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Imagining the Future. What can we do about the Quantum Noise Limit in Gravitational-wave Detectors?. Nergis Mavalvala Penn State October 2004. Quantum Noise in Optical Measurements. Measurement process Interaction of light with test mass Counting signal photons with a photodetector

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imagining the future

Imagining the Future

What can we do about the Quantum Noise Limit in Gravitational-wave Detectors?

Nergis MavalvalaPenn StateOctober 2004

quantum noise in optical measurements
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
Limiting Noise Sources: Optical Noise
  • Shot Noise
    • Uncertainty in number of photons detected a
    • Higher circulating power Pbsa low optical losses
    • Frequency dependence a light (GW signal) storage time in the interferometer
  • Radiation Pressure Noise
    • Photons impart momentum to cavity mirrorsFluctuations in number of photons a
    • Lower power, Pbs
    • Frequency dependence a response of mass to forces

 Optimal input power depends on frequency

in the presence of correlations
In the presence of correlations
  • Heisenberg uncertainty principle in spectral domain
  • Follows that
a quantum limited interferometer




Test mass thermal

Suspension thermal


A Quantum Limited Interferometer
how will we get there
How will we get there?
  • Seismic noise
    • Active isolation system
    • Mirrors suspended as fourth (!!) stage of quadruple pendulums
  • Thermal noise
    • Suspension  fused quartz; ribbons
    • Test mass  higher mechanical Q material, e.g. sapphire; more massive (40 kg)
  • Optical noise
    • Input laser power  increase to ~200 W
    • Optimize interferometer response signal recycling
signal recycled interferometer

Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM

Reflects GW photons back into interferometer to accrue more phase


Signal-recycled Interferometer

800 kW

125 W


advanced ligo sensitivity improved and tunable
Advanced LIGO SensitivityImproved and Tunable



thermal noise

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









Squeezed input vacuum state in Michelson Interferometer
back action produces squeezing

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







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
conventional interferometer with arm cavities

Coupling coefficient k converts Da1 to Db2

  • k and squeeze angle f depends on I0, fcav, losses, f



Conventional Interferometer with Arm Cavities

Amplitude  b1 = a1

Phase  b2 = -k a1 + a2 + h

Radiation Pressure

Shot Noise

optimal squeeze angle
Optimal Squeeze Angle
  • 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
  • “Squeeze angle” describes the quadrature being squeezed
realizing a frequency dependent squeeze angle
Realizing a frequency-dependent squeeze angle

filter cavities

  • Filter cavities
  • Difficulties
    • Low losses
    • Highly detuned
    • Multiple cavities
  • Conventional interferometers 
    • Kimble, Levin, Matsko, Thorne, and Vyatchanin, Phys. Rev. D 65, 022002 (2001).
  • Signal tuned interferometers 
    • Harms, Chen, Chelkowski, Franzen, Vahlbruch, Danzmann, and Schnabel, gr-qc/0303066 (2003).
squeezing the ubiquitous fix
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
sub quantum limited interferometer



Sub-quantum-limited interferometer

Quantum correlations(Buonanno and Chen)

Input squeezing

squeezed vacuum
Squeezed vacuum
  • Requirements
    • 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 (recent progress at ANU and MIT)
    • Radiation pressure effects in interferometers  ponderomotive squeezing (in design & construction phase)
  • Challenges
    • Frequency-dependence  filter cavities
      • Amplitude filters
      • Squeeze angle rotation filters
    • Low-loss optical systems
vacuum seeded opo
Vacuum seeded OPO

ANU group  quant-ph/0405137

the principle
The principle
  • A “tabletop” interferometer to generate squeezed light as an alternative 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
key ingredients
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
optical springs
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
speed meters30
Speed meters
  • Principle  weakly coupled oscillators
  • Energy sloshes between the oscillators
  • p phase shift after one slosh cycle
  • Driving one oscillator excites the other
implementation of a speed meter

homodyne detection

Implementation of a speed meter
  • Position signal from arm cavity enters “sloshing” cavity
  • Exits “sloshing” cavity with p phase shift
  • Re-enters arm cavity and cancels position signal
  • Remaining signal  relative velocity of test masses

sloshing cavity

Purdue and Chen, Phys. Rev. D66, 122004 (2002)

intra cavity readouts33
Intra-cavity readouts
  • Non-classical states of light exist inside cavities (ponderomotive squeezing)
  • Probe those intra-cavity squeezed fields

Braginsky et al., Phys. Lett. A255, (1999)

optical bars and optical levers
Optical Bars and Optical Levers
  • Couple a second “probe” mass to the test mass
  • Probe mass does not interact with the strong light field in the cavity
  • Analogous to mechanical lever with advantage in the ratio of unequal lever arms

Braginsky et al., Phys. Lett. A232, (1997)

white light interferometers
White Light Interferometers
  • Broadband antenna response
  • Make cavity longer for longer wavelengths





Guido Muller

all reflective interferometers


All-reflective Interferometers
  • Higher power-handling capability
  • Grating beamsplitters

Peter Byersdorf

technologies needed
Technologies needed
  • Low-noise high-power lasers
    • What wavelength?
  • Low absorption and scatter loss optics
  • Low loss diffraction gratings
  • High non-linearity optical materials
  • High quantum efficiency photodetection
  • Low mechanical loss oscillators
    • With optical spring effect, oooh
Next generation – quantum noise limited
  • Squeezing being pursued on two fronts
    • Nonlinear optical media
    • Back-action induced correlations
  • Other Quantum Non-Demolition techniques
    • Evade measurement back-action by measuring of an observable that does not effect a later measurement
      • Speed meters (Caltech, Moscow, ANU)
      • Optical bars and levers (Moscow)
    • Correlating SN and RPN quadratures
      • Variational readout
  • Power handling
    • All-reflective
    • Quadrature squeezing
imagining the future42

Imagining the Future

What can we do about the Quantum Noise Limit in Gravitational-wave Detectors?