Detection Of High Frequency Gravitational Waves At LIGO

Detection Of High Frequency Gravitational Waves At LIGO W. Butler , A. C. Melissinos University of Rochester 1. 2. 3. 4. 5. Parametric Conversion “Picture” Angle of Incidence of the G. W. Results from H 4 K Sensitivity Possibilities with Advanced LIGO 12/5/2020 LSC Presentation 3/17/03 G 030067 -00 -Z LIGO- 1

PARAMETRIC CONVERSION 1. THE LIGO IFO ADMITS A SPECTRUM OF DISCRETE FREQUENCIES n THE FREQUENCIES ARE EQUALLY SPACED Δ 0 = 2 L/c 0 IS THE FREE SPECTRAL RANGE (fsr) _____ 0 = 37. 52 k. Hz _____ n+1 _____ n-1 WHEN THE IFO IS LOCKED ONLY ONE MODE IS OCCUPIED n = n / 0 1010 THE WIDTH OF THE MODES IS /Q Q = F (2 L / ) 1012 _____ IN THE PRESENCE OF A PERTURBATION AT FREQUENCY THE (n+1) AND (n-1) MODES BECOME POPULATED 12/5/2020 LSC Presentation 3/17/03 G 030067 -00 -Z LIGO- 2

2. EXPECTED SIGNAL En FIELD IN MODE n En 1 FIELD IN MODE n 1 DIMENSIONLESS PERTURBATION FOR En 1 << En t >> Q / AND En 1 = 0. 5 En Q 3. EXAMPLE: END MIRROR (ETM) MOTION x = x 0 cos t = x 0 / L En 1 = En (x 0 / 0) F /[1 + ( / )2] 1/2 = 0 ( / F) 12/5/2020 LSC Presentation 3/17/03 G 030067 -00 -Z LIGO- 3

EFFECT OF A GRAVITATIONAL WAVE • TRANSFER FUNCTION FOR “OPTIMAL INCIDENCE”, = 0 H 1( ) = sinc( ) e-i = 2 L / c = 1 / 0 H 1( ) = 0 • TRANSFER FUNCTION FOR H 1( ) = cos 2 {sinc[ sin ]e-i + sinc[ +sin ] ei } e-i( )(2+sin ) • FOR F-P CAVITY HFP( ) = H 1( ) /[(1 - r 1)2 + 4 r 1 sin 2( /2)]1/2 • AVERAGE OVER ANGLES, POLARIZATION 1/ 5 • SIDEBANDS AT 12/5/2020 LSC Presentation 3/17/03 G 030067 -00 -Z LIGO- 4

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RESULTS FROM H 4 K (2002 -W. BUTLER) 1. SHAKE ITMX (SINGLE ARM) EXTRAPOLATE MIRROR MOTION FROM D. C. CALIBRATION. (FOR 1 V DRIVE) x 0( 0) = x. DC / (1 + ( 0/ p)2) = 8 x 10 -16 m (1) OBSERVE AT A. S. PORT EA CARRIER FIELD ON BS E 2 SIDEBAND FIELD ON BS ERF |EA / E 2| = 4 (x 0 / c) F (2) PHOTODIODE VOLTAGE VA = k |E 2|2 |ERF / E 2| |EA / E 2| 30 |EA / E 2| (V) OBSERVE (FOR 1 V DRIVE) VA = 3 x 10 -5 V |EA / E 2| 10 -6 FIND USING (2) x 0 10 -15 m IN AGREEMENT WITH (1). 12/5/2020 LSC Presentation 3/17/03 G 030067 -00 -Z LIGO- 7

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2. SHAKE ITMX (FULLY RECYCLED IFO) PARAMETRIC RESONANCE MUCH NARROWER GOVERNED BY “DOUBLE CAVITY POLE” cc 0 (1 – r. F*R) r. F*R REFLECTIVITY OF FRONT CAVITY MIRROR WHEN RECYCLING CAVITY ON RESONANCE 3. SENSITIVITY FOR TINT = 100 s OBSERVE VN = 2 x 10 -7 V (S/N 150) FOR TINT = 105 s (1 DAY) EXPECT VN = 0. 6 x 10 -8 V (S/N = 5) x 0 = 10 -18 m x 0 / L = h = 2. 5 x 10 -22 12/5/2020 LSC Presentation 3/17/03 G 030067 -00 -Z LIGO- 9

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LIGO WITH SIGNAL RECYCLING THE “RECYCLING” MIRROR NOW COUPLES THE TWO ARMS (CAVITIES) LASER THE CAVITY MODES SPLIT INTO S = 0 + (c / 2 L)(1/ ) tan{arctan [(1 -r 1)/(1+r 1) cot z/4]} A = 0 - (c / 2 L)(1/ ) tan{arctan [(1 -r 1)/(1+r 1) tan z/4]} z = 2 (2 a / ) 2 a = distance between cavities r 1 = cavity input mirror reflectivity LOCK LASER AT S SIGNAL APPEARS AT A 12/5/2020 LSC Presentation 3/17/03 G 030067 -00 -Z LIGO- 14

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