Quantum effects in Gravitational-wave Interferometers Nergis Mavalvala LIGO Laboratory Quantum Measurement Group September 2004

Quantum Noise in Optical Measurements Measurement process Interaction of light with test mass Counting signal photons with a photodetector Noise in measurement process Poissonian statistics of force on test mass due to photons  radiation pressure noise (RPN) (amplitude fluctuations) Poissonian statistics of counting the photons  shot noise (SN) (phase fluctuations)

Limiting Noise Sources: Optical Noise Shot Noise Uncertainty in number of photons detected a Higher circulating power Pbs a low optical losses Frequency dependence a light (GW signal) storage time in the interferometer Radiation Pressure Noise Photons impart momentum to cavity mirrors Fluctuations in number of photons a Lower power, Pbs Frequency dependence a response of mass to forces Shot noise: Laser light is Poisson distributed  sigma_N = sqrt(N) dE dt >= hbar  d(N hbar omega) >= hbar  dN dphi >= 1 Radiation Pressure noise: Pressure fluctuations are anti-correlated between cavities  Optimal input power depends on frequency

Initial LIGO

Advanced LIGO A Quantum Limited Interferometer LIGO I Ad LIGO Seismic Suspension thermal Test mass thermal Quantum

Sub-Quantum Interferometers Generation 2

Some quantum states of light Analogous to the phasor diagram 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 GW signal in the phase quadrature Not true for all interferometer configurations Detuned signal recycled interferometer  GW signal in both quadratures Orient squeezed state to reduce noise in phase quadrature X+ X- X+ X- X+ X-

Back Action Produces Squeezing f Squeezing produced by back-action force of fluctuating radiation pressure on mirrors b a Vacuum state enters anti-symmetric port Amplitude fluctuations of input state drive mirror position Mirror motion imposes those amplitude fluctuations onto phase of output field a1 a2 “In” mode at omega_0 +/- Omega  |in> = exp(+/- 2*j* beta) S(r, phi) |out> Heisenberg Picture: state does not evolve, only operators do. So |out> vacuum state is squeezed by factor sinh(r) = kappa/2 and angle phi = 0.5 arcot(kappa/2). Spectral densities assuming input vacuum state: S_b1 = exp(-2 r) ~ 1/kappa when kappa >> 1 S_b2 = exp(+2 r) ~ kappa S_{b1 b2} = 0

Sub-quantum-limited Advanced LIGO X+ X- Quantum correlations (Buonanno and Chen) Input squeezing

Squeezed state generation with nonlinear optical media

Vacuum seeded OPO ANU group  quant-ph/0405137

Key ingredients Media with high nonlinearity Quadrature-sensitive locking techniques Optically pure states Low losses

Squeezing using back-action effects

“Ponderomotive” Experiment A “tabletop” interferometer to generate squeezed light Use radiation pressure as the squeezing mechanism Alternative to crystal-based squeezing Test quantum-limited radiation pressure effects Gain confidence that the modeling is correct Expected noise sources do not prohibit squeezing Test noise cancellations via Michelson detuning Useful for all interferometers Squeezing produced even when the sensitivity is far worse than the Standard Quantum Limit Due to the optical spring Study intrinsic quantum physics of optical field --mechanical oscillator correlations

High circulating laser power High-finesse cavities Key ingredients High circulating laser power 10 kW High-finesse cavities 25000 Light, low-noise mechanical oscillator mirror 1 gm with 1 Hz resonant frequency Optical spring Detuned arm cavities

Ponderomotive squeezing

Noise budget