Attempts to measure the Optical Spring in GEO600

Stefan Hild(for the GEO-team)

January 2008 GEO simulation meeting

Attempts to measure the Optical Spring in GEO600

Stefan Hild GEO simulation Meeting 1/2008 Slide 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. :(


Jan’s Matlab code


Simulated quantum noise for different SR-tunings

From Labbook page 3408,Using Jan’s script


Simulated quantum noise for different optical powers

From Labbook page 3177,Using Jan’s script

SR-tuning of 350 Hz


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 10Hz≈1e-16, expected optical

spring at 10Hz ≈1e-22

Therefore we will never be able to see the optical spring in the GEO sensitivity !!


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




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




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




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 !!!


How to measure the optical gain ?Simplified diagram of the differential armlength control

1. Inject noise N into the servo2. Make sure N dominates the residual motion dx

(high noise level + long intigration)


In the real world …

things tend to be a bit more complicated …


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


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.


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 !!


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 GEO’s monolithic suspensions we encountered an especially strong longitutinal-to-tilt coupling.

Coupling from intermediate mass (coil magnet) longitudinal to mirror tilt:• DESIGN• REALITY


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: GEO’s tilt-to-long coupling….

Stolen from a talk of Martin Hewitson


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.

Ma

gn

itud

e [

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…)


At low frequency we don’t ‘understand’ the measured loop gain

Expected Measured

Since we do not understand the loop gain, we cannot trust the optical gain measurements !! :(

Labbook 2631


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


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)




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


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


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






Changing the SR sideband we use for locking Everything, APART from the optical spring, should be the same


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


‘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)


‘Best’ measurement so far…

So far no success in measuring optical spring….


‘Best’ measurement so far…

So far no success in measuring optical spring….

Attempts to measure the Optical Spring in GEO600

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