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 12

DARM TFs as CARM offset is reduced

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