Post on 10-Oct-2020
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