Nergis Mavalvala PAC @ MIT December 2004 Development of Technologies for Sub-Quantum-Noise-Limited Gravitational-wave Interferometers Nergis Mavalvala PAC @ MIT December 2004

Advanced LIGO

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

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

Sub-Quantum Interferometers

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)

Free particle SQL uncorrelated 0.1 MW 1 MW 10 MW

In the presence of correlations Output = Shot + Radiation pressure + Signal Heisenberg uncertainty principle in spectral domain Follows that

How to correlate quadratures? Make noise in each quadrature not independent of each other (Nonlinear) coupling process needed Squeezed states of light and vacuum

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 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 b1 b2 f Squeezing produced by back-action force of fluctuating radiation pressure on mirrors 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

Frequency-dependent coupling constant Couples radiation pressure to mirror motion Newton’s law Cavity pole a b Amplitude  b1 = a1 Phase  b2 = -k a1 + a2 + h Radiation Pressure Shot Noise

“Squeeze angle” describes the quadrature being squeezed Optimal Squeeze Angle “Squeeze angle” describes the quadrature being squeezed If we squeeze a2 shot noise is reduced at high frequencies BUT radiation pressure noise at low frequencies is increased If we could squeeze -k a1+a2 instead could reduce the noise at all frequencies

Sub-quantum-limited interferometer Narrowband Broadband Broadband Squeezed X+ X- Quantum correlations Input squeezing

Frequency-dependent Squeeze Angle Narrowband Broadband Conventional

Squeezing – the ubiquitous fix? All interferometer configurations can benefit from squeezing Radiation pressure noise can be removed from readout in certain cases Shot noise limit only improved by more power (yikes!) or squeezing (eek!) Reduction in shot noise by squeezing can allow for reduction in circulating power (for the same sensitivity) – important for power-handling

Squeezed vacuum Requirements Generation methods Challenges Squeezing at low frequencies (within GW band) Frequency-dependent squeeze angle Increased levels of squeezing Generation methods Non-linear optical media (c(2) and c(3) non-linearites)  crystal-based squeezing Radiation pressure effects in interferometers  ponderomotive squeezing Challenges Frequency-dependence  filter cavities Amplitude filters Squeeze angle rotation filters Low-loss optical systems

Squeezing using nonlinear optical media

Non-linear crystals Optical Parametric Amplification (OPA) Three (or four) wave mixing Pump (532nm) Seed (1064nm)

Optical Parametric Amplification Annihilation operator Amplitude and phase quadrature operators Amplification Violates commutation relation Need to include vacuum state

Optical parametric amplification Need phase sensitive amplification (parametric amplification) Amplify amplitude quadrature by Deamplify phase quadrature by Product of the gains is unity Commutation relations satisfied

Optical Parametric Oscillator

What has MIT group done so far? We are squeezing At high frequencies Evidence of modest levels of squeezing at low freqs. With multiple locking loops Next-generation crystals acquired Testing filter cavities Testing noise couplings Detailed calculations of noise budget Photo-thermal noise not a problem Pump noise coupling being considered

Experiment in NW17-069

Squeezed Vacuum

Low frequency squeezing at ANU ANU group  quant-ph/0405137 ANU group  quant-ph/0405137

PERFORM A SUSPENDED INTERFEROMETER TEST What’s next Most important goal Issues to work out Coupling into interferometer dark port through output mode cleaner etc Error signals for optimum quadrature PERFORM A SUSPENDED INTERFEROMETER TEST

Squeezing using back-action effects

The principle A “tabletop” interferometer to generate squeezed light as an alternative to nonlinear optical media Use radiation pressure as the squeezing mechanism Relies on intrinsic quantum physics of optical field-mechanical oscillator correlations Squeezing produced even when the sensitivity is far worse than the SQL Due to noise suppression a la optical springs

The Ponderomotive Interferometer

High circulating laser power High-finesse cavities Key ingredients High circulating laser power 10 kW High-finesse cavities 15000 Light, low-noise mechanical oscillator mirror 1 gm with 1 Hz resonant frequency Optical spring Detuned arm cavities

Optical Springs Modify test mass dynamics Suppress displacement noise (compared to free mass case) Why not use a mechanical spring? Thermal noise Connect low-frequency mechanical oscillator to (nearly) noiseless optical spring

Detuned cavity for optical spring Positive detuning Detuning increases Cavity becomes longer Power in cavity decreases Radiation-pressure force decreases Mirror ‘restored’ to original position Cavity becomes shorter Power in cavity increases Mirror still ‘restored’ to original position

Assumed experimental parameters

Noise budget

Noise budget – Equivalent displacement

Work so far Detailed simulation of noise couplings Uses first fully quantum mechanical simulation code for a GW interferometer (Corbitt) Used in AdLIGO simulations (Fritschel and Popescu) “Exported” to Hannover and Glasgow (Schnabel and Strain) Location and infrastructure LASTI laser, vacuum envelop and seismic isolation Cavity geometrical parameters Mini-mirror suspensions

High finesse cavity tests What’s next Design completion Suspension Control system High finesse cavity tests Fixed mini-mirror – optical tests Suspended mini-mirror – includes mirror dynamics and radiation-pressure coupling Complete interferometer

High finesse cavities with high laser power Mini-mirror dynamics Risk management High finesse cavities with high laser power Power density on optical surfaces Mini-mirror dynamics Suspension thermal noise Static displacement due to radiation pressure Electrostatic actuation

Why is this interesting/important? First ever demonstration of ponderomotive squeezing Probes quantum mechanics of optical field-mechanical oscillator coupling at 1 g mass scales Test of low noise optical spring Suppression of thermal noise Simulations and techniques useful for AdLIGO and other GW interferometers Michelson detuning Role of feedback control in these quantum systems

Resources

People Stan Whitcomb (Co-I) sage-at-large Dave Ottaway (Co-I) optics, suspension Eugeniy Mikhailov crystal squeezing Keisuke Goda (G) crystal squeezing Thomas Corbitt (G) ponderomotive interferometer Chris Wipf (G) crystal squeezing Gregg Harry suspensions, thermal noise Rai Weiss es actuator, electronics Si-Hui Tan (G) suspension design Marat Freytsis (UG) CO2 welding for suspension Caryn Bullard (UG) homodyne detection

Time Line Crystal squeezing Ponderomotive ifo Complete design for an interferometer test, including control system (2Q2005) Build and test at MIT (4Q2005) Integrate into (e.g.) 40m prototype (2Q2006) Sub-QNL (4Q2006) Go graduates Ponderomotive ifo Mini-suspension design (1Q2005) High finesse cavity optical test (2Q2005) High finesse cavity dynamics test (4Q2005) Full interferometer (2Q2006) Low noise (2Q2007) Thomas graduates

Acknowledgments Space Optics labs for crystal squeezing experiment LASTI laser, vacuum envelop and seismic isolation for ponderomotive interferometer LIGO lab personnel (MechE, ElecE, scientists) and equipment resources Support MIT seed money NSF exploratory grant Graduate fellowships ANU crystals Close collaborations ANU and Hannover (crystal squeezing) Integration with 40m program for suspended interferometer test AEI/Caltech/Maryland (theory)

In conclusion...

Time is ripe to develop squeezing techniques for GW interferometers Next generation interferometers likely to be almost entirely quantum noise limited Time is ripe to develop squeezing techniques for GW interferometers Nonlinear optical media Back-action induced correlations Other Quantum Non-Demolition techniques Program well-integrated with LIGO Laboratory in mission and execution

Budget OPO suspended interferometer test Personnel Travel 3 p-y post-doc 5 p-y grad student Travel International $10k/yr Domestic $10k/yr + $15k for OPO suspended interferometer test OPO suspended interferometer test $50k for optical bench $15k for control electronics Ponderomotive ifo $30k for core optics $40k for auxiliary optics and optoelectronics $20k for vacuum prep and custom tooling $80k for digital sensing and controls electronics

Signal-recycled Interferometer ℓ Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM 800 kW 125 W Reflects GW photons back into interferometer to accrue more phase Signal Recycling signal

Advance LIGO Sensitivity: Improved and Tunable broadband detuned narrowband SQL  Heisenberg microscope analog If photon measures TM’s position too well, it’s own angular momentum will become uncertain. thermal noise

Thermal Noise in Springs Why not use a mechanical spring? Displacements due to thermal noise introduced by the high frequency (mechanical) spring will wash out the effects of squeezing An optical spring with a high resonant frequency will not change the thermal force spectrum of the mechanical pendulum Use a low resonant frequency mechanical pendulum to minimize thermal noise Use an optical spring to produce a flat response out to higher frequencies