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

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

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

4. Detuned RSE Additional mirror at the dark port. = Signal Recycling Mirror RSE=Resonant Sideband Extraction 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.

5. 40m’s role as the final prototype of AdLIGO 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.

6. Part I : Lock Acquisition

7. Two frequency modulation scheme PRFPMI (4 DOFs)PR-BRSE (5 DOFs) Carrier : reso in arms and the PRC f1 : reso in the PRC Carrier : reso in the arms and the PRC f1 : reso in the PRC 33MHz f2 : reso in the PR-SRC 166MHz f2 brings the ls signal. The central part is locked only by SBs.

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

9. 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. CarrierBP BP, except l- signal Signals at the BPl+ Signals at the DPl- (no DC) 33MHzBP BP and DP (mostly) (a little) Signals at the BPl+, l-, and ls Signals at the DPl+, l-, and ls 166MHzBP DP, and DP BP Signals at the BPl+, l-, and ls Signals at the DPl+, l-, and ls No combination brings the l- signal well isolated from the others.

10. Example: l+ at the BP Four SBs resonate at different points Good signal obtained when +f2 resonates Signal for –f2 resonance has an opposite polarity Disturbed when +f2 and –f2 resonate at the same point Signals for  f1 resonance can be cancelled by proper DDM phases, which coincide with the phases for symmetric signal

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

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

13. Successful Locking l - lock l s lock l + lock DC@AP DC@SP DDM@SP (demod phase for l s ) Error of Dither DDM@SP (demod phase for l + ) 33MHz@SP l s lock at -5.2 sec l - lock at -5.3 sec l + lock at -5.6 sec Lock now: Control later: l - : dither @AP  DDM@AP l + : 33@SP  DDM@SP l s : DDM@SP  DDM@PO

14. Part II : Mach-Zehnder Noise

15. Disturbance by sub-sidebands Original concept Real world f1f1 -f 1 f2f2 -f 2 Carrier f1f1 -f 1 f2f2 -f 2 Carrier PortDem. Freq. LL LL ll ll l s SPf1f1 1-1.4E-8-1.2E-3-1.3E-6-6.2E-6 APf2f2 1.2E-711.4E-51.3E-36.5E-6 SP f1  f2f1  f2 7.4-3.4E-41-3.3E-2-1.1E-1 AP f1  f2f1  f2 -5.7E-4327.1E-117.1E-2 PO f1  f2f1  f2 3.31.71.9E-1-3.5E-21 PortDem. Freq. LL LL ll ll l s SPf1f1 1-3.8E-9-1.2E-3-1.3E-6-2.3E-6 APf2f2 -4.8E-911.2E-81.3E-3-1.7E-8 SP f1  f2f1  f2 -1.7E-3-3.0E-41-3.2E-2-1.0E-1 AP f1  f2f1  f2 -6.2E-41.5E-37.5E-117.1E-2 PO f1  f2f1  f2 3.6E-32.7E-34.6E-1-2.3E-21 Sub-sidebands are produced by two series EOMs. Beats between carrier and f2 ± f1 disturb the central part. Sub-sidebands should be removed. SB of SB (sub-SB)

16. Mach-Zehnder to eliminate the sub-SBs Series EOMs sub-sidebands are generated EOM2 EOM1 Mach-Zehnder interferometer no sub-sidebands PD EOM2 EOM1 PZT PMC trans To MC PZT mirror BS1 BS2 33MHz EOM 166MHz EOM 29MHz EOM PD PMC transmitted to MC 29MHz EOM has been moved to inside the MZ. But this MZ introduces additional noise on the frequency.

17. MZ differential motion noise PC2 Laser PC1 ~ ~ f1f1 f2f2 Differential Mode Common Mode f1Ca f2 Disturbance of orthogonality between the carrier and the SB. There are three paths via which MZ noise contributes to L-.

18. Three paths of MZ noise to L- (1) Direct coupling with contrast defect component (2) Via frequency stabilization system of the MC (3) Via frequency stabilization system of the L+ ~ 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%. ~ This can be suppressed by the FSS of L+. (1) and (3) are the same problems as RF phase noise of the EOM. Freq noise should be calculated to see if (2) and (3) limit the sensitivity.

19. Frequency noise of detuned RSE J.Camp calculated frequency noise for a PR-FPMI. J.Mason extended the calculation with the SR cavity. What we have; 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. What we should add;

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

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

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

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

24. MZ sensitivity requirement MZ noise will limit the sensitivity at 100~1kHz.

25. 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. 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 >> next page

26. 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.

27. 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]

28. 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 are a few ways to reduce the MZ noise and shall be tested in the 40m.