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Gravitational Wave Astronomy Dr. Giles Hammond Institute for Gravitational Research SUPA, University of Glasgow Universität Jena, August 2010

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Thermal Noise ( 100Hz) The impedance then becomes or and the displacement noise is The shape of the thermal noise spectrum depends on the type of damping (external velocity) or friction (internal).

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Thermal Noise ( 100Hz) For viscous damping proportional to velocity For internal friction a good assumption is that is independent of The RMS equals and is consistent with equipartition theory viscous Blue: viscous Green: constant

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Thermal Noise ( 100Hz) As loss decreases (or quality factor Q increases) more energy is pushed into the resonance. Gravitational wave detectors utilise this effect to operate between the modes of the suspension (low f ) and test mass (high f ) viscous Use low loss materials => low noise off resonance

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Dilution Thermal noise seen in suspension wires, test mass coatings and test mass materials => lower loss gives lower thermal noise In suspensions some of the pendulum energy is stored in gravity Gravity is lossless while elasticity is lossy (damping) and these effects lead to dilution (D) Storing more energy in gravity requires thin suspension fibres. Typically operate fibres close (within factor 4) to their yield stress

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Thermoelastic Noise Bending of materials (suspension fibres/coatings/test mass) creates a temperature gradient due to thermal expansion coefficient ( ) Heat flows across the temperature gradient and leads to Thermoelastic dissipation The “linear” Thermoelastic loss term is is characteristic time for heat to flow across sample Loaded suspension fibres also have a term due to the Young’s modulus variation with temperature (Y ). We will discuss this later!!!! “Non-linear” thermoelastic loss

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Quantum noise ( 100Hz) Quantum noise is comprised of photon shot noise at high frequencies and photon radiation pressure noise at low frequencies. The photons in a laser beam are not equally distributed, but follow a Poisson statistic. The number N; photon shot noise photon radiation pressure noise wavelength optical power Arm length Mirror mass

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Standard Quantum Limit (SQL) While shot noise contribution decreases with optical power, radiation pressure level increases: The SQL is the minimal sum of shot noise and radiation pressure noise. Advanced detectors will be quantum limited over most their frequency range (apart from thermal noise)

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Interferometry Fringe output of a simple Michelson interferometer Want to operate at point 1 where sensitivity maximum but this also is very sensitive to intensity fluctuations in the laser GW interferometers operate at point 2 or “the dark fringe” (better to look for small signal on small background)

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Interferometry Optical systems are described in terms of input/output scattering matrices Beamsplitters and mirrors are described by the matrix and result in a phase shift of the light (careful with sign at the beamsplitter). At the detector: or LyLy LxLx

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Interferometry Defining: or The output intensity is: LyLy LxLx

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Interferometry GW interferometers utilise lock-in techniques around the dark fringe Modulate light with EOM (Electro-Optic Modulator): n varies with E-field

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Interferometry The EOM applies sidebands onto the carrier light (typically few MHz) From Gradshteyn and Ryzhik's Table of Integrals, Series, and Products The above assumes that the modulation depth is small or that m<1

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Interferometry The EOM applies sidebands onto the carrier light (typically few MHz) The above assumes that the modulation depth is small or that m<1 carrier + sidebands

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Interferometry The EOM applies sidebands onto the carrier light (typically few MHz) The above assumes that the modulation depth is small or that m<1 carrier + sidebands To 1 st order:

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