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Shot noise in GW detectors. G González. bright. l /2. Power (ASDC). L- d L. L+ d L. dark. x. i d L ?. The dark fringe. P=P 0 sin 2 ( w t+k d l) = (P 0 /2) (1+sin (2 w t+2k d l)): insensitive to d l . If we phase-modulate the light:.

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## Shot noise in GW detectors

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**Shot noise in GW detectors**G González**bright**l/2 Power (ASDC) L-dL L+dL dark x i dL ? The dark fringe P=P0 sin2 (wt+kdl) = (P0/2) (1+sin (2wt+2kdl)): insensitive to dl If we phase-modulate the light: For wm=25 MHz (lm=12 m), sidebands have wwm=w0(1 1.4 10 -8). • 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(kdL)sin(kmDL)sin(wmt) + …(2wm t) • Then, “demodulate” : multiply by sin(wmt) or cos(wmt) to produce I and Q phases**Michelson interferometer**Shot noise at output : white noise with psd: Output signal: bright l/2 Power (ASDC) dark x**(green) PNI experiment**PRL, 80, p8131, 1998 Lossless, mid fringe: Lossless, demodulated at dark fringe: Lossy, demodulated at dark fringe:**L1 “noise budget”**~4x/ ~1e-12 rad/rtHz**Shot noise and radiation pressure**Standard quantum limit:**Advanced LIGO**Advanced LIGO: signal recycling**Beyond SQL**ALESSANDRA BUONANNO AND YANBEI CHEN PHYSICAL REVIEW D64042006**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 Proceedings LIGO document P020016-00.pdf http://www.ligo.caltech.edu/docs/P/P020016-00.pdf

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