Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i ...
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![Page 1: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/1.jpg)
Shot noise in GW detectors
G González
![Page 2: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/2.jpg)
x
Power(ASDC)
bright
dark
/2The dark fringe
L+L
L-L
i L
P=P0 sin2 (t+kl) = (P0/2) (1+sin (2t+2kl)): insensitive to l
If we phase-modulate the light:
• If the Michelson arms are equal length in average, power is same (dark) for carrier and sidebands: no signal yet. • If arms are not equal (Schnupp asymmetry), carrier is dark, but sidebands are not. • The “beat” of carrier and sidebands has then a signal (photocurrent):P=|E0+E++E-|2DC+ J0J1sin(kL)sin(kmDL)sin(wmt) + …(2wm t)
•Then, “demodulate” : multiply by sin(wmt) or cos(wmt) to produce I and Q phases
For m=25 MHz (m=12 m), sidebands have wwm=w0(1 1.4 10 -8).
![Page 3: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/3.jpg)
Michelson interferometerShot noise at output : white noise with psd:
φ2 ( f ) = 2hν
ηP
Output signal:
x
Power(ASDC)
bright
dark
/2
![Page 4: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/4.jpg)
Power-recycled Michelson:PNI experiment 1995-1999
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![Page 5: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/5.jpg)
(green) PNI experiment
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φ2 ( f ) = 2hν
ηP
φ2 ( f ) = Fns 2hν
ηP= 3
hν
ηP
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Lossless, mid fringe:
Lossless, demodulated at dark fringe:
Lossy, demodulated at dark fringe:
PRL, 80, p8131, 1998
![Page 6: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/6.jpg)
Power-recycled Fabry Perot Michelson interferometer
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Fabry Perot cavity
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LIGO cavity parameters
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L1 “noise budget”
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~4x/ ~1e-12 rad/rtHz
![Page 10: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/10.jpg)
Shot noise and radiation pressure
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m 2
Standard quantum limit:
![Page 11: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/11.jpg)
Advanced LIGO: signal recycling
Advance
d LIGO
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Beyond SQL
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ALESSANDRA BUONANNO AND YANBEI CHEN
PHYSICAL REVIEW D 64 042006
![Page 14: Shot noise in GW detectors G González. x Power (ASDC) bright dark /2 The dark fringe L+ L L- L i L P=P 0 sin 2 ( t+k l) = (P 0 /2) (1+sin.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649dbe5503460f94ab1e7a/html5/thumbnails/14.jpg)
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The references I used, in chronological order, were:
VOLUME 80, NUMBER 15 P H Y S I C A L R E V I E W L E T T E R S 13 APRIL 1998 High Power Interferometric Phase Measurement Limited by Quantum Noise and Application to Detection of Gravitational Waves P. Fritschel, G. González,* B. Lantz, P. Saha,† and M. Zucker
Shot noise in gravitational-wave detectors with Fabry–Perot arms Torrey T. Lyons, Martin W. Regehr, and Frederick J. Raab 20 December 2000 Vol. 39, No. 36 APPLIED OPTICS
Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors Alessandra Buonanno and Yanbei Chen PHYSICAL REVIEW D, VOLUME 64, 042006
Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO) Peter Fritschel SPIE ProceedingsLIGO document P020016-00.pdfhttp://www.ligo.caltech.edu/docs/P/P020016-00.pdf