shown in Fig. 5. The integrated rms motion (dashed line) wasfound to be 30.2 pm, comfortably meeting the cavity-linewidth requirement (solid horizontalline).Figure 5 also describes the stability of any offset from resonance (e.g. that introduced whenlocking the central degrees of freedom) as the performance of the ALS system does not vary asa function of arm cavity detuning.Combined, the above findings demonstrate the validity of arm-length stabilisation ap-proaches based on frequency-doubled auxiliary lasers. This positive result should, nevertheless,be considered in context. Any extrapolation of the work presented here to a kilometre-scale in-terferometer will require the differences in environment, test mass actuation and optical config-uration to be addressed. However, recent simulation work predicts that, taking these differencesinto account, the linewidth specification can still be met [19]. . Discussion The results presented in Fig. 5 reveal an increase in noise at low frequencies ( <
6. Conclusions
In this investigation we have developed the general method of arm-length stabilisation basedon auxiliary lasers. We have demonstrated the viability of this approach using a single cavity,stabilising its residual motion to within one cavity linewidth.Our method is described as a series of key measurements. Each of these measurements canbe made using several proven techniques, allowing the scheme to be easily modified withoutreducing capability.A conceptually identical arm-length stabilisation system, based on frequency-doubled aux-iliary lasers, has now been selected as a baseline technology for Advanced LIGO. Testing ofthis scheme on a fully-suspended, dual-recycled interferometer is underway at the CaliforniaInstitute of Technology.The integration of the ideas introduced here into the Advanced LIGO length sensing and con-trol architecture will not be without challenges. However, an effective arm-length stabilisationsystem would, for the first time, decouple the arm cavities from the central degrees of freedomand enable global control to be achieved from the start of a repeatable and diagnosable lockacquisition sequence.