Overview of quantum noise suppression techniques Helge MllerEbhardt

Overview of quantum noise suppression techniques Helge Müller-Ebhardt, Henning Rehbein, Kentaro Somiya, Roman Schnabel, Karsten Danzmann and Yanbei Chen Max-Planck-Institut für Gravitationsphysik (AEI) Institut für Gravitationsphysik, Leibniz Universität Hannover Helge Müller-Ebhardt ET meeting, 2008, Cascina

Quantum measurement noise = photon shot noise + radiation pressure noise • free mass dynamics • quantum measurement process • no correlation in shot and back-action noise measurement frequency Helge Müller-Ebhardt ET meeting, 2008, Cascina

Quantum measurement noise = photon shot noise + radiation pressure noise • free mass dynamics • quantum measurement process • use correlation in shot and back-action noise measurement frequency Helge Müller-Ebhardt ET meeting, 2008, Cascina

QND techniques scheme benefit balanced homodyne pushes quantum noise detection down to shot noise level variational output pushes quantum noise down to shot noise level frequency band in radiation pressure dominated regime overall frequencies squeezed input reduces quantum noise by overall frequencies the squeezing factor signal recycling increases sensitivity around resonances quantum noise parallel to standard quantum limit in radiation pressure dominated regime transducer increases sensitivity at low frequencies double carrier increases sensitivity at low frequencies and around resonances speed meter Helge Müller-Ebhardt ET meeting, 2008, Cascina

QND techniques balanced homodyne detection at frequency-independent quadrature angle variational output with frequencydependent quadrature angle [Kimble et al, 2001] Helge Müller-Ebhardt ET meeting, 2008, Cascina

QND techniques scheme benefit balanced homodyne pushes quantum noise detection down to shot noise level variational output pushes quantum noise down to shot noise level frequency band in radiation pressure dominated regime overall frequencies squeezed input reduces quantum noise by overall frequencies the squeezing factor signal recycling increases sensitivity around resonances quantum noise parallel to standard quantum limit in radiation pressure dominated regime transducer increases sensitivity at low frequencies double carrier increases sensitivity at low frequencies and around resonances speed meter Helge Müller-Ebhardt ET meeting, 2008, Cascina

QND techniques 10 d. B squeezed input at frequency-independent quadrature angle 10 d. B squeezed input with frequencydependent quadrature angle [Kimble et al, 2001] Helge Müller-Ebhardt ET meeting, 2008, Cascina

QND techniques scheme benefit balanced homodyne pushes quantum noise detection down to shot noise level variational output pushes quantum noise down to shot noise level frequency band in radiation pressure dominated regime overall frequencies squeezed input reduces quantum noise by overall frequencies the squeezing factor signal recycling increases sensitivity around resonances quantum noise parallel to standard quantum limit in radiation pressure dominated regime transducer increases sensitivity at low frequencies double carrier increases sensitivity at low frequencies and around resonances speed meter Helge Müller-Ebhardt ET meeting, 2008, Cascina

[Meers, 1988] Signal-recycled Michelson interferometer signal-recycling mirror at the dark output port → signal becomes amplified due to an increasing interaction time detuned signal-recycling cavity → optical spring produces additional resonance [Buonanno & Chen, 2001 – 2003] Helge Müller-Ebhardt ET meeting, 2008, Cascina

Optical spring effect a cavity which is detuned from the carrier's frequency makes the power inside the cavity dependent on the motion of the mirror Helge Müller-Ebhardt ET meeting, 2008, Cascina

Optical spring effect a cavity which is detuned from the carrier's frequency makes the power inside the cavity dependent on the motion of the mirror ng an tida pi am m d pi ng optical power lags behind the cavity motion → complex spring constant → system becomes unstable possible solution: stable double optical spring Helge Müller-Ebhardt ET meeting, 2008, Cascina

Speed meter idea measure position difference after time delay → measure speed [Braginsky & Khalili, 1990] conserved momentum usually proportional to speed → real QND? no: because the coupling to speed changes conserved momentum [Khalili, 2002] Helge Müller-Ebhardt ET meeting, 2008, Cascina

Speed meter realization two different optical realizations Michelson interferometer [Purdue, 2002] Helge Müller-Ebhardt Sagnac interferometer [Chen, 2003] ET meeting, 2008, Cascina

Optical inertia effect a speed meter which is detuned from the carrier's frequency makes the fluctuating radiation-pressure force dependent on the acceleration of the mirror dynamical mass is modified Helge Müller-Ebhardt ET meeting, 2008, Cascina

Signal-recycled Sagnac interferometer signal-recycling mirror at the dark output port - two optical resonances - degenerated resonance case → speed meter - bandwidth important factor Helge Müller-Ebhardt ET meeting, 2008, Cascina

Signal-recycled Sagnac interferometer optimize quantum noise in vicinity of standard classical noise budget Adv. LIGO-scale parameters fixed - 40 kg mirrors - 4 km arms - 800 k. W power optimization parameters - sr detuning - sr bandwidth - arm cavity bandwidth (250 Hz) → finesse (150) Helge Müller-Ebhardt improves Adv. LIGO by 45 % in the event rate ET meeting, 2008, Cascina

Signal-recycled Sagnac interferometer optimize quantum noise in vicinity of future classical noise budget Adv. LIGO-scale parameters fixed - 40 kg mirrors - 4 km arms - 800 k. W power optimization parameters - sr detuning - sr bandwidth - arm cavity bandwidth (125 Hz) → finesse (300) Helge Müller-Ebhardt improves Michelson by 230 % in the event rate ET meeting, 2008, Cascina

Transducer idea radiation pressure force can transduce motion between front and end mirror of a detuned cavity SQL of a local meter optical bar detector [Braginsky, Gorodetsky & Khalili, 1997] Helge Müller-Ebhardt ET meeting, 2008, Cascina

Position meter transducer rigid optical spring infinite optical inertia zero optical inertia every position meter transducer becomes an optical bar at low frequencies SQL beating narrowband SQL beating Helge Müller-Ebhardt ET meeting, 2008, Cascina

Speed meter transducer zero optical inertia infinite optical inertia speed meter transducer is more flexible at low frequencies Helge Müller-Ebhardt ET meeting, 2008, Cascina

Local readout scheme second carrier senses motion of input mirrors both outputs are optimally filtered Helge Müller-Ebhardt ET meeting, 2008, Cascina