Jan 17th 2006Ward Candicacy1 Length Sensing and Control for an Advanced Gravitational Wave Detector Robert Ward PhD Candidacy Caltech, 17 Jan 2006

Jan 17th 2006Ward Candicacy2 introduction lock acquisition modeling DC readout

Jan 17th 2006Ward Candicacy3 A New Window on the Universe Once Gravitational Waves are detected, a new field of Gravitational Wave Astronomy will open up. –GW stochastic background can tell us about cosmology (Big Bang, Inflation) –Cosmic Strings –Compact binary inspirals –GRBs –Supernova collapse –Black Hole ringdowns GW Astronomy will allow us to listen to what we cannot see.

Jan 17th 2006Ward Candicacy4 The Michelson Interferometer as a Gravitational Wave Detector Gravitational Waves act on freely falling masses: Antenna pattern laser Beam splitter mirrors Dark port photodiode Suspend the masses

Jan 17th 2006Ward Candicacy5 Upgrading the Michelson GWD LASER Gravitational Waves are tiny : they interact very weakly with matter. Need more than a simple michelson to have a chance of detection. OOM 1 km arms 10W NdYAG h = 10^-21 1 photon

Jan 17th 2006Ward Candicacy6 Upgrading the Michelson Fabry-Perot Arm Cavities (Like having longer arms) GWD

Jan 17th 2006Ward Candicacy7 Fabry-Perot Arm Cavities (Like having longer arms) Power Recycling (Like having a bigger LASER->lower shot noise) Upgrading the Michelson GWD

Jan 17th 2006Ward Candicacy8 Upgrading the Michelson Fabry-Perot Arm Cavities (Like having longer arms) Power Recycling (Like having a bigger LASER) Signal Recycling (Reshape the SIGNAL) GWD

Jan 17th 2006Ward Candicacy9 Why Signal Recycle? Why RSE? PRM BS FP cavity Laser GW signal Power Problem 2: Increasing the finesse of the arms causes the cavity pole frequency to decrease, leading to reduced bandwidth for GW signal. Solution 2: resonant sideband subtraction! SEM Problem 1: If the current Initial LIGO optical configuration (power-recycled Michelson with Fabry-Perot arms) is retained in AdLIGO, the increased laser power (needed for better sensitivity in the high-frequency shot-noise- limited regime) will put intolerable thermal load on the transmissive (absorptive, lossy) optics in the power recycling cavity (BS, ITM substrates). Solution 1: increase the finesse (optical gain) of the F-P arms, decrease the gain in the PRC.

Jan 17th 2006Ward Candicacy10 The Reason for AdLIGO: Initial and Advanced LIGO Factor 10 better amplitude sensitivity –(Reach) 3 = rate Factor 4 lower frequency bound NS Binaries: for three interferometers, –Initial LIGO: ~20 Mpc –Adv LIGO: ~300 Mpc BH Binaries: –Initial LIGO: 10 M o, 100 Mpc –Adv LIGO : 50 M o, z=2 Stochastic background: –Initial LIGO: ~3e-6 –Adv LIGO ~3e-9

Jan 17th 2006Ward Candicacy11 Improvement of reach with Advanced LIGO Virgo cluster LIGO I AdLIGO Improve amplitude sensitivity by a factor of 10x, and…  Number of sources goes up 1000x!

Jan 17th 2006Ward Candicacy12 AdLIGO noise curve Bench Active Seismic Isolation External Seismic Pre- Isolation Quadruple pendulum suspensions 40 kg, fused silica Test Masses 125W Laser Fight the Fundamental Noise Sources: 1)Seismic 2)Thermal 3)Quantum

Jan 17th 2006Ward Candicacy13 Caltech 40 meter prototype interferometer Objectives Develop a lock acquisition procedure for suspended-mass detuned RSE interferometer with power recycling, preferably one that will be applicable to Advanced LIGO BS PRM SRM X arm Dark port Bright port Y arm  Characterize and optimize optical configuration (for robust control and sensitivity)  Characterize noise mechanisms  Develop DC readout scheme  Test QND techniques  Extrapolate to AdLIGO via simulation  Prototyping will yield crucial information about how to build and run AdLIGO

Jan 17th 2006Ward Candicacy14 Bench: 40m Sensitivity Bench Not very likely that we’ll actually detect any gravitational waves here, but hopefully we’ll learn some things about operating interferometers, especially about the quantum noise.

Jan 17th 2006Ward Candicacy15 40m DARM Optical Plant The 40m operates in a detuned RSE configuration, which gives rise to two peaks in the DARM transfer function: 1)Optical Resonance 2)Optical Spring UGF

Jan 17th 2006Ward Candicacy16 Detune Cartoon Responses of GW USB and GW LSB are different due to the detuning of the signal recycling cavity. IFO Differential Arm mode is detuned from resonance at operating point DARM Carrier frequency frequency offset from carrier [Hz] Sideband amplitude [a.u.] FWHM USB LSB f sig IFO DARM/CARM slope related to spring constant IFO Common Arm mode is detuned from resonance at intial locking point PRCCARM SRC

Jan 17th 2006Ward Candicacy17 Signal Extraction Scheme Arm cavity signals are extracted from beat between carrier and f 1 or f 2. Central part (Michelson, PRC, SRC) signals are extracted from beat between f 1 and f 2, not including arm cavity information. Only +f 2 sideband resonates in combined PRC+SRC Double demodulation Central part information f1f1 -f 1 f2f2 -f 2 Carrier Single demodulation Arm information PRM

Jan 17th 2006Ward Candicacy18 5 DOF for length control : L  =( L x  L y ) / 2 : L  = L x  L y : l  =( l x  l y ) / 2 =2.257m : l  = l x  l y = 0.451m : l s =( l sx  l sy ) / 2 =2.15m PortDem. Freq. LL LL ll ll l s SPf1f APf2f SP f1  f2f1  f AP f1  f2f1  f PO f1  f2f1  f Signal Extraction Matrix (in-lock, DC) Common of arms Differential of arms Power recycling cavity Michelson Signal recycling cavity Laser ETMx ETMy ITMy ITMx BS PRM SRM SP AP PO lxlx lyly l sx l sy L x =38.55m Finesse=1235 L y =38.55m Finesse=1235 Phase Modulation f 1 =33MHz f 2 =166MHz 40m

Jan 17th 2006Ward Candicacy19 Lock Acquisition

Jan 17th 2006Ward Candicacy20 What does it mean to be locked? GW IFOs are actively-nulled instruments with narrow linear operating ranges. –Locked: All degrees of freedom are within linear operating range, held there by an active control system 40M single arm cavity:  = 1200 → less than 0.1% of available space offers good control signals less than 1 nm 1 ms at 1µm/s Pound-Drever-Hall error signal for a single cavity

Jan 17th 2006Ward Candicacy21 Lock Acquisition Gravitational Wave Interferometers do not come ‘ready to use’ –Natural state is totally uncontrolled (with nonlinear, heavily coupled signals) Lock Acquisition is the process by which an IFO is brought from an uncontrolled state to the controlled operating point. –Should be considered during the DESIGN phase of an IFO Money = commissioning + runtime –Can have a very large impact on duty cycle duty cycle = events

Jan 17th 2006Ward Candicacy22 From a Bunch of Swinging Mirrors to a Gravitational Wave Detector AdLIGO will be much harder to lock than LIGO-1 –4 DOFs to 5 DOFs + SRM scramble –factor smaller actuation potential –all signals come with offsets Prototyping can address: –Bootstrapping problem –LIGO I set itself a difficult problem by deciding to lock ONLY at the operating point. It’s better to cheat (offsets, misalignments, etc). –GOAL: A robust, reliable, and easily diagnosable LA procedure. Less time spent locking = more time for science!

Jan 17th 2006Ward Candicacy23 Transmitted light is used as 40m Lock Acquisition part I: Off-resonant lock scheme for a single cavity Off-resonant Lock point Resonant Lock 10x higher finesse than LIGO

Jan 17th 2006Ward Candicacy24 40m Lock acquisition procedure (v 1.0) Start with no DOFs controlled, all optics aligned. ITMy ITMx BS PRM SRM SP DDM 13m MC 33MHz 166MHz SP33 SP166 AP DDM AP166 PO DDM

Jan 17th 2006Ward Candicacy25 40m Lock acquisition procedure (v 1.0) DRMI + 2arms with offset ITMy ITMx BS PRM SRM SP DDM 13m MC 33MHz 166MHz SP33 SP166 AP DDM AP166 PO DDM Average wait : 3 minute (at night, with tickler) T =7% I Q 1/sqrt(TrY) 1/sqrt(TrX)

Jan 17th 2006Ward Candicacy26 40m Lock acquisition procedure (v 1.0) ITMy ITMx BS PRM SRM SP DDM 13m MC 33MHz 166MHz SP33 SP166 AP DDM AP166 To DARM PO DDM AP166 / sqrt(TrX+TrY) CARM DARM + + Short DOFs -> DDM DARM -> RF signal CARM -> DC signal 1/sqrt(TrX)+ 1/sqrt( TrY) CARM -> Digital CM_MCL servo

Jan 17th 2006Ward Candicacy27 40m Lock acquisition procedure (v 1.0) Reduce CARM offset: 1. Go to higher ARM power 2. Switch on AC-coupled analog CM_AO servo, using REFL DC as error signal. 3. Switch to RF error signal (POX) at half-max power. 4. Reduce offset/increase gain of CM_AO. ITMy ITMx BS PRM SRM SP DDM 13m MC 33MHz 166MHz SP33 SP166 AP DDM AP166 To DARM REFL DARM PO DDM AP166 / (TrX+TrY)

Jan 17th 2006Ward Candicacy28 DARM TFs as CARM offset is reduced

Jan 17th 2006Ward Candicacy29 Other Lock Acquisition Schemes Alternative Locking Schemes are on the way! Deterministic Locking: –Locking occurs in stages, with each stage having robust control –Each stage can (and should) lock on the first ‘fringe’, or be robust to fringes. –Transitions between stages are smooth and robust. Advantages: –Easier to diagnose problems –Should require less actuation potential If we can lock a single arm cavity, we can lock the IFO. 40M: 7 mN 1.3 kg test mass f/m = 5 AdLIGO 20 µN 40 kg test mass f/m =5e-4

Jan 17th 2006Ward Candicacy30 Digital length control system AP166 A/D mixer D/A

Jan 17th 2006Ward Candicacy31 Compensating the resonances 4kHz >> UGF no compensation AdLIGO: 180 Hz ~ UGF 40Hz < UGF no compensation AdLIGO: 70Hz? 1kHz -> 100Hz ~ UGF dynamic compensationcompensation 0->100Hz ~ UGF Not yet coherently compensated Compensation Filters for the two resonances associated with the signal cavity: OpticalOpto-mechanical DARM CARM UGFs ~ 250Hz

Jan 17th 2006Ward Candicacy32 Dynamic compensation filter for CARM servo Optical gain of CARM Open loop TF of CARM Optical gain (normalized by transmitted arm power) shows moving peaks due to reducing CARM offset. We have a dynamic compensative filter having nearly the same shape as optical gain except upside down. Designed using FINESSE. Open loop transfer function has no phase delay in all CARM offset.

Jan 17th 2006Ward Candicacy33 CARM optical springs Solid lines are from TCST Stars are 40m data Max Arm Power is ~80 Also saw CARM anti-springs, but don’t have that data

Jan 17th 2006Ward Candicacy34 Mode healing/injuring at Dark Port Negative spring constant with optical spring Positive spring constant with no optical spring Repeatable The same alignment quality Carrier power at DP is 10x smaller

Jan 17th 2006Ward Candicacy35 Modeling

Jan 17th 2006Ward Candicacy36 What’s modeling all about? With 5 DOFs and detuned cavities, Advanced LIGO will have a very complicated optical configuration, with a rich frequency response. We need good modeling tools, and we need to use them in order to understand AdLIGO, before it is built. We already rely heavily on modeling at the 40m because the configuration is so complicated. Building a prototype, and then using modeling to extrapolate, is a good way to understand AdLIGO in advance!

Jan 17th 2006Ward Candicacy37 Optickle: Frequency Domain IFO Simulation Optickle is a new frequency domain IFO modeling tool: –Written in Matlab Matlab allows easy integration to other modeling efforts (a frequency-domain e2e, like LinLIGO) Easily Extensible Uses Matlab classes for generality –Uses the methods outlined in T. Corbitt et al: “Mathematical framework for simulation of quantum fields in complex interferometers using the two-photon formalism” ( LIGO-P R ) to calculate the IFO opto-mechanical frequency response. –Designed for concrete units (Watts, meters, Hz)

Jan 17th 2006Ward Candicacy38 Optickle example: detuned FP cavity Response of front mirror to back mirror ‘excitation’ 1 nm detune finesse ~ 1200

Jan 17th 2006Ward Candicacy39 Optickle Example: AdLIGO Easy to create a frequency dependent coupling matrix, useful for, e.g., estimating the contribution of loop noise to DARM. This plot is Open Loop. Closed loop coming soon!

Jan 17th 2006Ward Candicacy40 Optickle v. the 40m Optickle Modeling

Jan 17th 2006Ward Candicacy41 DC Readout

Jan 17th 2006Ward Candicacy42 Quantum Noise: Heterodyne vs Homodyne Quantum noise curves plotting using formulas in: A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme” PHYSICAL REVIEW D 67,

Jan 17th 2006Ward Candicacy43 What is DC Readout and how does it relate to Homodyne Detection? DC Readout is Homodyne detection, using light circulating in the interferometer as a local oscillator. Advantage: LO light has been filtered by the <1Hz coupled cavity pole Disadvantage: limited ability to control homodyne phase OMC

Jan 17th 2006Ward Candicacy44 Technical noise sensitivity Noise SourceRF readoutDC readout Laser frequency noise~10x more sensitive Less sensitive since carrier is filtered Laser amplitude noise Sensitivity identical for frequencies below ~100 Hz; both driven by technical radiation pressure x more sensitive above 100Hz Carrier is filtered Laser pointing noiseSensitivity essentially the same Oscillator phase noise -140 dBc/rtHz at 100 Hz NA

Jan 17th 2006Ward Candicacy45 RF vs DC oPhase modulate the input light oRF sidebands act as local oscillator for GW signal, after passing through (unstable) recycling cavity(ies) oGW signal is an audio frequency sideband of RF photocurrent oMix GW signal down to near- DC oAcquire GW signal at DC with ADC Eliminate the RF sidebands at Dark Port with an Output Mode Cleaner Eliminate junk light at the Dark Port with Output Mode Cleaner Carrier light acts as a local oscillator GW signal is an audio frequency photocurrent Acquire GW signal at DC with ADC

Jan 17th 2006Ward Candicacy46 Making the DC local oscillator Two components –Carrier field due to loss differences (not controllable? TCS?) –Carrier field due to dark fringe offset (controllable) –An output mode cleaner should take care of the rest. (RF sidebands, junk light) Loss mismatch component –Average arm round trip loss: 200 ppm –Difference between arms: 50 ppm –Output power due to mismatch: 20 µW Detection angle, β –Tuned by adjusting fringe offset Can tune from 0-80 deg with 0-10pm of DARM offset 1 mW LO –Angle of GW is frequency dependent in detuned RSE Loss mismatch fringe offset β LIGO I GW parallel to DC offset Detuned RSE: GW signal gets f- dependent phase shift in SRC No slope Some linear component

Jan 17th 2006Ward Candicacy47 Laser Intensity Noise calculated using rsenoise 10 pm DARM offset for DC 1e-13m residual L- RF: noise sidebands of RF sidebands beat against residual length offset DC: dark port power proportional to input power Radiation pressure effects not included

Jan 17th 2006Ward Candicacy48 Laser Frequency Noise calculated using rsenoise 10 pm DARM offset for DC 1e-13m residual L- RF: frequency noise sidebands of RF sidebands beat against static carrier contrast defect DC: Arm cavity pole imbalance couples carrier frequency noise to dark port Radiation pressure effects not included

Jan 17th 2006Ward Candicacy49 OMC Properties The Output Mode Cleaner filters the light coming out of the dark port, cleaning away the junk and transmitting the GW-signal containing TEM00 mode of the carrier

Jan 17th 2006Ward Candicacy50 OMC design in SolidWorks Small number of pieces HV compatible –some glue near the PZT mirror Mirrors mounted mechanically, on silver washers (no glue) ALGOR FEA: lowest mech resonance at ~770 Hz Construct out of well-damped material, to minimize effect of resonances: Copper All high-quality (REO super-polished and coated) mirrors available from LIGO lab spares (the 4 th HR mirror, 0 o incidence, came from Newport) Mike Smith

Jan 17th 2006Ward Candicacy51 The Vacuum Compatible DC Photodiode Ben Abbott DC Readout

Jan 17th 2006Ward Candicacy52 Summary & Future Directions Lock Acquisition Modeling DC Readout Revamping the LSC Scheme QND Techniques SPI Data Analysis Things I’ve already spent significant time on, and will spend more on Things I may spend significant time on