Isola d’Elba, Italy 2006GWADW-VESF meeting

Diagonalizing sensing matrix of RSE interferometer

Shuichi Sato

TAMA projectNational Astronomical Observatory of Japan

IntroductionBackgroundOverview of RSE interferometerHistorical review

Signal extraction scheme(1)Modulation arrangementSignal sensing matrix

Signal extraction scheme(2)“Delocation”Signal sensing matrix

Summary

Contents

Isola d’Elba, Italy 2006GWADW-VESF meeting

BackgroundLCGT : (exact) broadband RSE

3km longUndergroundCryogenic

No specific R&D for broadband RSERSE

GoalDevelop length sensing scheme

Points(Sufficiently) Diagonal sensing matrixRobust sensing schemeScheme less sensitive to various noisesEasy to acquire lock

Introduction

Tokyo

Kamioka

~250 km

Isola d’Elba, Italy 2006GWADW-VESF meeting

Additional mirror (SEM) at dark portLCGT: (exact) broadband RSE

Length degrees of freedomCommon-arm: Lp = (L1+L2 )/2Differential-arm: Lm = (L1-L2 )/2Power-recycling cavity: lp = (l1+l2)/2Michelson : lm = (l1-l2 )/2Signal-extraction cavity: ls = (l3+l4 )/2

Signal portsBright (reflection)PickoffDark (GW-readout)

RSE interferometer

Isola d’Elba, Italy 2006GWADW-VESF meeting

Idea of RSEMPQ

Jun MizunoSeveral schemes and experiments (past)

MPQGerhard Heinzel et al.

CaltechJames Mason et al.

Australian National UniversityDaniel Shaddock et al.

University of FloridaGuido Müller et al.

NAOJ (Suspended w/o PRM as a part of full-RSE)Osamu Miyakawa, Kentaro Somiya

Several schemes and experiments (on-going)40m@Caltech : Suspended, detuned (broadband)

LIGO 40m team4m@NAOJ (full-RSE this time!) : Suspended, Broadband

Fumiko Kawazoe, Volker Leonhardt et al.Tabletop@ANU : Fixed, detuned

David Rabeling et al.

Historical review

Isola d’Elba, Italy 2006GWADW-VESF meeting

Readout schemeRF readoutDC readout is still under consideration

Modulation schemeDouble modulation (producing balanced sidebands)Double demodulationParallel EOM modulation (to avoid sub-sidebands)

Modulation arrangementCarrierPhase modulationAmplitude modulation

Signal extractionArm control signals from CR x PMSignals for central part of RSE from PM x AM

Base line

Isola d’Elba, Italy 2006GWADW-VESF meeting

CarrierCirculates inside arms and PRC

Phase modulation (f1) circulates inside PRC+SEC

Amplitude modulation (f2) circulates inside PRC

No longer coupled cavityFor both modulation side bandsPM: Michelson as a steering mirrorAM: Michelson as an ideal reflection mirror

Modulation design (1)

Isola d’Elba, Italy 2006GWADW-VESF meeting

Michelson interferometer (MI) is a kind of “mirror” rMI, tMI are functions of lsch and Ωm

rMI = cos(lsch Ωm/c)tMI = i sin(lsch Ωm/c)

Point 1MI is transparent to PM

rMIPM = cos(lsch ΩPM/c) = 0, lsch ΩPM/c = 0+nπ

Point 2MI is opaque to AM

rMIAM = cos(lsch ΩAM/c) = 1, lsch ΩAM/c = π/2+mπ

Example:lsch = 7.5 mΩPM = 10 MHzΩAM = 60 MHz (2ΩPM = 20MHz, 4ΩPM = 40MHz does not work)

Modulation design (2)

Isola d’Elba, Italy 2006GWADW-VESF meeting

L-signalsFrom CR x PMAlmost diagonal due to carrier enhancement in arms

l-signals (central part of RSE)From PM x AMOrthogonal (instead of diagonal)

LCGT base line

Signal extraction matrix

Black: Analytic resultsRed: Numerical simulation using “FINESSE”

lplp

lslsdiagonal orthogonal

Isola d’Elba, Italy 2006GWADW-VESF meeting

Same modulation arrangementsPM: circulates inside PRC+SECAM: circulates inside PRC

The ideaMake use of slight “off-resonance”

→ Causes rotation of sideband fieldsDifferent demodulation phasesTwo diagonal signals from one port

“Delocation”

0 1 2 3 4 5 6- 1

- 0.5

0

0.5

1

0 1 2 3 4 5 6- 1

- 0.5

0

0.5

1

lp lpls

ls

Isola d’Elba, Italy 2006GWADW-VESF meeting

Almost diagonal!Perfect separation for lp and ls (in principle)

Some effect on Signal strengthOff-diagonals

Sensing matrix

DMPort RF1 RF2

1 0

1 0

1 0

1 0

1 0

Phase Degrees of freedomLp Lm lp lm ls

Bright CRPM -1.3 - 0 0.00356 0 0.002561 0 -0.0026 -0.000062 -0.0013

Dark CRPM 90 - 0 0 0.001 00 1 0 0.0013 0

Bright AMPM -1.3 14.4 0.001 0 0 0-0.0017 0 1 0 0

Dark AMPM 90 -14.4 0 0.001 0 00 -0.0017 0 1 0

Pickoff AMPM -1.3 42.4 0.001 -0.001 0 010.00088 0 0 0

Black: Analytic resultsRed: Numerical simulation using “FINESSE”

Isola d’Elba, Italy 2006GWADW-VESF meeting

Base line signal sensing scheme for LCGT

Simple arrangement of modulations PM: inside PRC+SECAM: inside PRC

Delocation enables diagonal signal sensing

Still need to verifyLock acquisitionNoise issueRobustness

Summary

Isola d’Elba, Italy 2006GWADW-VESF meeting