1. Stefan Hild (for the GEO-team) January 2008 GEO simulation meeting Attempts to measure the Optical Spring in GEO600

2. Stefan HildGEO simulation Meeting 1/2008Slide 2 Optical spring in GEO600 Optical Spring in Dual-Recyled MI with armcavities: Buonanno and Chen (Phys. Rev. D 64, 042006 (2001) Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors) Optical Spring in GEO: Diploma thesis by Jan Harms http://www.amps.uni-hannover.de/diplomarbeiten/dipl.harms.ps.zip Many attempts to measure, by many different people, over many years… … so far without success. :(

3. Stefan HildGEO simulation Meeting 1/2008Slide 3 Jans Matlab code

4. Stefan HildGEO simulation Meeting 1/2008Slide 4 Simulated quantum noise for different SR-tunings From Labbook page 3408, Using Jans script

5. Stefan HildGEO simulation Meeting 1/2008Slide 5 Simulated quantum noise for different optical powers From Labbook page 3177, Using Jans script SR-tuning of 350 Hz

6. Stefan HildGEO simulation Meeting 1/2008Slide 6 How can we actually measure the optical spring? Typical frequencies of the optical spring with current GEO parameters (optical power and SR- tuning) are 10 to 20 Hz. Usually when showing the optical spring, people plot the quantum noise limited sensitivity-curves Too much noises covers the optical spring Current sensitivity at 10Hz1e-16, expected optical spring at 10Hz 1e-22 Therefore we will never be able to see the optical spring in the GEO sensitivity !!

7. Stefan HildGEO simulation Meeting 1/2008Slide 7 Where can we measure the optical spring? Sensitivity = Quantum noise / optical gain Only taking shot noise into account: quantum noise is flat optical gain has a single resonance

8. Stefan HildGEO simulation Meeting 1/2008Slide 8 Where can we measure the optical spring? Sensitivity = Quantum noise / optical gain Taking shot noise and radiation pressure (but no optical spring) into account: quantum noise is flat at high frequencies and increases at low frequencies optical has a single resonance

9. Stefan HildGEO simulation Meeting 1/2008Slide 9 Where can we measure the optical spring? Sensitivity = Quantum noise / optical gain Taking shot noise, radiation pressure and the optical spring into account: quantum noise is flat at high frequencies and increases at low frequencies optical gain shows two resonances

10. Stefan HildGEO simulation Meeting 1/2008Slide 10 Where can we measure the optical spring? Sensitivity = Quantum noise / optical gain Taking shot noise, radiation pressure and the optical spring into account: quantum noise is flat at high frequencies and increases at low frequencies optical gain shows two resonances The optical gain is the signal where we should be able to measure the optical spring !!!

11. Stefan HildGEO simulation Meeting 1/2008Slide 11 How to measure the optical gain ? Simplified diagram of the differential armlength control 1.Inject noise N into the servo 2.Make sure N dominates the residual motion dx (high noise level + long intigration)

12. Stefan HildGEO simulation Meeting 1/2008Slide 12 In the real world … things tend to be a bit more complicated …

13. Stefan HildGEO simulation Meeting 1/2008Slide 13 Complication 1: MI long loop is a 3-way split loop GEO employs triple suspensions. Each stage is equipped with actuators. Fast actuators at mirror level with small range (ESD). Slow actuators at intermediate mass level with large range (coil magnet) Unity gain frequency of the loop = 100 Hz Cross over between slow and fast path = 10 Hz

14. Stefan HildGEO simulation Meeting 1/2008Slide 14 Complication 1: MI long loop is a 3-way split loop IM electronicsIM actuators common elec. + IM-path term …. For measuring the optical spring we need to take the intermediate mass (IM) path into account.

15. Stefan HildGEO simulation Meeting 1/2008Slide 15 Complication 2: Measuring in a loop with high gain High in-loop-gain: Often it is hard to inject enough noise to dominate the loop (in- loop-suppression, actutor saturation, …) Often the signals within the loop are entirely dominated by sensor noise. At the expected frequency of the optical spring the gain is about 100. => We have to take in-loop-suppression into account !!

16. Stefan HildGEO simulation Meeting 1/2008Slide 16 Complication 3:The GEO triple suspension + long-tilt coupling In a real suspension all degrees of freedom (rotation, tilt, longitudinal,…) are coupled. Actuators are never perfectly balanced => if you want to introduce only longitudinal you also induce rot and tilt (and vice versa). In GEOs monolithic suspensions we encountered an especially strong longitutinal-to-tilt coupling. Coupling from intermediate mass (coil magnet) longitudinal to mirror tilt: DESIGN REALITY

17. Stefan HildGEO simulation Meeting 1/2008Slide 17 Complication 3:The GEO triple suspension + long-tilt coupling The crosscoupling of different degrees of freedom can: Can reduce the loop gain (fighting loops). Can cause loop instabilities. One example: GEOs tilt-to-long coupling…. Stolen from a talk of Martin Hewitson

18. Stefan HildGEO simulation Meeting 1/2008Slide 18 Complication 4: GEO local controls Each GEO suspension is equipped with a LOCAL CONTROL (LC). The task of the LC is to damp suspension resonances. The LC have gain up to a few Hz, i.e. not so far away from the expected frequency of the optical spring In total there are about 140 (!) LC loops in GEO. Magnitude [dB] Frequency [Hz] Open loop gain of CH1 of a GEO main suspension local control (Ch2-Ch5 loops open), personal Communication K.Strain Maybe the opticl spring is damped by one of the LCs ?? (would be hard to find out: LCs only poorly characterized, perhaps one is broken…)

19. Stefan HildGEO simulation Meeting 1/2008Slide 19 At low frequency we dont understand the measured loop gain ExpectedMeasured Since we do not understand the loop gain, we cannot trust the optical gain measurements !! :( Labbook 2631

20. Stefan HildGEO simulation Meeting 1/2008Slide 20 Potential Solution: Doing relative measurements We can do relative measurements: Compare 2 different states with different optical spring frequency (peaks or features appear or disappear or change frequency…) Changing the SR tuning frequency

21. Stefan HildGEO simulation Meeting 1/2008Slide 21 Problems associated with changing the tuning Changing the SR tuning means changed: Gains, phase of all control signals derived from the RF-world at the dark port (MI long gain, MI long phase, MIAA gain, MIAA phase, SR long gain, SR long phase)

22. Stefan HildGEO simulation Meeting 1/2008Slide 22 Potential Solution: Doing relative measurements We can do relative measurements: Compare 2 different states with different optical spring frequency (peaks or features appear or disappear or change frequency…) Changing the SR tuning frequency All signals and loops related to the RF world change. It is not possible to guarantee that ONLY the optical spring changed Changing the optical power All gains change with power. Radiation pressure changes, thermal load of the optics changes… It is not possible to guarantee that only the optical spring changed

23. Stefan HildGEO simulation Meeting 1/2008Slide 23 Potential Solution: Doing relative measurements We can do relative measurements: Compare 2 different states with different optical spring frequency (peaks or features appear or disappear or change frequency…) Changing the SR tuning frequency All signals and loops related to the RF world change. It is not possible to guarantee that ONLY the optical spring changed Changing the optical power All gains change with power. Radiation pressure changes, thermal load of the optics changes… It is not possible to guarantee that only the optical spring changed Changing the SR sideband we use for locking

24. Stefan HildGEO simulation Meeting 1/2008Slide 24 Changing the sign of the SR-tuning (jumping from upper to lower sideband) GEO can continuously tune the SR-frequency from 5kHz down to 200 Hz. Close to tuned SR the no useful errorsignals are available. For a long time GEO could only be locked to the upper sideband. In 2006 we developed a jumping technique that allowed to go to the lower sideband Lower SB Upper SB

25. Stefan HildGEO simulation Meeting 1/2008Slide 25 Changing the sign of the SR-tuning (jumping from upper to lower sideband) Changing the sign of the SR tuning (I.e. going from upper to lower SR sideband just swaps the RF-world We expect that GEO behaves exactly the same for positive and negative SR tuning……..…… at least the sensitivity looks astonishingly similar ! However, exactly ONE thing should be different: Upper sideband = optical spring Lower sideband = No optical spring

26. Stefan HildGEO simulation Meeting 1/2008Slide 26 Potential Solution: Doing relative measurements We can do relative measurements: Compare 2 different states with different optical spring frequency (peaks or features appear or disappear or change frequency…) Changing the SR tuning frequency All signals and loops related to the RF world change. It is not possible to guarantee that ONLY the optical spring changed Changing the optical power All gains change with power. Radiation pressure changes, thermal load of the optics changes… It is not possible to guarantee that only the optical spring changed Changing the SR sideband we use for locking Everything, APART from the optical spring, should be the same

27. Stefan HildGEO simulation Meeting 1/2008Slide 27 What do we expect? Simulated data: Optical power of 1.8kW (70) and 3.6 kW (80) at the BS SR tuning of 350 Hz Locked two upper and lower sideband We should see: A factor 10 difference at 10 or 15 Hz

28. Stefan HildGEO simulation Meeting 1/2008Slide 28 Best measurement so far… Labbook 3693: Two different powers (1.8 and 3.6 kW) each upper and lower sideband lock. Each curve contains 15 minutes of data (30 secs into 1 fft)

29. Stefan HildGEO simulation Meeting 1/2008Slide 29 Best measurement so far… So far no success in measuring optical spring….

30. Stefan HildGEO simulation Meeting 1/2008Slide 30 Best measurement so far… So far no success in measuring optical spring….