1. Cascina, January 25th, 20051 Coupling of the IMC length noise into the recombined ITF output Raffaele Flaminio EGO and CNRS/IN2P3 Summary - Recombined ITF - control architecture - noise budget - Evidences of sensitivity to IMC length noise - Effect of IMC length noise: theory - Effect of IMC length noise: exp tests - Discussion

2. Cascina, January 25th, 20052 I. Recombined ITF: control architecture and noise budget

3. Cascina, January 25th, 20053 Interferometer lock acquisition Injection control - Laser frequency stabilized to IMC (f<300 kHz) - IMC length locked to reference cavity (f<150 Hz) Interferometer lock acquisition - Each cavity locked independently - Michelson (= dark fringe) locked with B2_ACq

4. Cascina, January 25th, 20054 Cavities AA and ‘linear’ locking Automatic alignment on both cavities - Use of Anderson technique - One wave-front sensor for each cavity - Tidal control ON Switch ITF control architecture - Arms common mode controlled with B2_ACp - Arms differential mode controlled with B1’

5. Cascina, January 25th, 20055 Second stage of frequency stabilization Second stage of frequency stabilization (SSFS) - use of B2_ACp - feedback to IMC length below 150 Hz - feedback directly to laser frequency above 150 Hz - unity gain ~ 10 kHz Arms common mode control - use of reference cavity error signal

6. Cascina, January 25th, 20056 ‘Science’ mode OMC locking Arms differential mode control with high sensitivity phd (B1)

7. Cascina, January 25th, 20057 C4 run: Noise Sources ?

8. Cascina, January 25th, 20058 II. Coupling of IMC length noise into ITF output: evidences

9. Cascina, January 25th, 20059 Michelson control noise (I) B2_ACq ‘readout noise’ Beam splitter position noise Interferometer readout noise Michelson control Interferometer sensitivity to beam splitter position

10. Cascina, January 25th, 200510 Michelson control noise (II) Beam splitter induced displacement: d(l 1 -l 2 ) = TF m (f)·  2 · dl BS /dV DAC [m/V DAC ] · Sc_BS_zCorr [V DAC ] where: 1) TF m (f) = f 0 2 /(-f 2 + f 0 2 ) ; f 0 = 0.6 Hz 2) dl BS /dV DAC [m/V DAC ] estimated using calibration lines applied to BS during the run Effect of BS displacement on ITF output reduced by cavity finesse factor: d(l 1 -l 2 )  d(L 1 -L 2 ) = d(l 1 -l 2 )  /(2·F) / TF cavity F = 50 TF cavity = (1 + f 2 /f c 2 ) -1/2 f c = 500 Hz

11. Cascina, January 25th, 200511 Michelson control noise (III)

12. Cascina, January 25th, 200512 ‘Michelson control noise’ (IV) B2 quad (C4) Input bench resonances (Feb 04) Due to input bench resonances

13. Cascina, January 25th, 200513 Input Bench resonances B1_ACp (C1) TF IB (Feb 04)

14. Cascina, January 25th, 200514 Three important questions 1) What are these resonances ? 2) What drives these resonances ? 3) How do they couple into the B2_ACq ?

15. Cascina, January 25th, 200515 1) What are these resonances ?

16. Cascina, January 25th, 200516 1) What are these resonances ? y, tx and tz payload modes (F.Richard) Unknown (not present in F.Richard model) Wires violin modes

17. Cascina, January 25th, 200517 Injection system alignment control Input bench damped respect to ground Mode cleaner mirror automatically aligned to input beam Input beam automatically aligned to reference cavity

18. Cascina, January 25th, 200518 2) What drives these resonances ? A) IB local control noise. If local control noise sufficiently low …. …. B) Coil driver noise - Coherence between coil driver outputs and B2_ACq during C4 confirms this hypothesis (see L.Holloway presentation at the last detector meeting) -Better results when driving has been moved from the ground coils to the marionetta coils 26/06 C4: control from the ground coils 07/09 DT: control from the marionetta

19. Cascina, January 25th, 200519 Input bench resonances + input bench local control noise Input bench vibrates Spurious signal on Spurious signal laser frequency on B2 quad stabilization Spurious signal in Michelson control Spurious signal on dark fringe 3) How do they couple in B2_ACq ? ? ?

20. Cascina, January 25th, 200520 3) How do they couple in B2_ACq? Observations: A) 1) They couple also on B7_ACq and B8_ACq 2) Couple much less on B7_ACp and B8_ACp Why only in the in quad signals ? B) Noise appears when the SSFS is switched ON SSFS OFF SSFS ON

21. Cascina, January 25th, 200521 III. Coupling of IMC length noise into ITF output: theory

22. Cascina, January 25th, 200522 Synchronous detection (I) Phase modulation:  + =  0 + ,  - =  0 -  A 0 = J 0 (m) A, A + = J 1 (m) A, A - = -J 1 (m) A Propagation to photodiode: A 0  A 0 = P 0 A 0, A +  A + = P + A +, A -  A - = P - A - Demodulated signal: in phase S p = - 2 Im{ A + A 0 * + A 0 A - * } in quad S q = 2 Re{ A + A 0 * + A 0 A - * }

23. Cascina, January 25th, 200523 Synchronous detection (II) Phase modulated beam (input beam): A 0 = J 0 (m) A A + = J 1 (m) A  S p = 0 A - = -J 1 (m) A S q = 0 Carrier phase shift: A 0  A 0 = a e i  A 0 A +  A + = b A +  S p = 2 a b J 0 (m) J 1 (m) A 2  A -  A - = b A - S q = 0 Sidebands amplitude change: A 0  A 0 = a A 0 A +  A + = b (1+  A +  S p = 0 A -  A - = b (1-  A - S q = 2 a b J 0 (m) J 1 (m) A 2 

24. Cascina, January 25th, 200524 B2 Signals: B2_ACp & B2_ACq Variation of cavity common mode length ( = laser frequency variation):  carrier phase shift  B2 signal in phase  B2_ACq = 0 Variation of Michelson differential length (l 1 -l 2 )  sidebands amplitude variation  B2 signal in quadrature  B2_ACp = 0 ACp ACq B2 ACp ACq l 1 -l 2 (a.u.) A-A- A+A+ A0A0

25. Cascina, January 25th, 200525 B2 Effect of IMC length noise (I) ACp ACq l IMC (a.u.) Variation of IMC length (due to input bench resonances)  1) carrier phase shift = sideband phase shift  2) carrier and sidebands amplitude variation: second order effect  B2_ACp = 0, B2_ACq = 0 A-A- A+A+ A0A0

26. Cascina, January 25th, 200526 B2 Effect of IMC length noise (II) ACp ACq A-A- A+A+ A0A0 l IMC (a.u.) Variation of IMC length (due to input bench resonances)  sidebands amplitude variation: if A +  then A -  first order effect  signal on B2_ACq (and on all quadratures)

27. Cascina, January 25th, 200527 B2 Effect of IMC length noise (III) ACp ACq A-A- A+A+ A0A0 l IMC (a.u.) Variation of IMC length (due to input bench resonances) compensated with a frequency variation by the fast frequency stabilization loop (300 kHz bandwidth)  no sidebands amplitude variation  no spurious signal Signal here is zero

28. Cascina, January 25th, 200528 B2 Effect of IMC length noise (IV) A-A- A+A+ A0A0 l IMC (a.u.) Laser frequency locked to interferometer  IMC length variation (due to input bench resonances) not completely compensated by the SSFS  sidebands amplitude variation: if A +  then A -   signal on B2_ACq (and on all quadratures) Signal here is zero Signal here is NOT zero (= SSFS_Corr) Signal here is NOT zero (= - SSFS_Corr)

29. Cascina, January 25th, 200529 SSFS: OFF vs ON

30. Cascina, January 25th, 200530 IV. Coupling of IMC length noise into ITF output: experimental tests

31. Cascina, January 25th, 200531 B2 Effect of IMC length noise A-A- A+A+ A0A0 l IMC (a.u.) Laser frequency locked to interferometer  IMC length variation (due to input bench resonances) not completely compensated by the SSFS  signal on B2_ACq (and on all quadratures)  effect deducible from measured SSFS_Corr Signal here is zero Signal here is NOT zero (= SSFS_Corr) Signal here is NOT zero (= - SSFS_Corr)

32. Cascina, January 25th, 200532 Effect of IMC: prediction vs measurement Deduce B2_ACq from SSFS_Corr Ingredients: - calibration of B2_ACq - calibration of SSFS_Corr - some geometrical parameter (Michelson asymmetry, IMC length) - one free parameter: modulation frequency detuning Prediction if detuning = 70 Hz

33. Cascina, January 25th, 200533 B2 ACp ACq B2 Effect of IMC: exp verification sinusoidal perturbation at 2222 Hz 1) Misalign all mirrors but NI 2) Inject line at 2222Hz on the laser frequency 3) Look at 2222 Hz line from B2 4) Minimize the 2222Hz line by changing the modulation frequency f = 6.264080 MHz f = 6.264150 MHz Observation: optimal modulation frequency change by a few Hz when ISYS is unlocked and re-locked

34. Cascina, January 25th, 200534 Effect of modulation frequency tuning Signal on B2_ACq with SSFS ON: before tuning vs after f = 6.264080 MHz f = 6.264150 MHz

35. Cascina, January 25th, 200535 Discussion C3 sensitivity C4 sensitivity Virgo goal 10 6

36. Cascina, January 25th, 200536 Discussion Effect decreases linearly with modulation frequency offset: with  f = 70 Hz (= 1.5 mm) the resonances exceed Virgo sensitivity by 10 6  need to reduce the effect by 6 orders of magnitude Recycling will help: - with recycling the effect on B5_ACq and B2_ACq (signals used to control the BS) will be reduced by ~ 20  need to reduce the effect by ‘only’ 5 orders of magnitude

37. Cascina, January 25th, 200537 Discussion Several solutions available: 1) Reduce IMC length noise - reduce DAC & coil driver noise - steeper low pass the control signals (or equivalently feedback only to the marionette) - use cleaner signals to control the input bench position (AA signals)

38. Cascina, January 25th, 200538 Discussion Several solutions available: 2) Add a servo to tune the modulation frequency and the IMC length - feedback to modulation frequency (need to adjust the demodulation phases as well) ….. - …. or feedback to IMC length (i.e. to the arms common mode when in ‘science mode’) - error signal readout ? add a modulation into the laser frequency modulate the modulation frequency demodulate the IMC transmission at 2  - control noise ? probably rather high, feedback possible only at very low frequency (TBC)

39. Cascina, January 25th, 200539 Discussion Several solutions available: 3) Measure and subtract the noise injected into the beam splitter by the Michelson control

40. Cascina, January 25th, 200540 Discussion

41. Cascina, January 25th, 200541 Discussion

42. Cascina, January 25th, 200542 Discussion