Optical Springs at the 40m
QND Workshop, Hannover
Dec 14, 2005
Robert Ward
for the 40m Team
Osamu Miyakawa, Rana Adhikari, Matthew Evans, Benjamin
Abbott, Rolf Bork, Daniel Busby, Hartmut Grote, Jay Heefner,
Alexander Ivanov, Seiji Kawamura, Michael Smith, Robert Taylor,
Monica Varvella, Stephen Vass, and Alan Weinstein
Optical Springs at the 40m
1
Caltech 40 meter prototype interferometer
An interferometer as close as possible to
the Advanced LIGO optical configuration and control system
 Detuned Resonant
Sideband Extraction
(DRSE)
 Power Recycling
 Suspended mass
Single pendula
 Digital controls system
 Same cavity finesse as
AdLIGO baseline design
100x shorter storage
times.
Optical Springs at the 40m
2
AdLIGO signal extraction scheme
ETMy
4km

f2


ITMy
PRM
BS
ITMx
ETMx
Mach-Zehnder will be installed to
eliminate sidebands of sidebands.
Only + f2 is resonant on SRC.
Unbalanced sidebands of +/-f2 due
to detuned SRC produce good error
signal for Central part.
4km
f1
SRM
-f2
Carrier (Resonant on arms)
• Single demodulation
• Arm information
-f1
f1
f2
• Double demodulation
• Central part information


Arm cavity signals are extracted from beat between carrier and f1 or f2.
Central part (Michelson, PRC, SRC) signals are extracted from beat
between f1 and f2, not including arm cavity information.
Optical Springs at the 40m
3
The Story So Far
To understand why we saw the optical springs in the
way we have, it helps to know the story of Lock
Acquisition at the 40m.
Optical Springs at the 40m
4
40m Lock Acquisition part I:
Off-resonant lock scheme for a single cavity
Transmitted light is used
as
1
 offset
Transmitte d power
Resonant Lock
Off-resonant
Lock point
Optical Springs at the 40m
5
40m Lock acquisition procedure
Start with
no DOFs
controlled,
all optics aligned.
ITMy
166MHz
ITMx
13m MC
BS
33MHz
PRM
SP33
PO DDM
SRM
SP166
SP DDM
AP166
AP DDM
Optical Springs at the 40m
6
40m Lock acquisition procedure
1/sqrt(TrY)
DRMI + 2arms
with offset
Average wait : 3 minute
(at night, with tickler)
ITMy
166MHz
ITMx
13m MC
33MHz
1/sqrt(TrX)
BS
PRM
T =7%
SP33 SP166
I
SP DDM
Q
SRM
T =7%
PO DDM
AP166
AP DDM
Optical Springs at the 40m
7
40m Lock acquisition procedure
Short DOFs -> DDM
DARM -> RF signal
CARM -> DC signal
CARM -> Digital
CM_MCL servo
1/sqrt(TrX)+ 1/sqrt( TrY)
Alternative path
+
ITMy
166MHz
-1
DARM
+
ITMx
13m MC
33MHz
CARM
BS
PRM
SP33 SP166
SP DDM
PO DDM
SRM
To DARM
AP166
AP DDM
Optical Springs at the 40m
AP166 / (TrX+TrY)
8
40m Lock acquisition procedure
Reduce CARM offset:
1. Go to higher ARM power
2. Switch on AC-coupled analog
CM_AO servo, using REFL
DC as error signal.
3. Switch to RF error signal (POX)
at half-max power.
4. Reduce offset/increase gain of
CM_AO.
-1
166MHz
GPR=5
13m MC
ITMx
BS
SP166
33MHz
PRM
PO DDM
SRM
SP33
5. Packup MOPA
and send it to
LLO for S5
DARM
ITMy
SP DDM
REFL
To DARM
AP166
AP DDM
Optical Springs at the 40m
AP166 / (TrX+TrY)
9
Optical spring in detuned RSE
Optical spring in detuned RSE was first predicted using two-photon formalism.

D
 b1  1  2i (    )  C11 C12  a1 
i (   )  1  h
  






e

2


e

C
 
D  h 
 b2  M 
 21 C22  a2 
 2  SQL 
a :input vacuum
b :output
D:
M:
h :strain
hn 
h
hSQL:standard quantum limit
t: transmissivity of SRM
k: coupling constant
F: GW sideband phase shift in SRC
b: GW sideband phase shift in IFO
hSQL
b
2
C sin   C21 cos   a1  C12 sin   C22 cos   a2
b  11
 D1 sin   D2 cos  
laser
h
D
Signal recycling
mirror
a
b
z: homodyne phase
A. Buonanno, Y.Chen, Phys. Rev. D 64, 042006 (2001)
Optical Springs at the 40m
10
Detune Cartoon
IFO DARM/CARM
•IFO Differential Arm mode is
detuned from resonance at
operating point
500
200
 0
slope related to
spring constant?
100
SRC
fsig
50
LSB
-10000
USB
-5000
0
5000
 0
 0
FWHM
Carrier frequency
Sideband amplitude [a.u.]
1000
10000
frequency offset from carrier [Hz]
•Responses of GW USB and GW LSB are
different due to the detuning of the signal
recycling cavity.
•IFO Common Arm mode is
detuned from resonance at
intial locking point
 0
 0
PRC
Optical Springs at the 40m
DARM
CARM
11
DARM TFs as CARM offset is reduced
Optical Springs at the 40m
12
CARM optical springs
CARM optical springs at different CARM offsets
140
Arm power = 6
Arm power = 8
Arm power = 10
•Solid lines are from TCST
•Stars are 40m data
•Max Arm Power is ~80
•Also saw CARM anti-springs,
but don’t have that data
130
CARM optical response (dB)
120
110
100
90
80
2
3
10
10
f (Hz)
Optical Springs at the 40m
13
Optical spring and Optical resonance in
differential arm mode of detuned RSE
• Optical gain of L- loop
Measured optical gain of arm differential mode in detuned RSE
Oct 22, 2005
60
Measured data
Theoretical line
Mag[dB]
40
• Optical spring and optical
resonance of detuned RSE
were measured.
• Frequency of optical spring
depends on cavity power,
mass, detuning phase of SRC.
• Frequency of optical
resonance depends on
detuning phase of SRC.
20
0
-20
150
100
Phase[deg]
DARM_IN1/DARM_OUT divided by
pendulum transfer function
50
0
• Theoretical line was calculated
using A. Buonanno and
Y.Chen’s equations.
-50
-100
-150
2
10
3
4
5 6 7 8 9
2
3
4
100
5 6 7 8 9
2
3
4
5 6 7
1000
Frequency[Hz]
Optical Springs at the 40m
14
Positive spring constant
Measured optical gain of arm differential mode in detuned RSE
Oct 13, 2005
40
Measured data
Theoretical line
• SRM is locked at opposite
position from anti-resonant
carrier point(BRSE).
Mag[dB]
20
• Optical spring disappeared
due to positive spring
constant.
0
-20
-40
150
Phase[deg]
100
50
0
Broadband
SR
-50
-100
Broadband
RSE
-150
2
10
3
4
5 6 7 8 9
2
3
4
5 6 7 8 9
100
2
3
4
5 6 7
1000
Frequency[Hz]
Optical Springs at the 40m
15
Simple picture of optical spring in
detuned RSE
Let’s move arm differentially, X arm longer, Y arm shorter from full RSE
Wrong SRM position
Correct SRM position
BRSE
Power(W)
Power(W)
X arm
X arm
Y arm
Power(W)
Y arm
DARM (Lx-Ly)
DARM (Lx-Ly)



Power
X arm down, Y arm up
Radiation pressure
X arm down, Y arm up
Spring constant
Negative(optical spring)
DARM (Lx-Ly)
X arm down, Y arm down
X arm up, Y arm down
X arm down, Y arm down
X arm up, Y arm down
N/A
Optical Springs at the 40m
Positive(no optical spring)
16
Relationship between the CARM and
DARM springs at the 40m
 With the 40m Lock Acquisition scheme, we only see a CARM
spring if there’s also a DARM spring.
 Details tomorrow
•Using the DC-locking scheme for the arms, there are, prima facie, four locking
points corresponding to the four possible gain combinations, but only two will
acquire lock.
Correct SRM position
Incorrect SRM position
Xarm
Yarm
DARM CARM
Xarm
Yarm
DARM CARM
+
+
x
x
+
+
0
-
-
-
0
+
-
-
x
x
+
-
x
x
+
-
-
+
-
+
+
-
-
+
x
x
Optical Springs at the 40m
17
Will it lock?
Good SRM position
2
ERRDCY
NO
1
0.5
Error Signals
•x-axis: EY position
•y-axis: signal
•blue:X err
•green: Y err
•black: DARM
•red: CARM
ERRDCX
1.5
0
-0.5
-1
modeled with
FINESSE
-1.5
-2
-1
ETMX phi=90.0733
-0.8
-0.6
-0.4
-0.2
0
0.2
ETMY phi
Good SRM position
0.4
0.6
0.8
1
2
ERRDCX
1.5
ERRDCY
1
YES
Error Signals
0.5
0
-0.5
-1
-1.5
-2
-1
ETMX phi=89.9267
-0.8
-0.6 Springs
-0.4 at the
-0.2
Optical
40m
0
0.2
ETMY phi
0.4
0.6
0.8
1
18
DRMI lock using double demodulation with
unbalanced RF sideband in SRC
Carrier
Carrier
33MHz
166MHz
ITMy
BS
ITMx
Unbalanced
166MHz
PRM
DDM PD
33MHz
Belongs to
next carrier
DDM PD
Belongs to
next carrier
SRM
OSA
DDM PD
OSA
Belongs to
next carrier
Optical Springs at the 40m
19
Unbalanced Sideband Detection
Can not be used to circumvent the standard quantum
limit, due to heterodyne noise
Can be used to change the measurement
quadrature, and thus reshape the GW response

b2
demodulation
phase
+166MHz sideband

Kentaro Somiya “Photodetection method
using unbalanced sidebands for
squeezed quantum noise in a
gravitational wave interferometer”
PHYSICAL REVIEW D 67,122001 2003
A. Buonanno, Y. Chen, N. Mavalvala,
“Quantum noise in laser-interferometer
gravitational-wave detectors with a
heterodyne readout scheme” PHYSICAL
REVIEW D 67,122005 2003
b1
Optical Springs at the 40m
20
Changing the DARM quadrature
Story:
1. Lock IFO with CARM offset
2. Handoff DARM to RF
3. Adjust RF demodulation
phase
4. Reduce CARM offset
5. This changes the quadrature
of the signal. As we are not
compensating for this by
adjusting the demod phase,
the shape of the response
changes.
May also be some overall
gain change due to
imperfect normalization
Optical Springs at the 40m
21
Optickle Results
DARM opto-mechanical response in Q=1.07pi at different CARM offsets
220
•GW response in a
single, chosen
quadrature at multiple
CARM offsets
210
200
dB
190
180
170
160
150
1
10
2
3
10
10
4
10
f (Hz)
Optical Springs at the 40m
22
Why is the correct SRM position
harder to lock?
DRFPMI3
Tue Dec 13 00:07:37 2005
0.016
0.014
0.012
0.01
Abs
The correctly detuned SRC
doesn’t lock as easily as the
oppositely tuned SRC
True for both full IFO and
just the DRMI (though less
noticeable on DRMI)
For full IFO, lock time goes
from 1 to 5 minutes.
Have we just not tuned-itup it right yet?
0.008
0.006
0.004
0.002
0
0
20
40
60
80
100
120
140
160
180
phi [deg] (SRM)
S21AP n2 :
CAP n2 :
S11AP n2 :
S12AP n2 :
Optical Springs at the 40m
S22AP n2 :
23
Mode healing/injuring at Dark Port
Negative spring constant
with optical spring
Positive spring constant
with no optical spring
Carrier power at DP is 10x
smaller
• Repeatable
• The same alignment quality
Optical Springs at the 40m
24
Compensating the resonances
UGFs ~ 250Hz
Compensation Filters for the various resonances:
Optical
DARM
CARM
Opto-mechanical
4kHz >> UGF
no compensation
AdLIGO: 180 Hz ~ UGF
40Hz < UGF
no compensation
AdLIGO: 70Hz?
1kHz -> 100Hz ~ UGF
dynamic compensation
0->100Hz ~ UGF
not coherently
compensated
Optical Springs at the 40m
25
DARM loop: Calibration questions
N
1 G
N
N
G
1 G
P
pendulum
N
D
C
S
DARM
Cavity
response
Sensing
G  DCSFAP
DCS
1 G
DARM_IN1
EXC
DARM_IN2
Use DARM_IN1
A
Actuator
Feedback filter
F
•Measure DARM_IN2/EXC=
1
1 G
•Estimate S
•Measure (or estimate) C
DARM_OUT
DCSF
 G / AP
N
N
1 G
1 G
Use DARM_OUT
•Measure DARM_IN1/EXC=
•Estimate A
•Estimate P
Optical Springs at the 40m
26
G
1 G