Caltech 40 m Current Issues Kentaro Somiya University

Caltech 40 m Current Issues Kentaro Somiya University of Florida 2004. 10. 19

Contents • Introduction : Advanced LIGO and the 40 m • Part I : Lock acquisition of the 40 m • Part II : Frequency noise and Mach-Zehnder noise

LIGO and Ad. LIGO Comparison of the quantum noise sensitivity. Detuned RSE technique improves the sensitivity.

Detuned RSE=Resonant Sideband Extraction Additional mirror at the dark port. = Signal Recycling Mirror Detune the SR cavity from the carrier’s resonant point. (= Broadband RSE) Totally 5 degrees of freedom to be controlled ~ L+, L-, l+, l-, and ls.

40 m’s role as the final prototype of Ad. LIGO • Development of lock-acquisition scheme. • Clear observation of optical spring in the TF measurement. • Observation of the higher peak (and maybe the lower too) in the noise spectrum measurement. • DC readout.

Part I : Lock Acquisition

Two frequency modulation scheme PRFPMI (4 DOFs) PR-BRSE (5 DOFs) f 2 brings the ls signal. Carrier : reso in arms and the PRC f 1 : reso in the PRC Carrier : reso in the arms and the PRC f 1 : reso in the PRC 33 MHz f 2 : reso in the PR-SRC 166 MHz The central part is locked only by SBs.

Lock Acquisition Lock the central DR part somehow. Lock the central DR part only by RF SBs. Lock the arms by the carrier.

Lock Acquisition of the central part It has turned out to be quite difficult. When the Michelson is far from the dark fringe, All the signals, l+, l-, and ls, are mixed. Even when the Michelson is at the dark fringe, All the signals are still mixed. Carrier 33 MHz BP BP BP, except l- signal BP and DP (mostly) 166 MHz BP (a little) DP, and DP BP Signals at the BP l+ Signals at the DP l- (no DC) Signals at the BP l+, l-, and ls Signals at the DP l+, l-, and ls No combination brings the l- signal well isolated from the others.

Example: l+ at the BP l Four SBs resonate at different points l Good signal obtained when +f 2 resonates l Signal for –f 2 resonance has an opposite polarity l Disturbed when +f 2 and –f 2 resonate at the same point l Signals for f 1 resonance can be cancelled by proper DDM phases, which coincide with the phases for symmetric signal

Dither Locking 10 k. Hz mechanical modulation on l. It’s like a SB injected from the DP. All the 10 k. Hz SB returns to the DP except the l- signal component. Carrier Dither 10 k. Hz BP DP BP, except l- signal DP, except l- signal Signals at the BP l+ Signals at the DP l- (no DC) Signals at the BP l- (no DC) Signals at the DP ls The error signal taken from the beat of 10 k. Hz, divided by the power at the pick-off port, shows a clear l- signal.

Locking the PRM-SRM cavity After locking the l-, the condition is simple. The PRM follows the swinging SRM Then, once ls is locked, we’ll recover l+ = 0º.

Successful Locking DDM@SP (demod phase for ls ) Error of Dither DC@AP l- lock ls lock DC@SP l+ lock 33 MHz@SP DDM@SP Lock now: l- : dither @AP l+ : 33@SP ls : DDM@SP Control later: DDM@AP DDM@SP DDM@PO (demod phase for l+ ) ls lock at -5. 2 sec l- lock at -5. 3 sec l+ lock at -5. 6 sec

Part II : Mach-Zehnder Noise

Disturbance by sub-sidebands Original concept Real world Carrier -f 2 -f 1 SB of SB (sub-SB) Carrier f 1 f 2 -f 1 f 2 • Sub-sidebands are produced by two series EOMs. • Beats between carrier and f 2 ± f 1 disturb the central part. 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 SP f 1 1 -1. 4 E-8 -1. 2 E-3 -1. 3 E-6 -6. 2 E-6 AP f 2 -4. 8 E-9 1 1. 2 E-8 1. 3 E-3 -1. 7 E-8 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 -1. 7 E-3 -3. 0 E-4 1 -3. 2 E-2 -1. 0 E-1 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 -6. 2 E-4 1. 5 E-3 7. 5 E-1 1 7. 1 E-2 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. 6 E-3 2. 7 E-3 4. 6 E-1 -2. 3 E-2 1 PO f 1 f 2 3. 3 1. 7 1. 9 E-1 -3. 5 E-2 1 Sub-sidebands should be removed.

Mach-Zehnder to eliminate the sub-SBs Mach-Zehnder interferometer no sub-sidebands Series EOMs sub-sidebands are generated PMC trans PZT EOM 2 EOM 1 EOM 2 To MC EOM 1 PD PMC transmitted PD BS 1 166 MHz EOM 33 MHz EOM PZT mirror BS 2 29 MHz EOM has EOM been moved to to MC inside the MZ. But this MZ introduces additional noise on the frequency.

MZ differential motion noise f 1 ~ f 1 Ca f 2 Laser PC 1 ~ f 2 PC 2 Differential Mode Common Mode Disturbance of orthogonality between the carrier and the SB. There are three paths via which MZ noise contributes to L-.

Three paths of MZ noise to L(1) Direct coupling with contrast defect component ~ This is not a problem with the DC readout scheme. ~ Seiji’s calculation says this is not a problem even with RF readout and if the finesse differs for 10%. (2) Via frequency stabilization system of the MC ~ This can be suppressed by the FSS of L+. (3) Via frequency stabilization system of the L+ 1. (1) and (3) are the same problems as RF phase noise of the EOM. 2. Freq noise should be calculated to see if (2) and (3) limit the sensitivity.

Frequency noise of detuned RSE What we have; • J. Camp calculated frequency noise for a PR-FPMI. • J. Mason extended the calculation with the SR cavity. What we should add; • Radiation pressure effect caused by freq noise sideband. • Storage time difference will be larger with higher finesse arms. • RMS cavity fluctuation converts freq noise to amplitude noise and it appears as freq noise because of the detuning.

Calculated frequency noise TF of the 40 m GW Signal >> two peaks Freq noise around Carrier >> two peaks >> spectrum shows no dips Freq noise around RF SB >> flat >> spectrum shows two dips

Requirement of freq fluctuation after MC Goal sensitivity divided by freq noise TF

Frequency stabilization servo ~preliminary x: laser freq noise y: MC displacement noise z: MZ differential noise G >> 40 m MC servo G’, H’ >> TAMA servo (just for example)

MC sensitivity requirement This is hopefully not a big problem since the total noise level is limited by PSL noise at high frequencies.

MZ sensitivity requirement MZ noise will limit the sensitivity at 100~1 k. Hz.

Is there a way to prove the contribution of MZ noise? • We have seen the offset voltage on the MC error signal when MZ is not locked to the bright fringe. • We can measure the MZ noise on the reflected light of the MC, although the contribution is less than on the transmitted light. >> next page x: laser freq noise, y: MC motion noise, z: MZ diff noise F: finesse and LPF of the MC, G: VCO gain, H: MCL gain

Comparison of MC noise and MZ noise on the MC reflected light true only around this region, where FSS gain is high enough • We are able to measure the TF from MZ noise to MC noise. • We cannot see the direct contribution on the noise spectrum.

How to reduce the MZ noise? • Installation of a phase-correcting pockels cell in a MZ arm. • Alternative to the MZ; Virtual Mach-Zehnder [ref. P. Beyersdorf’s document]

Conclusion • The lock acquisition scheme with the dither locking has been developed and we have succeeded in locking the central part. • So far the PRC is locked to the carrier, and the next step is to lock the PRC to the sidebands. • Frequency noise of DRSE has been analytically calculated. • We have installed the MZ to remove sub-sidebands, but it introduces additional MZ noise via freq noise. • There a few ways to reduce the MZ noise and shall be tested in the 40 m.