Quantum mechanics on giant scales

Nergis MavalvalaMIT, September 2008

Gravitational wavedetectors

Quantum nature of light

Quantum states of mirrors

Outline

Quantum limit for gravitational wave detectorsOrigins of the quantum limit

Vacuum fluctuations Interactions of light with mirrors

Quantum states of light Squeezed state injection and generation

Quantum states of the mirrorsObserving quantum effects in macroscopic objects Burgeoning field of macroscopic quantum measurement

Gravitational Waves “Ripples in space-time”Stretch and squeeze the space transverse to direction of propagation

Basics of GW Detection

Lh LΔ=

GW from space

Laser

Photodetector

Laser

Photodetector

Want very large L

21

1810 4000

~ 10 meters

GWL h L−

−

Δ == ×

Mirrors hang as pendulums• Quasi-free particles

Optical cavities• Mirrors facing each other • Builds up light power

/h L L

GW detector at a glance

= Δ

Lots of laser power P• Signal μ P• Noise μ

10 W

20 kW

P

Quantum noise in Initial LIGO

Shot noisePhoton counting statistics

Radiation pressure noiseFluctuating photon number exerts a fluctuating force

The Standard Quantum Limit

Advanced LIGO Quantum noise everywhere

Origin of the Quantum NoiseVacuum fluctuations

Quantum states of light

Heisenberg Uncertainty Principle

Coherent state (laser light)Squeezed state

Two complementary observablesMake on noise better for one quantity, BUT it gets worse for the other X1

X2

X1 and X2 associated with amplitude and

phase

Quantum Noise in an Interferometer

X1

X2

X1

X2

Laser

X1

X2

Caves, Phys. Rev. D (1981)Slusher et al., Phys. Rev. Lett. (1985)Xiao et al., Phys. Rev. Lett. (1987)McKenzie et al., Phys. Rev. Lett. (2002)Vahlbruch et al., Phys. Rev. Lett. (2005)

X1

X2

Shot noise limited μ(number of photons)1/2

Vacuum fluctuations Squeezed vacuum

Arbitrarily below shot noise

Quantum EnhancementSqueezed state injection

How to squeeze?

My favorite wayA tight hug

How to squeeze?

But with photons…Need to simultaneously amplify one quadrature and de-ampilify the other

Create correlations between the quadraturesSimple idea nonlinear optical material where refractive index depends on intensity of light illumination

Squeezing injection in Advanced LIGO

Laser

SqueezeSource

Prototype GW detector

GW Signal

HomodyneDetector

Faraday isolatorSHG

OPO

Quantum enhancement

K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K.McKenzie, R. Ward,S. Vass, A. J. Weinstein, and N. Mavalvala, Nature Physics 4, 472 (2008)

2.9 dB or 1.4x

Squeezing injection in Advanced LIGO

Laser

SqueezeSource

GWDetector

GW Signal

HomodyneDetector

Faraday isolatorSHG

OPO

Advanced LIGO with squeeze injection

Radiation pressure

Shot noise

Radiation pressureThe other side of the quantum optical coin

Radiation pressure rules!Experiments in which radiation pressure forces dominate over mechanical forces

Study radiation pressure effects on large masses to inform future GW detectors

Major spin-offs – opportunity to study quantum effects in macroscopic systems

Observation of quantum radiation pressureGeneration of squeezed states of lightQuantum state of the gram-scale mirrorEntanglement of mirror and light quantum states

Classical light-oscillator coupling effects en routeOptical cooling and trappingLight is stiffer than diamond

Quantum mechanics of macroscopic oscillators

Quantum control of light and matter noise reduction techniques

Precision measurements of forces and displacements

Explore the quantum-classical boundaryGround state cooling

Direct observation of quantum effectsSuperpositionsEntanglementDecoherence

Quantum backaction evading measurements

A radiation pressure dominated interferometer

Key ingredientsTwo identical cavities with 1 gram mirrors at the endsHigh circulating laser powerCommon-mode rejection cancels out laser noiseOptical spring effect to suppress external force (thermal) noise

lasersource

end mirror (1 gm)

BS

input mirror (250 gm)

squeezed light (vacuum)

1 W

10 kW

The optical spring effect and optical trapping of mirrors

Reaching the quantum limit in mechanical oscillators

The goal is to measure non-classical effects with large objects like the (kilo)gram-scale mirrorsThe main challenge thermally driven mechanical fluctuationsNeed to freeze out thermal fluctuationsZero-point fluctuations remainOne measure of quantumness is the thermal occupation number

Want N 1

Colder oscillator

B eff

eff

k TN =

ΩhStiffer oscillator

Mechanical vs. optical forcesMechanical forces

thermal noiseStiffer spring (Ωm ↑) larger thermal noiseMore damping (Qm ↓) larger thermal noise

Optical forces do not affect thermal noise spectrum

4 mF Bm

S k TQΩ

∝

Connect a high Q, low stiffness mechanical oscillator to a stiff optical spring DILUTION

True for any non-mechanical force ( non-dissipative or “cold” force),

e.g. gravitation, electronic, magnetic

How to make an optical spring?

Detune a resonant cavity to higher frequency (blueshift)

Change in cavity mirror position changes intracavity powerChange in radiation-pressure exerts a restoring force on mirrorTime delay in cavity response introduces a viscous anti-damping force

Px

Optical springs and damping

Detune a resonant cavity to higher frequency (blueshift)Real component of optical force

restoringBut imaginary component (cavity time delay)

anti-dampingUnstableStabilize with feedback

Restoring

Damping

Anti-damping

Anti-restoring

Cavity cooling

Observable quantum effects

Radiation pressureAnother way to squeeze…

Create correlations between light quadratures using a movable mirrorAmplitude fluctuations of light impart fluctuating momentum to the mirrorMirror displacement is imprinted on the phase of the light reflected from it

Radiation pressureAnother way to squeeze…

Create correlations between light quadratures using a movable mirrorAmplitude fluctuations of light impart fluctuating momentum to the mirrorMirror displacement is imprinted on the phase of the light reflected from it

Squeezing

T. Corbitt, Y. Chen, F. Khalili, D.Ottaway, S.Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev A 73, 023801 (2006)

7 dB or 2.25x

Squeezing

Entanglement

Correlate two optical fields by coupling to mechanical oscillatorQuantum state of each light field not separable (determined by measuring density matrix)Quantify the degree of non-separability using logarithmic negativity

Entanglement

C. Wipf, T. Corbitt, Y. Chen, and N. Mavalvala, New J. Phys./283659 (2008)

Classical ExperimentsExtreme optical stiffness

Stable optical trap Optically cooled mirror

Experimental layout

5 W

10%

90%

1 m

Experimental Platform

10 W, frequency and intensity stabilized laser

Vacuum chamber

External vibrationisolation

Seismically isolated optical table

Mechanical oscillator

Coil/magnet pairs for actuation(x5)

Optical fibers

1 grammirror

Extreme optical stiffnessHow stiff is it?

100 kg person Fgrav ~ 1,000 N x = F / k = 0.5 mm

Very stiff, but also very easy to break

Maximum force it can withstand is only ~ 100 μN or ~1% of the gravitational force on the 1 gm mirror

Replace the optical mode with a cylindrical beam of same radius (0.7mm) and length (0.92 m) Young's modulus E = KL/A

Cavity mode 1.2 TPaCompare to

Steel ~0.16 TpaDiamond ~1 TPaSingle walled carbon nanotube ~1 TPa (fuzzy)

Dis

plac

emen

t /

Forc

e

5 kHz K = 2 x 106 N/mCavity optical mode diamond rod

Frequency (Hz)

Phase increases unstable

Double optical spring stable optical trap

Two optical beams double optical springCarrier detuned to give restoring forceSubcarrier detuned to other side of resonance to give damping force with Pc/Psc = 20Independently control spring constant and damping

T. Corbitt et al., Phys. Rev. Lett 98, 150802 (2007)

Stable!

Supercold mirrors Toward observing mirror quantum states

Optical cooling with double optical spring(all-optical trap for 1 gm mirror)

Increasing subcarrierdetuning

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf and N. Mavalvala, Phys. Rev. Lett 98, 150802 (2007)

Optical spring with active feedback cooling

Experimental improvementsReduce mechanical resonance frequency (from 172 Hz to 13 Hz)Reduce frequency noise by shortening cavity (from 1m to 0.1 m)Electronic feedback cooling instead of all opticalCooling factor = 43000

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, 160801 (2007)

Teff = 6.9 mKN = 105

Present status

lasersource

end mirror (1 gm)

BS

input mirror (250 gm)

squeezed light (vacuum)

1 W

10 kW

Even bigger mirror, even cooler

Meanwhile, Initial LIGO detectors much more sensitive operate at 10x above the standard quantum limitBut these interferometers don’t have strong radiation pressure effects no optical spring or dampingIntroduce a different kind of cold spring use electronic feedback to generate both restoring and damping forces

Cold damping ↔ cavity coolingServo spring ↔ optical spring cooling

Quantum measurement in Initial LIGO

Cooling the kilogram scale mirrors of Initial LIGO

LIGO Scientific Collaboration

Teff = 1.4 μKN = 234T0/Teff = 2 x 108

Mr ~ 2.7 kg ~ 1026 atomsΩosc = 2 π x 0.7 Hz

Some other cool oscillatorsNEMS

10−12 g

SiN3 membrane 10−8 g

Toroidal microcavity10−11 g

Micromirrors10−7 g

Minimirror 1 g

LIGO 103 g

AFM cantilevers10−8 g

Cavity cooling

200x

1012x

Closing remarks

In conclusion

MIT experiments in the extreme radiation pressure dominated regime have yielded several important classical results

Extreme optical stiffness few MegaNewton/mStiff and stable optical spring optical trapping of mirrors Optical cooling of 1 gram mirror few milliKelvin

Established path toward quantum regime where we expect to observe radiation pressure induced squeezed light, entanglement and quantum states of very macroscopic objects

In conclusion

Initial LIGO completed a scientific data taking run at design sensitivity in 2007An intermediate-scale upgrade – Enhanced LIGO – is currently being commissionedAdvanced LIGO is funded and commissioning is expected to start in 2011Quantum noise is a significant limitation in these detectorsApplication of quantum optics techniques to improve LIGO detector sensitivity

Squeezed state generation and injection is a mature technique and poised to be deployed in the LIGO detectors in the near future

In conclusion

LIGO detectors operate close to the standard quantum limit

An excellent testbed for observing quantum behavior in macroscopic objects Feedback cooling in Initial LIGO interferometers achieved occupation number N ~ 200Present upgrade (Enhanced LIGO, 2010) should have N ~ 50Advanced LIGO (2015) should operate at the Standard Quantum Limit and lead to N ~1

Will also detect gravitational waves

And now for the most important part…

Cast of characters

MITTimothy BodiyaThomas CorbittSheila Dwyer Keisuke GodaNicolas SmithChristopher WipfEugeniy MikhailovEdith InnerhoferDavid OttawaySarah AckleyJason PelcMIT LIGO Lab

CollaboratorsYanbei ChenCaltech MQM groupStan WhitcombDaniel SiggRolf BorkAlex IvanovJay HeefnerCaltech 40m LabKirk McKenzieDavid McClellandPing Koy LamHelge Müller-EbhardtHenning Rehbein

Thanks to…

Our colleagues atLIGO LaboratoryThe LIGO Scientific Collaboration

Funding fromSloan FoundationMITNational Science Foundation

The End

Cooling

MassTeff

EnvironmentT0

Γ = damping rateΩ = resonant frequency

Γ0Ω0

Gravitational, optical, electronic, magnetic...T1(>Γ0 )

(Teff – T0) Γ0 + (Teff – T1)Γ1 = 0

Teff = (T1Γ1 + T0 Γ0) / (Γ0 + Γ1)

Teff ≈ T0 Γ0/ Γ1Cooling factor limited by Ω0 / Γ0

Dilution

MassTeff

EnvironmentT0

Γ = damping rateΩ = resonant frequency

Γ0Ω0

Gravitational, optical, electronic, magnetic...T1(>Ω0)

Use second spring to stiffen and cool system

Cooling factor limited by Ω1 / Γ0

Maximize Ω1Minimize Ω0 , Γ0

A note about calibration

Mirror +

Controller

+Force noise

Sensor noise

What we measure

What we want to measure

For each frequency band, we assume the worst case scenario for force or sensor noise in order to estimate the real mirror motion

Mirror Position

Servo spring

Measurement performed at LIGO Hanford ObservatoryController comprised a restoring force and a variable damping forceChoose 150 Hz as most sensitive measurement bandMeasure response of servo spring for various damping gainsDeviations from perfect spring due to various filters for low frequency gain and high frequency cutoffs

Opening remark

Quantum noise in gravitational wave interferometersQuantum behavior of macroscopic objects (“giants”)Quantum states of light

…

Nat

ure

446

(Apr

il 20

07)

Initial LIGO Quantumness

SQL

1.4 μK

Quantum radiation pressure effects

Squeezing

Entanglement

Mirror-light entanglement Squeezed vacuum generation

Wipf et al. (2007)

Classical radiation pressure effects

Stable OS

Stiffer than diamond 6.9 mK

Radiation pressure dynamics Optical cooling

5 W

10%

90%~0.1 to 1 mCorbitt et al. (2007)

Ground state cooling

At room temperature

With optical trapping

eff m

12

2 1 Hz

6 10N

πΩ = Ω = ×

= ×

eff

8

2 1 kHz

5 10 K 1T N

π−

Ω = ×

= × ⇒ =

Quantum mechanics on giant scalesOutlineBasics of GW DetectionQuantum noise in Initial LIGOThe Standard Quantum LimitAdvanced LIGO �Quantum noise everywhereOrigin of the Quantum Noise�Vacuum fluctuationsQuantum states of lightQuantum Noise in an InterferometerQuantum Enhancement�Squeezed state injectionHow to squeeze?How to squeeze?Squeezing injection in Advanced LIGOQuantum enhancementSqueezing injection in Advanced LIGOAdvanced LIGO with squeeze injectionRadiation pressureRadiation pressure rules!Quantum mechanics �of macroscopic oscillatorsA radiation pressure dominated interferometerThe optical spring effect and optical trapping of mirrorsReaching the quantum limit �in mechanical oscillatorsMechanical vs. optical forcesHow to make an optical spring?Optical springs and dampingObservable quantum effectsRadiation pressure�Another way to squeeze…Radiation pressure�Another way to squeeze…SqueezingEntanglementClassical ExperimentsExperimental layoutExperimental PlatformMechanical oscillatorExtreme optical stiffnessDouble optical spring stable optical trapSupercold mirrors �Toward observing mirror quantum statesOptical cooling with double optical spring�(all-optical trap for 1 gm mirror)Optical spring with �active feedback coolingPresent statusEven bigger mirror, even coolerQuantum measurement in Initial LIGOCooling the kilogram scale mirrors of Initial LIGOSome other cool oscillatorsCavity coolingClosing remarksIn conclusionIn conclusionIn conclusionAnd now for the most important part…Cast of charactersThanks to…The EndCoolingDilutionA note about calibrationServo springOpening remarkInitial LIGO QuantumnessQuantum radiation pressure effectsClassical radiation pressure effectsGround state cooling