Path to Sub-Quantum-NoiseLimited Gravitational-wave Interferometry MIT Corbitt, Goda,
Path to Sub-Quantum-NoiseLimited Gravitational-wave Interferometry MIT Corbitt, Goda, Innerhofer, Mikhailov, Ottaway, Wipf Caltech Australian National University Universitat Hannover/AEI LIGO Scientific Collaboration TeV Particle Astrophysics August 2006 Outline
The quantum noise limit in GW ifos Sub-quantum noise limited ifos Injecting squeezed vacuum Setting requirements the wishlist Generating squeezed states Nonlinear optical media crystal Radiation pressure coupling ponderomotive Recent progress and present status Optical Noise Shot Noise Uncertainty in number of photons
h( detected Higher circulating power Pbs low optical losses Frequency dependence light (GW signal) storage time in the interferometer f) 1 Pbs Radiation Pressure Noise Photons impart momentum to cavity mirrors
Fluctuations in number of photons Lower power, Pbs Frequency dependence h( f ) response of mass to forces Optimal input power depends on frequency Pbs 2 4 M f Initial LIGO Input laser
power ~6W Circulating power ~ 20 kW Mirror mass 10 kg A Quantum Limited Interferometer Input laser power > 100 W
Q ua n tu m LIGO I Circulating power > 0.5 MW n si o
en sp l Su rma the ic Seism Mirror mass 40 kg Ad LIGO Tes
t ther mass m al Some quantum states of light Heisenberg Uncertainty Principle for EM field X X 1
Associated with amplitude and phase Phasor diagram analogy Stick dc term Ball fluctuations Common states Coherent state Vacuum state
Amplitude squeezed state Phase squeezed state McKenzie Squeezed input vacuum state in Michelson Interferometer Consider GW signal in the phase quadrature Not true for all interferometer configurations Detuned signal recycled interferometer GW signal in both
quadratures Laser X X++ X X+ Orient squeezed state to reduce noise in phase quadrature
Squeezed vacuum states for GW detectors Requirements Squeezing at low frequencies (within GW band) Frequency-dependent squeeze angle Increased levels of squeezing Long-term stable operation
Generation methods Non-linear optical media ((2) and (3) non-linearites) crystal-based squeezing Radiation pressure effects in interferometers ponderomotive squeezing How to make a squeezed state? Correlate the amplitude and phase quadratures Correlations noise reduction How to correlate quadratures? Make noise in each quadrature not independent of the other (Nonlinear) coupling process needed
For example, an intensity-dependent refractive index couples amplitude and phase 2 n( I ) z 0 Squeezed states of light and vacuum Squeezing using nonlinear optical media
Optical Parametric Oscillator SHG H i a a b a a b Squeezed Vacuum Low frequency squeezing at ANU
McKenzie et al.,quant-ph/0405137 PRL 93, 161105 (2004) ANU group Injection in a power recycled Michelson interferometer K.McKenzie et al. Phys. Rev. Lett., 88 231102 (2002) Injection in a signal recycled interferometer
Vahlbruch et al. Phys. Rev. Lett., 95 211102 (2005) Squeezing using radiation pressure coupling The principle Use radiation pressure as the squeezing mechanism Consider an optical cavity with high stored power and a phase sensitive readout Intensity fluctuations (radiation pressure) drive the motion of the cavity mirrors Mirror motion is then imprinted onto the phase of the light
Analogy with nonlinear optical media Intensity-dependent refractive index changes couple amplitude and phase 2 n( I ) z 0 The ponderomotive interferometer Key ingredients Low mass, low noise mechanical oscillator
mirror 1 gm with 1 Hz resonant frequency High circulating power 10 kW High finesse cavities 15000 Differential measurement common-mode rejection to cancel classical noise Optical spring noise suppression and frequency independent squeezing
Noise budget Noise suppression Displacement / Force 5 kHz K = 2 x 106 N/m Cavity optical mode diamond rod Frequency Conclusions
Advanced LIGO is expected to reach the quantum noise limit in most of the band QND techniques needed to do better Squeezed states of the EM field appears to be the most promising approach Crystal squeezing mature 3 to 4 dB available in f>100 Hz band Ponderomotive squeezing getting closer Factors of 2 to 5 improvements foreseeable in the next decade Not fundamental but technical
Need to push on this to be ready for future instruments The End
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