40m Modeling and Experiment 1

Modeling the 40m

QND Workshop, HannoverDec 15, 2005

Robert Ward

Seiji Kawamura, Osamu Miyakawa, Hiro Yamamoto, Matthew Evans, Monica Varvella

40m Modeling and Experiment 2

Modeling tools used at the 40m

Twiddle» Frequency domain, analytical, no radiation pressure

Finesse » Frequency domain, no radiation pressure

E2E » Time domain, now with classical radiation pressure

TCST (Thomas Corbitt Simulation Tool)» Two-photon formalism, frequency-domain

Optickle» Frequency domain, Matlab, two-photon formalism

40m Modeling and Experiment 3

Finesse

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odul

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dc=0l+l-ls

Dem

odu

latio

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hase

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Lockingpoint

Finesse used extensively at the 40m lab 2004-2005

Seiji Kawamura modeled the DRMI very thoroughly using Finesse

Very useful for investigating quirks of double & differential demodulation

40m Modeling and Experiment 4

Differential Demodulation:offset vs gain

40m Modeling and Experiment 5

Finesse

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CARM response

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•Also used to investigate the coupled cavity response in our offset CARM state, and design compensation.

•Unfortunately has no radiation pressure effects

40m Modeling and Experiment 6

Straight from the ilog

Location of peak RSE response (in CARM) as a function of offset, modeled in Finesse, and then measured.

40m Modeling and Experiment 7

Dynamic compensation filterfor CARM servo

Optical gain of CARMOpen loop TF of CARM• Optical gain (normalized by transmitted power) shows moving peaks due to reducing CARM offset.

• We have a dynamic compensative filter having an nearly the same shape as optical gain except for upside down. Designed using FINESSE.

• Open loop transfer function has no phase delay in all CARM offset.

40m Modeling and Experiment 8

Error signal sweeps at 10-9 m/s for the 40m IFO obtained in

E2E framework and compared with TWIDDLE predictions

Example:DARM @ AP 166 MHz

TWIDDLE and E2E comparison

e2e SIMULATION:4Om/AdvLIGO package

TWIDDLE

E2E

40m Modeling and Experiment 9

e2e SIMULATION: 4Om/AdvLIGO package

Comparison between real data (black) and e2e simulated data (red) of the transmitted light for both the arms (full IFO): the mirror velocities used in

E2E simulation are the values obtained fitting the real data

Real data have been used to estimate relative mirror velocity for

both the arms:

Vxarm= (0.35 ± 0.13) μm/s

Vyarm= (0.26 ± 0.13) μm/s

E2E

E2E

real data

real data

Tr X

Tr Y

40m Modeling and Experiment 10

e2e SIMULATION: 4Om/AdvLIGO package

Comparison between real data , e2e simulated data and the

theoretical prediction V(t) of the SP error signal @ 166 MHz

The τ and the velocity v is the value obtained fitting real data

τ = 0.7 msv = 0.26 μm/s

V(t) ~ exp(t/τ) sin( a t2)

with a = (k v) / (2 T)

40m Modeling and Experiment 11

E2E: 40m Lock Acquisition

Simulation indicates that controlled reduction of CARM offset should work.

E2E simulation by Matthew Evans in June 2005

40m Modeling and Experiment 12

Optical spring in E2E

• Calculated by time domain simulation

• No length control• Lock lasts ~0.7sec, so

statistics at low frequency is not good.

• Simple length control required

• Calculation time ~5min using DRMI summation cavity

Hiro Yamomoto

40m Modeling and Experiment 13

E2E DARM TF to I and Q

•5W Input•Arms controlled with POX, POY (no DARM)•no MICH control

Hiro Yamomoto

40m Modeling and Experiment 14

E2E Optical Noise

40m Modeling and Experiment 15

Optical noise of 40m in E2E

• Simple length control (UGF~100Hz)

• Err2/(Err1/DARM) DARM: DARM excitation on mirrorsErr1: error signal with DARM

excitationErr2: error signal with optical noise

• How much further does E2E need to go? 2-photon?

• input vacuum?• Quantum control?• Or just classical physics +

shot noise + radiation pressure noise ?

Err2/(Err1/DARM)

40m Modeling and Experiment 16

TCST

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140CARM optical springs at different CARM offsets

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pons

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Arm power = 6

Arm 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

40m Modeling and Experiment 17

Optickle

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40m DataOptickle

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40m DataOptickle

40m Modeling and Experiment 18

CARM optical springs, with no offsets (TCST)