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Optical Springs at the 40m 1
Optical Springs at the 40m
QND Workshop, HannoverDec 14, 2005
Robert Wardfor 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 2
Caltech 40 meter prototype interferometer
An interferometer as close as possible tothe Advanced LIGO optical configuration and control system
Detuned Resonant Sideband Extraction (DRSE)Power RecyclingSuspended mass
Single pendulaDigital controls systemSame cavity finesse as AdLIGO baseline design
100x shorter storage times.
Optical Springs at the 40m 3
AdLIGO signal extraction scheme
f1-f1 f2-f2
Carrier (Resonant on arms)
• Single demodulation• Arm information
• Double demodulation• Central part information
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.
ETMy
4km
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.
ETMxITMxBSPRM
SRM
ITMy
4km
f2
f1
Optical Springs at the 40m 4
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 5
40m Lock Acquisition part I: Off-resonant lock scheme for a single cavity
Transmitted light is used as
Off-resonantLock point
Resonant Lock
offsetpower dTransmitte
1+
Optical Springs at the 40m 6
40m Lock acquisition procedure
Start withno DOFscontrolled, all optics aligned.
ITMy
ITMxBS
SRM
PRM
SP DDM
13m MC
166MHz
33MHz
SP33 SP166
AP166
PO DDM
AP DDM
Optical Springs at the 40m 7
40m Lock acquisition procedure
DRMI + 2armswith offset
ITMy
ITMxBS
PRM
SRMSP DDM
13m MC
166MHz
SP33 SP166
AP DDM
AP166
33MHz
PO DDM
Average wait : 3 minute(at night, with tickler)
T =7%
T =7%IQ
1/sqrt(TrY)
1/sqrt(TrX)
Optical Springs at the 40m 8
40m Lock acquisition procedure
ITMy
ITMxBS
SRM
PRM
SP DDM
13m MC
166MHz
SP33 SP166
AP DDM
AP166To DARM
33MHz
PO DDM
AP166 / (TrX+TrY)
CARM
DARM+
-1+
Short DOFs -> DDMDARM -> RF signalCARM -> DC signal
1/sqrt(TrX)+ 1/sqrt( TrY)
CARM -> Digital CM_MCL servo
Alternative path
Optical Springs at the 40m 9
40m Lock acquisition procedure
Reduce CARM offset:1. Go to higher ARM power2. 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.
ITMy
ITMxBS
SRM
PRM
SP DDM
13m MC
166MHz
SP33
SP166
AP DDM
AP166To DARMREFL
DARM-1
33MHz
PO DDM
AP166 / (TrX+TrY)
GPR=5
5. Packup MOPA and send it to LLO for S5
Optical Springs at the 40m 10
Optical spring in detuned RSEOptical spring in detuned RSE was first predicted using two-photon formalism.
a :input vacuumb :outputD :M :h :strain
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛ Φ+Φ+
SQL2
1)(
2
1
2221
1211)(2
2
1 21h
hDD
eaa
CCCC
eMb
b ii ββ τκ
( ) ( )( )ζζτ
ζζζζκ
ζ
ζ
cossin cossin cossin
2
21
2221212111
SQL
DDaCCaCCb
bh
hn
++++
=∆
∆=
A. Buonanno, Y.Chen, Phys. Rev. D 64, 042006 (2001)
hSQL:standard quantum limitt: transmissivity of SRMk: coupling constantF: GW sideband phase shift in SRCb: GW sideband phase shift in IFO
h
h
Dlaser
Signal recyclingmirror
baz: homodyne phase
Optical Springs at the 40m 11
Detune Cartoon
0≠δC
arrie
r fre
quen
cy
-10000 -5000 0 5000 10000
50
100
200
500
1000
frequency offset from carrier [Hz]
FWHM
USBLSB
fsig
•Responses of GW USB and GW LSB aredifferent due to the detuning of the signal recycling cavity.
•IFO Differential Arm mode is detuned from resonance at operating point
0=δ0≠δ
SRC DARM
IFO DARM/CARM
slope related to spring constant?
•IFO Common Arm mode is detuned from resonance at intial locking point
0≠δ0=δ
PRC CARM
Side
band
am
plitu
de [a
.u.]
Optical Springs at the 40m 13
CARM optical springs
102 10380
90
100
110
120
130
140CARM optical springs at different CARM offsets
f (Hz)
CA
RM
opt
ical
resp
onse
(dB
)
Arm power = 6Arm power = 8Arm 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
Optical Springs at the 40m 14
Optical spring and Optical resonance in differential arm mode of detuned RSE
• Optical gain of L- loopDARM_IN1/DARM_OUT divided by
pendulum transfer function
• 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.
• Theoretical line was calculated using A. Buonanno and Y.Chen’s equations.-150
-100
-50
0
50
100
150
Phas
e[de
g]
102 3 4 5 6 7 8 9
1002 3 4 5 6 7 8 9
10002 3 4 5 6 7
Frequency[Hz]
60
40
20
0
-20
Mag
[dB]
Measured data Theoretical line
Measured optical gain of arm differential mode in detuned RSEOct 22, 2005
Optical Springs at the 40m 15
Positive spring constant
-150
-100
-50
0
50
100
150
Phas
e[de
g]
102 3 4 5 6 7 8 9
1002 3 4 5 6 7 8 9
10002 3 4 5 6 7
Frequency[Hz]
-40
-20
0
20
40
Mag
[dB]
Measured data Theoretical line
Measured optical gain of arm differential mode in detuned RSEOct 13, 2005
• SRM is locked at opposite position from anti-resonant carrier point(BRSE).
• Optical spring disappeared due to positive spring constant.
BroadbandRSE
BroadbandSR
Optical Springs at the 40m 16
Simple picture of optical spring in detuned RSE
Let’s move arm differentially, X arm longer, Y arm shorter from full RSE
DARM (Lx-Ly) DARM (Lx-Ly)
DARM (Lx-Ly)
Pow
er(W
)
Pow
er(W
)
Pow
er(W
)
BRSECorrect SRM position Wrong SRM position
X arm X armY arm Y arm
PowerX arm down, Y arm up X arm down, Y arm down X arm up, Y arm downRadiation pressureX arm down, Y arm up X arm down, Y arm down X arm up, Y arm downSpring constantNegative(optical spring) N/A Positive(no optical spring)
Optical Springs at the 40m 17
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
+ + x x
- - 0 +
+ - x x
- + + -
Xarm Yarm DARM CARM
+ + 0 -
- - x x
+ - - +
- + x x
Optical Springs at the 40m 18
Will it lock?
- 1 - 0 . 8 - 0 . 6 - 0 . 4 - 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 1- 2
- 1 . 5
- 1
- 0 . 5
0
0 . 5
1
1 . 5
2
E T M X p h i = 9 0 . 0 7 3 3
E T M Y p h i
Erro
r Sig
nals
G o o d S R M p o s i t i o n
E R R D C X
E R R D C Y
NO
- 1 - 0 . 8 - 0 . 6 - 0 . 4 - 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 1- 2
- 1 . 5
- 1
- 0 . 5
0
0 . 5
1
1 . 5
2
E T M X p h i = 8 9 . 9 2 6 7
E T M Y p h i
Erro
r Sig
nals
G o o d S R M p o s i t i o n
E R R D C X
E R R D C Y
YES
•x-axis: EY position•y-axis: signal•blue:X err•green: Y err•black: DARM•red: CARM
modeled with FINESSE
Optical Springs at the 40m 19
DRMI lock using double demodulation with unbalanced RF sideband in SRC
Carrier33MHz166MHz
ITMy
ITMxBS
PRM
SRM
OSA DDM PD
DDM PD
DDM PD
Carrier
33MHz
Unbalanced166MHz
Belongs tonext carrier
Belongs tonext carrier
Belongs tonext carrier
OSA
Optical Springs at the 40m 20
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
Kentaro Somiya “Photodetection method using unbalanced sidebands for squeezed quantum noise in a gravitational wave interferometer”PHYSICAL REVIEW D 67,122001 2003A. Buonanno, Y. Chen, N. Mavalvala, “Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme” PHYSICAL REVIEW D 67,122005 2003
+166MHz sideband
demodulation phase
b1
b2
Optical Springs at the 40m 21
Changing the DARM quadrature
Story:1. Lock IFO with CARM offset2. Handoff DARM to RF 3. Adjust RF demodulation
phase4. Reduce CARM offset5. 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 22
Optickle Results
•GW response in a single, chosen quadrature at multiple CARM offsets
101 102 103 104
150
160
170
180
190
200
210
220DARM opto-mechanical response in Q=1.07pi at different CARM offsets
f (Hz)
dB
Optical Springs at the 40m 23
Why is the correct SRM position harder to lock?
The correctly detuned SRC doesn’t lock as easily as the oppositely tuned SRCTrue 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-it-
up it right yet?
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0 20 40 60 80 100 120 140 160 180
Abs
phi [deg] (SRM)
DRFPMI3 Tue Dec 13 00:07:37 2005
S21AP n2 : S11AP n2 :
CAP n2 : S12AP n2 :
S22AP n2 :
Optical Springs at the 40m 24
Mode healing/injuring at Dark Port
Positive spring constant with no optical spring
Negative spring constant with optical spring
Carrier power at DP is 10x smaller
• Repeatable• The same alignment quality
Optical Springs at the 40m 25
Compensating the resonancesUGFs ~ 250HzCompensation Filters for the various resonances:
Optical Opto-mechanical
4kHz >> UGF no compensationAdLIGO: 180 Hz ~ UGF
40Hz < UGFno compensationAdLIGO: 70Hz?
1kHz -> 100Hz ~ UGFdynamic compensation
0->100Hz ~ UGFnot coherently compensated
DARM
CARM
Optical Springs at the 40m 26
DARM loop: Calibration questions
D C S
P pendulum
DARM Cavityresponse
Sensing
A Actuator
F
Feedback filter
DARM_IN1
DARM_OUT
N GN+1
DCSFAPG =
GDCSN+1
GAPGN
GDCSFN
+−
=+ 1
/1
GGN+−
1EXC
DARM_IN2
Use DARM_IN1
•Measure DARM_IN2/EXC=
•Estimate S•Measure (or estimate) C
Use DARM_OUT
•Measure DARM_IN1/EXC=
•Estimate A•Estimate P
G+11
GG+1