#### Transcript Attempts to measure the Optical Spring in GEO600

```Attempts to measure the Optical
Spring in GEO600
Stefan Hild
(for the GEO-team)
January 2008
GEO simulation meeting
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. :(
Stefan Hild
GEO simulation Meeting 1/2008
Slide 2
Jan’s Matlab code
Stefan Hild
GEO simulation Meeting 1/2008
Slide 3
Simulated quantum noise for
different SR-tunings
From Labbook page 3408,
Using Jan’s script
Stefan Hild
GEO simulation Meeting 1/2008
Slide 4
Simulated quantum noise for
different optical powers
SR-tuning of 350 Hz
From Labbook page 3177,
Using Jan’s script
Stefan Hild
GEO simulation Meeting 1/2008
Slide 5
How can we actually measure the
optical spring?
 Typical frequencies of the optical spring with
current GEO parameters (optical power and SRtuning) 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 !!
Stefan Hild
GEO simulation Meeting 1/2008
Slide 6
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 7
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 8
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 9
Where can we measure the optical
spring?
The optical gain is the signal where we should
be able to 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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 10
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)
Stefan Hild
GEO simulation Meeting 1/2008
Slide 11
In the real world …
things tend to be a bit
more complicated …
Stefan Hild
GEO simulation Meeting 1/2008
Slide 12
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 13
Complication 1: MI long loop is a
3-way split loop
….
+ IM-path term
common elec.
IM actuators
IM electronics
For measuring the optical spring we need to take the intermediate mass
(IM) path into account.
Stefan Hild
GEO simulation Meeting 1/2008
Slide 14
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 (inloop-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 !!
Stefan Hild
GEO simulation Meeting 1/2008
Slide 15
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 16
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 17
Complication 4: GEO local controls
 Each GEO suspension
is equipped with a
LOCAL CONTROL
(LC).
 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
loops in GEO.
(Ch2-Ch5 loops open), personal Communication K.Strain
Magnitude [dB]
 The task of the LC is
to damp suspension
resonances.
Open loop gain of CH1 of a GEO main suspension local control
Frequency [Hz]
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…)
Stefan Hild
GEO simulation Meeting 1/2008
Slide 18
At low frequency we don’t
‘understand’ the measured loop gain
Expected
Measured
Labbook 2631
Since we do not understand the loop gain, we cannot trust the optical
gain measurements !! :(
Stefan Hild
GEO simulation Meeting 1/2008
Slide 19
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 20
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)
Stefan Hild
GEO simulation Meeting 1/2008
Slide 21
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.
 It is not possible to guarantee that only the optical spring changed
Stefan Hild
GEO simulation Meeting 1/2008
Slide 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.
 It is not possible to guarantee that only the optical spring changed
 Changing the SR sideband we use for locking
Stefan Hild
GEO simulation Meeting 1/2008
Slide 23
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.
Lower SB
Upper SB
 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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 24
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 25
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.
 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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 26
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
Stefan Hild
GEO simulation Meeting 1/2008
Slide 27
‘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)
Stefan Hild
GEO simulation Meeting 1/2008
Slide 28
‘Best’ measurement so far…
So far no success in measuring optical spring….
Stefan Hild
GEO simulation Meeting 1/2008
Slide 29
‘Best’ measurement so far…
So far no success in measuring optical spring….
Stefan Hild
GEO simulation Meeting 1/2008
Slide 30
```