Optical spring and optical resonance in the 40

Optical spring and optical resonance in the 40 m Detuned RSE interferometer LIGO seminar November 1, 2005 Osamu Miyakawa, Robert Ward, Rana Adhikari, Matthew Evans, Benjamin Abbott, Rolf Bork, Daniel Busby, Hartmut Grote, Jay Heefner, Alexander Ivanov, Seiji Kawamura, Michael Smith, Robert Taylor, Monica Varvella, Stephen Vass, and Alan Weinstein LIGO- G 050568 -00 -R LIGO seminar, November 2005

Today’s talk 1. 2. 3. 4. Advanced optical configuration Caltech 40 m prototype Lock acquisition of detuned RSE Optical spring and optical resonance LIGO- G 050568 -00 -R LIGO seminar, November 2005

1. Advanced optical configuration LIGO- G 050568 -00 -R LIGO seminar, November 2005

Development of Michelson type interferometer as a gravitational wave detector FP cavity § Gravitational wave detection using Michelson interferometer § Signal and power enhancement using Fabry-Perot cavity in each arm FP cavity Laser BS FP cavity § Power enhancement using Power Recycling Laser FP cavity PRM BS LIGO- G 050568 -00 -R LIGO seminar, November 2005

Advanced LIGO optical configuration § LIGO: Power recycled FPMI » Optical noise is limited by Standard Quantum Limit (SQL) FP cavity § Adv. LIGO: GW signal enhancement using Detuned RSE » Two dips by optical spring, optical resonance » Can overcome the SQL　　QND detector Laser PRM Power FP cavity BS GW signal Detuning LIGO- G 050568 -00 -R LIGO seminar, November 2005

Resonant Sideband Extraction and Signal Recycling § Resonant Sideband Extraction(RSE) » Anti-resonant carrier on SRC » High finesse arm cavities required » Low power recycling, or power recycling not required » Less thermal effect » Better for long arm based interferometer § Signal Recycling(SR) Ad. LIGO LCGT LIGO VIRGO TAMA 300 » Resonant carrier on SRC » Low finesse arm cavities, or arm cavities not required » High power recycling required, so-called dual recycling(DR) » Higher thermal effect » Better for short arm based interferometer LIGO- G 050568 -00 -R LIGO seminar, November 2005 GEO 600

Historical review of Advanced interferometer configuration ~1986 Signal Recycling (Dual Recycling) [B. Meers] ~1998 Garching 30 m [G. Heinzel] GEO 600 Glassgow 10 m ~1993 RSE • Idea [J. Mizuno] • Tabletop [G. Heinzel] ~2000 Tabletop with new control • Caltech(RSE)[J. Mason] • Florida(DR) • Australia(RSE)[D. Shaddock] ~2002 NAOJ 4 m Susp. mass BRSE [O. Miyakawa] ~2005 Caltech 40 m • Suspended mass • DRSE+PR ~2004 NAOJ 4 m Susp. mass DRSE [K. Somiya] ~2001 QND study[Y. Chen, A. Buonanno] • Optical spring • Readout scheme LIGO- G 050568 -00 -R LIGO seminar, November 2005 ~2013 Ad. LIGO(DRSE) LCGT(BRSE)

2. Caltech 40 m prototype LIGO- G 050568 -00 -R LIGO seminar, November 2005

Caltech 40 meter prototype interferometer An interferometer as close as possible to the Advanced LIGO optical configuration and control system § Detuned Resonant Sideband Extraction(DRSE) § Power Recycling § Suspended mass § Digital controls system LIGO- G 050568 -00 -R LIGO seminar, November 2005

Caltech 40 meter prototype interferometer Objectives § Develop a lock acquisition procedure for suspended-mass detuned RSE interferometer with power recycling § Verify optical spring and optical resonance PRM § Characterize noise mechanisms § Develop DC readout scheme Bright § Extrapolate to Ad. LIGO via port simulation BS SRM Dark port X arm Y arm LIGO- G 050568 -00 -R LIGO seminar, November 2005 10

Optical spring in detuned RSE was predicted using two-photon mode. a : input vacuum b : output D : input carrier M : constant h : gravitational wave h. SQL: standard quantum limit t: transmissivity of SRM k: coupling constant F: GW sideband phase shift in SRC b: GW sideband phase shift in IFO laser arm cavity h am D Be l sp er itt h arm cavity Signal recycling mirror a b z: homodyne phase A. Buonanno, Y. Chen, Phys. Rev. D 64, 042006 (2001) LIGO- G 050568 -00 -R LIGO seminar, November 2005

Target sensitivity of Adv. LIGO and 40 m prototype Sta nd ard Qu an tum Lim it • 2 dips, optical spring and optical resonance in detuned RSE LIGO- G 050568 -00 -R LIGO seminar, November 2005

Differences between Adv. LIGO and 40 m prototype § 100 times shorter cavity length § Arm cavity finesse at 40 m chosen to be = to Adv. LIGO ( = 1235 ) » Storage time is x 100 shorter § Control RF sidebands are 33/166 MHz instead of 9/180 MHz » Due to shorter PRC length, less signal separation § LIGO-I 10 -watt laser, negligible thermal effects » 180 W laser will be used in Adv. LIGO. § Noisier seismic environment in town, smaller isolation stacks » ~1 x 10 -6 m at 1 Hz § LIGO-I single pendulum suspensions » Adv. LIGO will use triple (MC, BS, PRM, SRM) and quad (ITMs, ETMs) suspensions. LIGO- G 050568 -00 -R LIGO seminar, November 2005

Ad. LIGO signal extraction scheme ETMy 4 km § f 2 § § ITMy PRM BS ITMx 4 km ETMx Mach-Zehnder will be installed to eliminate sidebands of sidebands. Only + f 2 is resonant on SRC. Unbalanced sidebands of +/-f 2 due to detuned SRC produce good error signal for Central part. f 1 SRM -f 2 § § Carrier (Resonant on arms) -f 1 f 2 • Single demodulation • Arm information • Double demodulation • Central part information 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. LIGO- G 050568 -00 -R LIGO seminar, November 2005

§ Double Demodulation used for l+, l-, and ls § Demodulation phases optimized to suppress DC and to maximize desired signal LIGO- G 050568 -00 -R Demodulation Phase of f 2 Double Demodulation LIGO seminar, November 2005 Locking point 15

5 DOF for length control Signal Extraction Matrix (in-lock) ETMy Phase Modulation f 1=33 MHz f 2=166 MHz Ly=38. 55 m Finesse=1235 Port Dem. Freq. L L l l ls SP f 1 1 -3. 8 E-9 -1. 2 E-3 -1. 3 E-6 -2. 3 E-6 AP f 2 -4. 8 E-9 1 1. 2 E-8 1. 3 E-3 -1. 7 E-8 SP f 1 f 2 -1. 7 E-3 -3. 0 E-4 1 -3. 2 E-2 -1. 0 E-1 AP f 1 f 2 -6. 2 E-4 1. 5 E-3 7. 5 E-1 1 7. 1 E-2 PO f 1 f 2 3. 6 E-3 2. 7 E-3 4. 6 E-1 -2. 3 E-2 1 ITMy PRM Laser ly lx lsy BS SRM PO AP LIGO- G 050568 -00 -R ETMx Lx =38. 55 m Finesse=1235 lsx SP ITMx Common of arms : L =( Lx Ly) / 2 Differential of arms : L = Lx Ly Power recycling cavity : l =( lx ly) / 2 =2. 257 m Michelson : l = lx ly = 0. 451 m Signal recycling cavity : ls=( lsx lsy) / 2 =2. 15 m LIGO seminar, November 2005

Disturbance by sidebands of sidebands Original concept Real world Carrier -f 2 -f 1 Carrier f 1 -f 2 -f 1 f 1=33 MHz f 2=166 MHz 133 MHz 199 MHz § Sidebands of sidebands are produced by two series EOMs. § Beats between carrier and f 2 +/- f 1 disturb central part. LIGO- G 050568 -00 -R Port Dem. Freq. L L l l ls SP f 1 1 -1. 4 E-8 -1. 2 E-3 -1. 3 E-6 -6. 2 E-6 AP f 2 1. 2 E-7 1 1. 4 E-5 1. 3 E-3 6. 5 E-6 SP f 1 f 2 7. 4 -3. 4 E-4 1 -3. 3 E-2 -1. 1 E-1 AP f 1 f 2 -5. 7 E-4 32 7. 1 E-1 1 7. 1 E-2 PO f 1 f 2 3. 3 1. 7 1. 9 E-1 -3. 5 E-2 1 LIGO seminar, November 2005

Mach-Zehnder interferometer on 40 m PSL to eliminate sidebands of sidebands Series EOMs with sidebands of sidebands f 1 Mach-Zehnder interferometer with no sidebands of sidebands PMC trans f 2 PZT EOM 2 EOM 1 EOM 2 f 1 EOM 1 Locked by internal modulation To MC PD PMC transmitted to MC LIGO- G 050568 -00 -R LIGO seminar, November 2005

Pre-Stabilized Laser(PSL) and 13 m Mode Cleaner(MC) BS East Arm ITMx ITMy PSL ETMx FSS 40 m a PMC VCO C M AOM m 13 Mode Cleaner South Arm MOPA 126 Detection bench ETMy LIGO- G 050568 -00 -R § § 10 W MOPA 126 Frequency Stabilization Servo (FSS) Pre-Mode Cleaner (PMC) 13 m Mode Cleaner LIGO seminar, November 2005 rm ca vity

LIGO-I type single suspension § Each optic has five OSEMs (magnet and coil assemblies), four on the back, one on the side § § The magnet occludes light from the LED, giving position Current through the coil creates a magnetic field, allowing mirror control LIGO- G 050568 -00 -R LIGO seminar, November 2005 20

Digital length control system D/A mixer LIGO- G 050568 -00 -R LIGO seminar, November 2005 Output to suspensions A/D Feedback filters AP 166 Demodulated signal from PD D/A

Off-resonant lock scheme for arm cavity Transmitted light is used as Resonant Lock Off-resonant Lock point LIGO- G 050568 -00 -R LIGO seminar, November 2005 to avoid coupling of carrier in PRC when arm cavity is locked.

3. Lock acquisition of detuned RSE LIGO- G 050568 -00 -R LIGO seminar, November 2005

The way to full RSE Oct. 2004 Detuned dual recycled Michelson Nov. 2004 Arm lock with offset in common mode ETMy Reducing offset Shutter ITMy PRM BS ITMx ETMx Shutter SRM Carrier 33 MHz 166 MHz LIGO- G 050568 -00 -R LIGO seminar, November 2005 Oct. 2005 RSE

DRMI lock using double demodulation with unbalanced sideband by detuned cavity Carrier 33 MHz 166 MHz ITMy BS ITMx Unbalanced 166 MHz PRM DDM PD 33 MHz Belongs to next carrier SRM OSA DDM PD OSA Typical lock acquisition time : ~1 min LIGO- G 050568 -00 -R LIGO seminar, November 2005 Belongs to next carrier

Lock acquisition procedure towards detuned RSE Low gain High gain Tr. Y PDs Start POY ITMy 166 MHz POX 13 m MC ITMx BS 33 MHz PRM SP 33 PO DDM SRM SP 166 SP DDM AP 166 AP DDM LIGO- G 050568 -00 -R LIGO seminar, November 2005 High gain Tr. X PDs Low gain

Lock acquisition procedure towards detuned RSE Low gain High gain Tr. Y PDs DRMI Ly=38. 55 m POY ITMy 166 MHz POX 13 m MC 33 MHz ITMx BS Lx =38. 55 m PRM T =7% SP 33 Q SP 166 I SP DDM SRM T =7% PO DDM AP 166 AP DDM LIGO- G 050568 -00 -R High gain LIGO seminar, November 2005 Tr. X PDs Low gain

Lock acquisition procedure towards detuned RSE 1/sqrt(Tr. Y) Low gain Tr. Y PDs DRMI + 2 arms with offset Typical lock acquisition time: 3 minutes Ly=38. 55 m Finesse=1235 POY ITMy 166 MHz POX 13 m MC 33 MHz ITMx BS 1/sqrt(Tr. X) Lx =38. 55 m Finesse=1235 PRM T =7% SP 33 SP 166 I SP DDM Q SRM T =7% PO DDM AP 166 AP DDM LIGO- G 050568 -00 -R Normalization process High gain LIGO seminar, November 2005 High gain Tr. X PDs Low gain

Lock acquisition procedure towards detuned RSE 1/sqrt(Tr. Y) Low gain Tr. Y PDs Switching DRMI to DDM Normalization process High gain Ly=38. 55 m Finesse=1235 POY ITMy 166 MHz POX 13 m MC 33 MHz ITMx BS Lx =38. 55 m Finesse=1235 PRM T =7% SP 33 SP 166 SP DDM SRM T =7% PO DDM AP 166 AP DDM LIGO- G 050568 -00 -R 1/sqrt(Tr. X) LIGO seminar, November 2005 High gain Tr. X PDs Low gain

Lock acquisition procedure towards detuned RSE Low gain Switching to CARM and DARM control CARM: offset DARM: no offset Tr. Y PDs 1/sqrt(Tr. X)+ 1/sqrt( Tr. Y) (1/sqrt(Tr. X)- 1/sqrt( Tr. Y)) (1/sqrt(Tr. X)+ 1/sqrt( Tr. Y)) Ly=38. 55 m Finesse=1235 POY ITMy 166 MHz + -1 DARM + ITMx BS High gain Lx =38. 55 m Finesse=1235 PRM T =7% SP 33 SP 166 SP DDM SRM T =7% PO DDM AP 166 AP DDM LIGO- G 050568 -00 -R CARM POX 13 m MC 33 MHz Normalization process High gain LIGO seminar, November 2005 Tr. X PDs Low gain

Lock acquisition procedure towards detuned RSE Low gain Tr. Y PDs Ly=38. 55 m Finesse=1235 + + Switching CARM and DARM to RF CARM: offset DARM: no offset (POX+POY)/(Tr. X+Tr. Y) POY ITMy 166 MHz + CARM -1 DARM ITMx BS High gain Lx =38. 55 m Finesse=1235 PRM T =7% SP 33 SP 166 SP DDM SRM T =7% PO DDM AP 166 AP DDM LIGO- G 050568 -00 -R + POX 13 m MC 33 MHz Normalization process High gain AP 166/(Tr. X+Tr. Y) LIGO seminar, November 2005 Tr. X PDs Low gain

Lock acquisition procedure towards detuned RSE Low gain Tr. Y PDs Reduce CARM offset to Full RSE Ly=38. 55 m Finesse=1235 + + 166 MHz 33 MHz (POX+POY)/(Tr. X+Tr. Y) + ITMy 13 m MC Normalization process High gain -1 DARM ITMx BS High gain Lx =38. 55 m Finesse=1235 PRM T =7% SRM T =7% PO DDM AP 166 AP DDM LIGO- G 050568 -00 -R + POX GPR=14. 5 SP 33 SP 166 SP DDM CARM AP 166/(Tr. X+Tr. Y) LIGO seminar, November 2005 Tr. X PDs Low gain

Lock acquisition procedure towards detuned RSE Low gain CARM to MC and Laser frequency In Progress High gain Tr. Y PDs Ly=38. 55 m Finesse=1235 -1 POY ITMy 166 MHz POX GPR=14. 5 13 m MC ITMx BS PRM T =7% SP 33 SP DDM SRM T =7% PO DDM AP 166 AP DDM LIGO- G 050568 -00 -R High gain Lx =38. 55 m Finesse=1235 SP 166 33 MHz DARM LIGO seminar, November 2005 Tr. X PDs Low gain

Dynamic compensative filter for CARM servo by Rob Ward Open loop TF of CARM Optical gain of CARM • Optical gain (normalized by transmitted power) shows moving peaks due to reducing CARM offset. • We have a dynamic compensative filter having an exactly the same shape as optical gain except for upside down. • Open loop transfer function has no phase delay in all CARM offset. LIGO- G 050568 -00 -R LIGO seminar, November 2005

Residual displacement noise on arm Requirement of RMS noise for offset lock (10% of FWHM of offset lock on CARM) Requirement of RMS noise for full lock (10% of FWHM of RSE) • RMS residual displacement noise was 30 times larger than requirement. Probably 30% of FWHM is OK. But still 10 times noisier. LIGO- G 050568 -00 -R LIGO seminar, November 2005

Noise investigation in DRMI+single arm Requirement of RMS noise for full lock (10% of FWHM of RSE) LIGO- G 050568 -00 -R LIGO seminar, November 2005

Lock acquisition for DRMI+2 arms Maximum power Trial of re-alignment Lost lock • Lock lasts 1 -2 hours • Lock acquisition time 5 -10 minutes Start reducing offset 5 DOF locked LIGO- G 050568 -00 -R • Drift exists by alignment, offset, or thermal effect. LIGO seminar, November 2005

4. Optical spring and optical resonance LIGO- G 050568 -00 -R LIGO seminar, November 2005

L- optical gain with RSE peak Measured in June 2005 • Optical gain of L- loop DARM_IN 1/DARM_OUT, divided by pendulum transfer function Design RSE peak ~ 4 k. Hz • No offset on L- loop • 150 pm offset on L+ loop • Optical resonance of detuned RSE can be seen around the design RSE peak of 4 k. Hz. • Q of this peak is about 6. LIGO- G 050568 -00 -R LIGO seminar, November 2005

Simple picture of optical resonance FWHM Carrier frequency Sideband amplitude at output [a. u. ] Fdet (=4 k. Hz at 40 m) LSB fsig USB Signal sideband frequency offset from carrier [Hz] LIGO- G 050568 -00 -R LIGO seminar, November 2005 • Response between GW USB and GW LSB is different due to the detuned signal recycling cavity. • the resonance of the SR cavity and is maximally enhanced for fsig = fdet

Mathematical description for optical spring in detuned RSE arm cavity h a : input vacuum b : output D : input carrier M : constant h : gravitational wave h. SQL: standard quantum limit t: transmissivity of SRM laser k: coupling constant F: GW sideband phase shift in SRC b: GW sideband phase shift in IFO Measurement of optical transfer function a <<h; non-quantum measurement LIGO- G 050568 -00 -R LIGO seminar, November 2005 am D Be l sp er itt h arm cavity Signal recycling mirror a b

Simple picture of optical spring in detuned RSE Let’s move arm differentially, X arm longer, Y arm shorter from full RSE Wrong SRM position Correct SRM position BRSE Power(W) X arm Y arm Power(W) Y arm DARM (Lx-Ly) § § § Power X arm down, Y arm up Radiation pressure X arm down, Y arm up Spring constant Negative(optical spring) LIGO- G 050568 -00 -R DARM (Lx-Ly) X arm down, Y arm down X arm up, Y arm down N/A LIGO seminar, November 2005 Positive(no optical spring)

Optical spring and Optical resonance in differential arm mode of detuned RSE • Optical gain of L- loop DARM_IN 1/DARM_OUT divided by pendulum transfer function • Optical spring and optical resonance of detuned RSE were measured. • Frequency of optical spring depends on cavity power, mass, detuning phase of SRC. • Frequency of optical resonance depends on detuning phase of SRC. • Theoretical line was calculated using A. Buonanno and Y. Chen’s equations. LIGO- G 050568 -00 -R LIGO seminar, November 2005

Positive spring constant • SRM is locked at opposite position from anti-resonant carrier point(BRSE). • Optical spring disappeared due to positive spring constant. Broadband SR LIGO- G 050568 -00 -R LIGO seminar, November 2005 Broadband RSE

Frequency sweep of optical spring ~1900 W ~270 W LIGO- G 050568 -00 -R LIGO seminar, November 2005

Optical spring in E 2 E • Calculated by time domain simulation • No length control • Lock lasts ~0. 7 sec, so statistics at low frequency is not good. • Simple length control required • Calculation time ~5 min using DRMI summation cavity LIGO- G 050568 -00 -R LIGO seminar, November 2005

How much power inside arm? Design Cavity reflectivity PRM reflectivity Loss in PRC Achievable PRG Coupling Input power Power in one arm Optical spring LIGO- G 050568 -00 -R Measured(estimated) 93% 85%(X arm 84%, Yarm 86%) 93% 92. 2% 0% 2. 3% 14. 5 5. 0 Over coupled Under coupled 0. 1 W 1 W 560 W 1900 W 23 Hz 41 Hz LIGO seminar, November 2005

CARM optical spring LIGO- G 050568 -00 -R LIGO seminar, November 2005

Mode healing at Dark Port? Negative spring constant with optical spring Positive spring constant with no optical spring • Repeatable • The same alignment quality • Under investigation. LIGO- G 050568 -00 -R LIGO seminar, November 2005

Next step § § § § § Stable operation and noise hunting E 2 E simulation for Ad. LIGO DC readout Squeezer Alignment control with wave front sensors Cleaning arms Narrow-band operation LF RF modulation scheme Etc. LIGO- G 050568 -00 -R LIGO seminar, November 2005

GW readout, Systems l DC rather than RF for GW sensing » Requires Output Mode-Cleaner to reject RF » Offset ~ 1 picometer from dark fringe can tune from 0 to 80 deg with 0 -100 m. W of fringe offset power Noise Source Laser frequency noise Laser amplitude noise RF readout DC readout ~10 x more sensitive Less sensitive since carrier is filtered Sensitivity identical for frequencies below ~100 Hz; both driven by technical radiation pressure 10 -100 x more sensitive above 100 Hz Carrier is filtered Laser pointing noise Sensitivity essentially the same Oscillator phase noise LIGO- G 050568 -00 -R -140 d. Bc/rt. Hz at NA 100 Hz LIGO seminar, November 2005 fringe offset β Loss mismatch

Output Optic Chamber Existing in-vac seismically isolated optical table (OOC) to OMCR beamline Mike Smith has designed a compact, monolithic MMT, similar to our input MMT, using spherical mirrors. Pair of DC PDs with in-vac electronics on monolithic base. 4 -mirror monolithic OMC. from SRM 2 nd PZT steering mirrors and their controls are duplicates of a pair that we have already installed and commissioned for steering from IMC to main IFO (in-vac); controls are fully implemented in the ASC system (by Rolf). Similar systems can be used for “LIGO I. V”. to OMCT beamline IMCR, IMCT, and SP beamlines to AS RF beamline (roughly 1/3 of AS power) also a convenient path for autocollimator beam, for initial alignment in air LIGO- G 050568 -00 -R from PSL to IMC LIGO seminar, November 2005 Piezosystem Jena PSH 5/2 SG-V, PZT tilting mirror mount with strain gauge, and associated drivers and power supplies Mike Smith

Squeezing Tests at the 40 m § Audio frequency squeezed sources now available at MIT § Time to take steps toward eventual implementation on long baseline interferometers 10 1 1 k. Hz 100 k. Hz » Homodyne detection along with ifo signals and noise couplings – Most interesting and relevant for complex ifo configurations » A few interferometer configurations possible – narrow- or broadband RSE, DRMI, FPMI » Noise coupling studies possible » LIGO-like control systems for eventually porting squeezing technology to long baseline ifos LIGO- G 050568 -00 -R LIGO seminar, November 2005

Interface to ongoing 40 m experiments LIGO- G 050568 -00 -R LIGO seminar, November 2005 54

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 Mo, 100 Mpc » Adv LIGO : 50 Mo, z=2 § Stochastic background: » Initial LIGO: ~3 e-6 » Adv LIGO ~3 e-9 LIGO- G 050568 -00 -R LIGO seminar, November 2005