Post on 22-May-2020
Optomechanics for Gravitational Wave Detection
David Blair Australian Interna1onal
Gravita1onal Research Centre University Of Western Australia
Les Houches August 2015
Two fundamental spectrums
150 years ago • 1865 Maxwell
– EM spectrum predicted • 1886 Hertz
– EMW discovered • 1900 Marconi
– First radios • 2015
– Full EM spectrum harnessed
100 years ago • 1915 Einstein
– GW predicted • 1993 Taylor
– Proved to exist • 2017??
– GW discovered • 2115??
– GW spectrum harnessed
Four lectures on electro-‐mechanics
• History of GW Detec1on: impedance matching, sidebands, imminent detec1on
• History of parametric transducers from 30MHz to op1cs.
• Parametric instability: a tool and a problem • Towards thermal noise free optomechanics for noise exceeding the standard quantum limit
Gravita1onal Wave Detec1on, Parametric Transducers and
Optomechanics
• 1960: Weber proposed GW detec1on • 1965 300K bars with piezo transducers • 1969 Weber announced detec1on
• Cryogenic Bars • First Parametric Transducers
– 30MHz • Microwave Parametric Transducers
– 10GHz • Sapphire whispering gallery oscillators to
solve phase noise problem – Sapphire transducers: resolved sideband
parametric transducers • Optomechanics from 40kg tp ng test masses
Weber’s Pioneering Work • Joseph Weber Phys Rev 117, 306,1960 • Gravita1onal wave excita1on of mechanical oscillators • Mass Quadrupole Harmonic Oscillator: Bar, Sphere or Plate
• Designs to date: Bar
Sphere
Torsional Quadrupole Oscillator
Weber’s sugges1ons:
Earth: GW at 10-‐3 Hz.
Piezo crystals: 107 Hz
Al bars: 103 Hz
Detectable flux spectral density: 10-‐7Jm-‐2s-‐1Hz-‐1
( h~ 10-‐22 for 10-‐3 s pulse)
Waves unstopable by mader • Space1me s1ffness ~ c4/8πG
• Enormous energy
• Small amplitude h
• Travel at the speed c
For typical waves the fractional strain amplitude is ~ 10-24
The gravitational wave luminosity of black hole binary coalescence = c5/G =1023 x Lsun !
h =ΔL
L
10-24
10-21
10-18
10-15
1970 1980 1990 2000
h
A
SpaceVoyager
Cassini
LISACertain
LIGO IILIGO I
TAMAlaser
IGEC
certain detection
? ?
? ?
terrestrial stochastic pulsars
quantum foam?superstrings?GUTS?
Progress in Gravita1onal Wave Detec1on 108 fold improvement in energy sensi4vity so far and more to
come!
ESA:2034
A/LIGO 2015
2015 2015
A slide from 2002
Response to Weber 1972
Bar concept 1972
Proposed Cryogenic Detectors
AURIGA
Bar
C
Pump Oscillator
Modulated Output
Persistent Current 1
SQUIDOutput ωa
Two Transducer Concepts Parametric Direct
Signal detected as modula4on sidebands of pump frequency
Cri1cal requirements:
• low pump noise
• low noise amplifier at modula1on frequency
Signal at antenna frequency
Cri1cal requirements:
• low noise SQUID amplifier
• low mechanical loss circuitry
SQUID Transducer concept
First Superconduc1ng Parametric Transducer 1973
Niobium-‐on-‐sapphire RF LC pancake resonator
Nb levitated tube Nb on sapphire sensing surface
1000-‐amp current levitates test mass
Problems
• Sensi1vity limited by pump oscillator phase noise
• RF Q-‐factor strongly power dependent • Failure to understand electromechanical impedance matching.
40 years later: Current Status of GWD
• All cryogenic bars are switched off. • Their legacy can be found in modern opto-‐mechanics
• Laser Interferometers are on the point of first detec1on.
• Opto-‐mechanics is fundamental to current detectors and offers exci1ng solu1ons for the future
Hot EOS: high-mass binary
Animations: Kaehler, Giacomazzo, Rezzolla
1973: What we expected to detect
Central parsec of Milky Way • 1 supermassive black hole
• 20,000 stellar mass black holes
• 50 intermediate mass black holes
• 107 stars • 3-‐body interac1ons • Close binary black holes forming
Bence Kocsis 2013
BH Capture Events create extreme eccentric binaries
Kocsis 2013
PSR 1913+16: prototype gw source
Prototype NS -NS: binary radio pulsar PSR B1913+16
Chirp Waveform
GW emission causes orbital shrinkage leading to higher
GW frequency and amplitude
orbital decay
PSR B1913+16
Weisberg &Taylor 03
Binary Pulsars and Coalescence Event rate Order of magnitude es1mate • 5 observed binary pulsars in Milky Way Correct for beaming factor and luminosity func4on to es4mate total popula4on – many unseen due to wrong beam direc4on or low luminosity. • Total popula1on ~103 per Milky Way galaxy • Life1me to coalescence ~ 108 years • Coalescence rate in Milky Way ~ 1 per 105 years • Number of Milky Way equivalent galaxies to achieve 10 events per year: about 106
• Horizon distance to encompass 106 galaxies ~ 100Mpc • design criterion for Advanced LIGO and Virgo.
Vladimir Braginsky 1975
• Standard quantum limit - Linear amplifier
measurement limit • Quantum non-‐demoli1on - Achievable using phase
sensi1ve amplifiers
History of Laser Interferometer Gravita1onal Wave Detectors
• 1990: Large Interferometers designed to detect known sources at reasonable rate.
• Three stages – 1990s: Proof of principle: 40m – 2000s: LIGO 1: 4km facility, cau1ous design, expected signals: 2 events per 100 years.
– 2015-‐2020: Advanced LIGO: 10 x beder sensi1vity, 1000 x larger volume, expected signals 40 per year
Hoped for
events
Predicted events
Ron Drever, Les Houches 1983
Power recycling
Brian Meers 1988
• Signal Recycling
• Tuned output stage allows greater power build-‐up and significantly improved sensi1vity if combined with improved test masses.
end test mass
beam splitter signal
Laser
input test mass
Very long optical cavities build up light by resonance
Power recycling mirror
Photodetector
Light intensity ~MW can create optical spring stiffer than diamond!
Signal recycling mirror
Gravita1onal Wave Interferometer
Radia1on Pressure and Op1cal Springs
• Detuned optical cavities • Radiation pressure creates
optical spring • Changes the detector
dynamics to enable more GW energy to be absorbed
P= 1MW op1cal power F=2P/c ~ 10mN
P= 100kW op1cal power F=2P/c ~ 1mN
F =Kx K=ΔF/Δx ~10mN/nm = 107N/m = 1000 tonnes/m
Δx = 1nm or much less
Virgo Cascina, Italy
Gravita1onal Wave Detector
Advanced LIGO and the Dawn of Gravitational Astronomy
David ReitzeLIGO Laboratory
California Institute of Technology
for the LSC and Virgo
LIGO-‐G1500451-‐v1 LIGO Hanford Observatory
The Next Detectors for Gravitational Wave Astronomy, Beijing, April-May, 2015
Kilometer-‐scale precision laser interferometers: • 4km x 4km high vacuum • Nanometer precision op?cs • 180W ultrastable CW lasers • Most sensi?ve instrument ever created • Working near quantum limits of precision measurement
Adv LIGO Strain Sensi1vity Early commissioning results Feb 2015
33
10-24
10-23
10-22
10-21
10-20
10-19
Str
ain
(1/
Hz)
102 3 4 5 6 7 8 9
1002 3 4 5 6 7 8 9
10002 3 4 5
Frequency (Hz)
Hanford 4 km S6
Livingston 4 km S6
AdvLIGO Design, ZeroDetuning (High Power)
Preliminary: Calibra1on is uncertain by 20%
D Reitze KITPC, Beijing 2015
Horizon range already 70 Mpc, sufficient to expect detec1on quite soon.
LIGO USA
Range for neutron stars
Ini1al LIGO 50 million light years
Advanced LIGO 600 million light years
One event every 20 years
One event per week
Development of Parametric Transducers
1975 • Braginsky suggests microwave re-‐entrant cavity.
• First experiments at UWA 1976-‐80 – 6kg magne1cally levitated Nb bar with 10GHz levitated re-‐entrant cavity transducer.
C ~ 1pF L ~ 1nH f ~ 10GHz Q ~ 105 -‐ 106
Levitated Antenna with Superconduc1ng Transducer
Levitated Re-‐Entrant Cavi1es
Problems with Levitated Re-‐entrant Cavity
• Control noise – Current noise in the non-‐contac1ng voice coil control system that
maintained cavity spacing 10µm from the bar • Phase noise
– Klystron oscillator phase noise indis1nguishable from displacement noise
• Thermal noise – Low Q-‐factor levita1on assembly introduced mechanical thermal
noise. • Tunability Conflict: easy frequency tunability of free floa1ng re-‐
entrant cavity – incompa1ble with crea1ng a strong mechanically coupled oscillator.
(needs s1ff spring not achievable magne1cally.) • Noise enters down microwave cables.
effa M
m⋅=Δ ωω
Two Mode Resonant transformer
Two normal modes split by
Narrow Band impedance matching
Mechanical model: transducer with impedance matching using an intermediate mass resonant transformer
Infinitely rigid reference surface
Impedance matching and Bandwidth
Four resonant bars
Resonant
Mass
Detectors
Niobe 1.5 tonnes 3m x 30cm
• T=4K • Liquid helium: 0.5l/hr • Cryogenic vibra1on isola1on • Q= 2.3 x 108
High Q for Thermal Noise Reduc1on
Q= 2.3 x 108
• Perfect harmonic oscillator is noiseless: amplitude and phase perfectly predictable
• Q-‐1 measures coupling of oscillator to thermal reservoir: • Highest observed Q-‐factor for any metal resonator • Time constant ~ 1 day = 1me constant for energy exchange
between normal mode and the thermal reservoir = 1me to reach thermal equilibrium.
Mul1mode Mode Impedance Matching
As the number of resonators increases bandwidth increases, coupling becomes easier Mechanical amplifica1on!
Resonant bar: m1= mbar/2
Whip Mechanical transformers
D G Blair et al 1987 J. Phys. D: Appl. Phys. 20 162. doi:10.1088/0022-‐3727/20/2/002
• Tapered bars amplify transverse displacements
• Taper size needs to be large comared to wavelength
• Also works for lonitudinal displacements at cost of very large length.
Experimen1ng with designs
Bending Flap Secondary Resonator • Annealed Nb bending flap creates secondary resonator.
• Non-‐contac1ng microwave coupling.
• Mo1on between two resonators measured by re-‐entrant cavity.
• Chokes used to reduce radia1on loss
• Assembled using very thin epoxy resin
Niobium bar
1500kg
Secondary resonator 0.6kg
Microwave cavity transducer
Transducer 9.5GHz, 300MHz/µm
Impedance Matching on Niobe
Lecture 2
Solving the Phase Noise Problem Observa1on of Op1cal Spring effect Observa1on of Radia1on Pressure Self-‐calibra1on of parametric transducers Sapphire transducers
Fundamental Limits of Macroscopic Oscillators Δf
f=ΔL
L
ΔLmin =!
mωm2τ
"
#$
%
&'
12
ω 2 =k
mωm
2 ~EL3
mL2
Δfmin
f=ΔLmin
L=!
EL3τ
"
#$
%
&'
12
Frequency is determined by dimension fluctua1on
Standard quantum limit for length measurement
Frequency is linked to Youngs Modulus E, dimension and mass
ΔLmin =!mL2
mEL3τ
"
#$
%
&'
12
Hence
For sapphire Δfmin
f=10−20τ
−12
Lowest mechanical mode
Op1misa1on: SQL
N1/2
N-‐1/2
Op1mum energy density E opt = Modulus of Elas1city/ Q-‐factor
Whispering gallery modes in sapphire
Amplifier excita1on: loop oscillator
• Simple • Q> 109 at 4K, 3 x 107 at 77K • Filtered output • Amplifier driven into satura1on causes excess noise
• Flat turning point at 6K due to paramagne1c impuri1es balancing temperature dependence of superconduc1ng penetra1on depth.
Sapphire clocks and oscillators
Stabilised Loop Oscillators
1.4MHz oscillator
Early Q-‐results. Later ~1010
Radia1on Pressure Inflates the resonator
φ
BPF
LOOP OSCILLATOR
Microwave Interferometer
LO RF
LNA
Circulator
Phase error detector
mixer
Loop filter
Sapphire loaded cavity resonator Qe~3×107
ϕ
varactor
DC Bias
µW-‐amplifier
µW-‐amplifier
Filtered output
+
+
Non-‐filtered output
Pump Oscillators for Parametric Transducer A low noise oscillator is an essen1al component of a parametric transducer
A stabilised NdYAG laser provides a similar low noise op1cal oscillator for op4cal parametric transducers and for laser interferometers which are similar parametric devices.
phase noise
Next steps: tunable low noise oscillator + carrier suppression interferometer
Note Coupling antenna carries acous1c noise and low frequency swinging mo1on ~ 10-‐100µm. Design needs a) worlds worst
transducer for radia1ve coupling
b) worlds best transducer for signal readout.
ϕ
ϕ
ϕ
α
Data Acquisi1on
Mixers
Phase shisers
Filter
Electronically adjustable phase shiser & adenuator Σ Δ
SO Filter
Phase servo
Frequency servo
µW-‐amplifier Primary
µW-‐amplifier Spare µW-‐amplifier
Microstrip antennae
Microwave interferometer
Cryogenic components
Bar
Bending flap
Transducer
RF
9.049GHz 451MHz
9.501GHz
Composite Oscillator
Microwave Readout System of NIOBÉ Non-‐contact readout and microwave interferometer
LO
Detec1on Condi1ons • Detectable signal Es ≥ Noise energy Un
• Transducer: 2-‐port device: !!"
#$$%
&=!!
"
#$$%
&
Current
velocity
Z
Z
Z
Z
Voltage
Force
22
12
21
11
M, TA
Ta ωa
F
v
Z11 Z12
Z21 Z22
Se
SiG
V
Iτi
Bar Transducer Amplifier Recorder
• Amplifier , gain G, has effec1ve current noise spectral density Si and voltage noise spectral density Se
Mechanical input impedance Z11
Forward transductance Z21 (volts m-‐1s-‐1)
Reverse transductance Z12 (kg-‐amp-‐1)
Electrical output impedance Z22
computer
τa
General Results on Linear Transducers
• All linear transducers can be modelled as 2-‐port devices.
• GW transducers are amplifiers with mechanical input and electrical output.(also interferometers)
• Reverse transductance can never be zero: no such thing as a perfect one way valve. • Classical back ac1on leads to minimum detectable signal (uncertainty principle) and a minimum 1me resolu1on.
• Current noise, radia1on pressure fluctua1ons and microwave amplitude noise are the sources of back ac1on noise.
• Mechanical input impedance of transducer should match the mechanical output impedance of the resonant mass system.
Impedance Matching • The above picture emphasises that the bar-‐transducer
system is simply a transmission line. • Like all transmission lines impedance matching is of cri1cal
importance. It is essen1al to consider energy flow. • All gravity wave detec1on is extremely inefficient because
of the impossibility of impedance matching between the very high mechanical impedance of space 1me and the low impedance of atomic mader and electromagne1c fields.
• Mechanical impedance of free space ~ c3/G ~ 1033 ohms. Impedance of resonant bar ~ ωM ~ 107 ohms. For a s1ffer denser material resonant mass impedance is higher….up to 1010 is possible.(100 tonne sapphire sphere!)
Impedance of free electromagne1c waves: 377 ohms. • Electromechanical impedance matching can be achieved in
many ways…requiring maximal experimental ingenuity. • Impedance matching to heavy masses is much more
difficult. (see later)
The impedance mismatch ra1o between bar and transducer is iden1cal to the
electromechanical Coupling Coefficient of Transducer to Antenna β
signal energy in transducer
signal energy in bar β=
• In direct transducer β = (1/2CV2)/Mω2x2
• In parametric transducer β=(ωp/ωa)(1/2CV2)/Mω2x2
• Total sideband energy is sum of AM and PM sideband energy, depends on pump frequency offset
• Advantage of high modula1on frequency
x =capacitance gap
Similar for induc1ve readout or op1cal cavity transducer
X2
X1
P1P2
X1=Asinφ Resonant mass
transducer
Vsinωat ~
X G β
X2=Acosφ
Reference oscillator
mul1ply
0o 90o
Bar, Transducer and Phase Space Coordinates
β determines 1me for transducer to reach equilibrium. (impedance matching condi1on)
• X1 and X2 are symmetrical phase space coordinates
• Antenna undergoes random walk in phase space
• Change of state measured by length of vector (P1,P2)
• High Q resonator varies its state slowly. GW energy is stored over many cycles.
Asin(ωat+φ)
Mechanical Impedance Matching in Prac1ce • High bandwidth requires good impedance matching between acous1c output impedance of mechanical system and transducer input impedance: βω ~ bandwidth
• Massive resonators offer high impedance
• All electromagne1c fields offer low impedance (limited by energy density in electromagne1c fields)
• Hence mechanical impedance trasforma1on is essen1al
• Generally one can match to masses less than 1kg at ~1kHz
Note:Interferometers are another example of impedance matching: high light intensity gives highest mechanical impedance match to the GW signal.
effa M
m⋅=Δ ωω
Resonant transformer creates two mode system
Two normal modes split by
This is narrow band impedance matching.
Mechanical model of transducer with impedance matching using an intermediate mass resonant transformer
Infinitely rigid reference surface
Triumph
• Superconduc1vity + Low acous1c loss systems + Microwave optomechanics.
• Lowest noise temperature GW detector…later improved to < 1mK
• Harnessing op1cal spring proper1es, controlling parametric instability, outstanding immunity to environmental noise, even earthquakes!
Coupling and Parametric Transducer Scadering Picture
ωa
ωp
ω+=ωp+ωa
ω-‐=ωp-‐ωa
Direc1on depends on rela1ve couplings
transducer
Pump photons
Signal phonons
Output sidebands
Phonon-‐Photon Scadering
Because transducer has negligible loss use energy conserva1on to understand signal power flow-‐ Manley-‐Rowe rela1ons.
Note that power flow may be altered by varying β .
0=−+−
−
+
+ωωωPPP
a
a
0=++−
−
+
+ωωωPPP
p
p
Formal solu1on but results are intui1vely obvious
Upper sideband can only exist if signal phonons enter transducer.
Lower sideband can only exist if phonons are injected into mechanical resonator.
ω-‐ ω+
Upper mode Lower mode
Self damping an important tool to allowing rapid recovery from transients
Op1cal spring tuning of 1.5 tonnes of Nb with a few mW of microwave power.
Observa1on of Op1cal Spring Effect and Self Damping 1994
Self-‐Calibra1on Feature of Parametric Transducers using AM Noise Injec1on
• AM signal induces back ac1on on the resonator.
• Resonator mo1on detected as phase modula1on
Transducer
Sapphire whispering gallery loop oscillator
Sapphire Transducer
Locking feedback
SDR SDRT
Tests on VIRGO Superadenuator
High sensi1vity accelerometer
Sapphire Transducer Ac
celera1o
n g/rtHz
Frequency Hz
Undetectable normal modes become visible with sapphire transducer
10-‐4
10-‐6
10-‐8
10-‐10
Optomechanics for Gravitational Wave Detection
David Blair Australian Interna1onal
Gravita1onal Research Centre University Of Western Australia
Les Houches August 2015
Lecture 3
Lecture 3
• Do Gravity wave Detectors Absorb Energy from GW?
• Three mode interac1ons and Parametric Instability
• Harnessing three mode interac1ons: • Tilt interferometer • the opto-‐acous1c parametric amplifier
Two approaches to improved sensi1vity
• Reduce effect of quantum fluctuations which enter the detector at the dark port and set the standard quantum limit.
• Increase the size of the gravitational wave signal by changing the detector dynamics.
• Build a 40km long detector
Classical Force: Quantum Effects
M
K
Detector is a Mechanical Oscillator in Quantum Regime
Gravitational wave is a classical wave with enormous occupation number
Free Mass Detectors • Laser interferometers: free mass detectors? • Does this not violate the need for GWs to do work?
• Is a GWD not a receiver of GW energy? • Is a laser interferometer not a transducer for GW energy?
• Why can we measure GW without absorbing energy? – Can all the side band energy come from the laser?
Example: Ocean Wave Monitor Floa1ng Hovering
Dynamo energy output
Control system
Energy source
Electronic Amplifier Analog
+
-
Feedback around an amplifier: change the input impedance, change the gain.
φ=0
φ=π
Mapping Signal Recycling Interferometer to three mirror cavity.
Laser frequency ω0, gravity wave frequency ωm creates signal sidebands at ω0 + ωm and ω0 - ωm
signal recycling mirror.
Parametric Transducer feedback system
GW signal
Op1cal Cavi1es
Upper sideband
Test masses
Main beam
ACRadia1on pressure φ=π
ACRadia1on pressure φ=0
Lower sideband
Sideband beating
actuation
φ=0 φ=π
Sideband Roles
• Upper sideband represents energy absorp1on from GW
• Lower sideband is a feedback circuit that nulls the
dynamical response, causing the detector to have low input impedance and negligible energy absorp1on from the GW.
• A detector with single (upper) sideband readout maximises the energy absorp1on
Quantum Picture
Creates an optical spring
Nulls the optical spring
Op1cal “Bar”
• Improved sensi1vity due to opto-‐mechanical response of detector
See references in Yanbei Chen J Phys B 2013
Detuning creates unbalanced sidebands
Rela1ve sideband coupling is altered according to detuning: cavity amplifies sideband closest to resonance.
Unbalanced sidebands create optical spring, modify the detector dynamics and allow detection below the free mass SQL by increasing the energy coupling from the GW
Unbalanced Sidebands – double optical spring interferometer
Ques1ons
• Does increasing the energy absorbed always enable improvements in SNR
• Can we find broadband solu1ons? • Yes, see white light cavity tomorrow
Three Mode Interac1ons and Parametric Instability
Our Predic1on 2005 • 2005 Phys Rev Led: Advanced LIGO will experience three-‐mode parametric instability at 5%-‐10% of full input power
• Par1al method of control proposed • May 2014 observed in 80m high power op1cal cavity at our Gingin Research centre
• 2014 Confirmed in LIGO (PRL Evans et al 2015) • We are working with LIGO to find solu1ons since full sensi1vity cannot be achieved without a solu1on
3-‐mode Interac1on in an Op1cal Cavity
mωωω =− 10
Cavity fundamental mode ωo
(Stored energy)
Stimulated scattering into high order mode ω1
Acoustic modes ωm
Radiation pressure force from beating of ω0 and ω1.
Input frequency ωo
• 3-mode interaction requires frequency matching and spatial overlap of acoustic and optical modes
• Multiple modes interaction
Thermal vibration of the mirror
(R = 2076m
Δfax
f [kHz] 0 37.47 74.95
0 1
2 3
4 5
ΔfTEM = 0 kHz 4.6 kHz
g = 0.926)
Mode Structure 4km Arm Cavity
HOM not symmetric: Upconversion or down conversion occur separately.
Down conversion always potentially unstable.
ΔfFSR=37.47kHz
Typical transitions shownTEM00 – TEM04 : 53kHzTEM00 – TEM01: 32.9kHz
Instability Condition
1)/1/1
(2
21
21
112
121
112
>Δ+
Λ−
Δ+
Λ≈
aa
aa
m
m QQ
McL
PQR
δωδωω
Parametric gain[1]
[1] V. B. Braginsky, S.E. Strigin, S.P. Vyatchanin, Phys. Lett. A, 305, 111, (2002)
Stokes mode contribution
Anti-Stokes mode contribution Cavity Power
Mechanical Q
Λ—overlap factor
)(1
)(1)(1 2 a
aa Q
ωδ =maa ωωωω −−=Δ )(1(0)(1
Fundamental mode
frequency
Acoustic mode
frequency
High order transverse mode
frequency
44.66 kHz
HGM12
Examples of Mode Overlaps
47.27 kHz
HGM30
0.203 0.800
89.45kHz
0.607
LGM20
acoustic mode
optical mode
Λ overlapping parameter
Λ
Mechanical mode shape (fm=28.34kHz)
Summing over diagrams: multiple Stokes modes can drive a single acoustic mode.
Λ=0.007 R=1.17
Λ=0.019 R=3.63
Λ=0.064 R=11.81
Λ=0.076 R=13.35
Optical modes
Example
Thermal tuning
• Temperature gradients change mirror radius of curvature
• Radius of curvature changes the cavity mode spacing.
• Hence 3MI tuned by thermal lensing • Op1cal modes are tuned and distorted by
thermal abera1ons • Hence 3MI tuned by thermal abera1on
Input Test Mass ROC = 410m Absorbed Power = ~2W
End Test Mass ROC = 721m
Thermal Gradient: Jerome Degallaix
Thermal lens changes test mass radius of curvature
Power recycling cavity simulation
Demonstra1on of Thermal Tuning
Thermal Tuning (Heating Power: 15W)
60
70
80
90
100
110
120
130
140
15:00:00 15:07:12 15:14:24 15:21:36 15:28:48 15:36:00 15:43:12 15:50:24
time
Mod
e S
paci
ng (
kHz)
Thermal tuning of optical mode spacing between LG00 and LG01
Early predic1ons: thermal tuning
PRL 2005 Zhao et al
Sapphire: sparse acous1c modes
Fused silica: dense acous1c mode spectrum
Only low order op1cal modes considered
Bad news: no windows free of instability Note: most predic1ons give unstable modes per test mass
With mode summing
100
101
102
103
104
2050 2060 2070 2080 2090 2100
Parametrica Gain R
Radius of curvature (m)
S Gras 2007
Rmax=2207, Freq=33.39kHz (17)
Power Recycling Mirror resonance amplification
Early Predictions for Adv LIGO 2007 led to some design changes
Example of R change with RoC
Observa1ons • May 2014 we observed PI at Gingin
• Nov 2014 LIGO Louisiana observe PI as predicted at 7% of full laser power
• They use thermal tuning to improve and enable ~12% power opera1on
• Similar results at LIGO Hanford May 2015
• Last Friday an electrosta1c feedback system implemented at LIGO
• Expect 40 unstable modes per test mass at full power: may need many techniques such as op1cal feedback, mechanical feedback or frequency selec1ve dampers
First suspended cavity able to achieve instability condi1ons 2014 Gingin Western Australia
Finesse: 15,000 Parametric Gain = 6 Not the ring up we expected 1nm figure errors Gain= 1.4
New Instability Discovered at Gingin
• Nega1ve op1cal spring drives suspension normal modes.
• Two manifesta1ons: – torsional mode driving for non-‐centred beam spots
– Longitudinal pendulum mode driven when spot is centred.
• Results if extrapolated to LIGO would expect observa1on at 30% full power.
Threshold power for 0.9Hz instability
Signatures
Local control monitor shows growth of instability followed by decay aser cavity loses lock. Ring up of 0.9Hz pendulum oscilla1on
Harnessing three mode interac1ons
UWA – LKB Collabora1on
Parametric Gain of designed three mode interac1ng system
R = ±2ΛI0Q0Q1Qm
mω0ωm2 L2
For low loss op1cal cavi1es with low mass resonator gain can be very high because of the Q-‐product Assume perfect tuning.
How do we observe PI?
( ) ( )( )1 12 2 2 202
41 1m
S S AS ASm
cQ QR
m L
P
cω κ ω κ
ω
− −= +Δ − +Δ
Λ
Too heavy, too difficult
?ny and easy to excite
10/07/2013 Amaldi10 LIGO-‐G1300681 116
F-‐P cavity with a membrane
• length: 10 cm • finesse: 4000 • Pin threshold: 5.7 µW • effec1ve mass: 40 ng • Resonant f : 400kHz ̴ few MHz • mechanical Q: 105
• overlap: 0.1 • Maximum Pin > 5 mW
SiNx membrane 50nm thick 1x1 mm2
10/07/2013 Amaldi10 LIGO-‐G1300681 117
TEM00
frequency p p+1
Tuning membrane posi1on x0 to achieve ω0- ωS
TEM01
TEM02
X0
10/07/2013 Amaldi10 LIGO-‐G1300681 118
1718 kHz
Tuning membrane posi1on x0 to achieve ω0- ωS
00 mode 1st order mode 2nd order mode
membrane posi1on(x0/λ)
00 20 mω ω ω− ≈
X0
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Spa1al overlap in reality
Op1cal mode TEM02 mode Mechanical mode 26 mode 1.8 MHz
Op1cal mode TEM02 mode
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Spa1al overlap in reality
overlap factor: 0
laser spot is at the membrane centre
overlap factor: 0.2
op1mised laser spot posi1on is not at the membrane centre
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Phonon-‐laser oscilla1on observed 2013 Xu Chen et al Arxiv 2014, PRA 2015
Membrane ring-‐up 1me
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Experimental measured ring-‐up 1me constant vs theore1cal predic1on
Experimental measured steady state bea1ng fided with theore1cal predic1on
3 Mode readout at Gingin 1. ETM 1lts : observed high sensi1vity to test mass mode equivalent to a 1lt vibra1on
Thermally excited acous1c mode readout
Simple system very sensitive to acoustic modes in the 100kHz range. 100kHz gravitational wave detector!
10-‐16m
10-‐17m
Radius of curvature cavity tuning
High SNR when transverse mode is correctly tuned by CO2 laser tuning
Spa1al Overlap
G0 =Λω0ω1
mωmL2
Tilt Interferometer
Engineered Three Mode Interac1on Devices
• Strong opto-‐acous1c coupling can be engineered.
• Special op1cal cavity design for compact devices
• Silicon microresonators – Low acous1c loss, low op1cal loss – Qopt ~ 1010, Qmech ~ 106
– Linewidth ~ 1 Hz – Strong self-‐cooling
Opto-‐Acousic Parametric Amplifier OAPA Silicon torsion mirror oscillates at ~MHz Sensi1ve to weak electromagne1c RF fields Can in principle be cooled to quantum ground state using thermodynamic cooling + self cooling. Could detect single RF quanta through 3-‐mode interac1on: acous1c detec1on for transi1on from TEM00 to TEM01 mode.
Opto-‐acous1c parametric amplifier • Compact tunable table top device for three mode interactions. • Three mirror near self-imaging cavity • Low acoustic loss silicon micro-resonator.
Observed Q=106 :Gain Breakdown power limit ~20mW
Available self cooling factor > 20,000
Phonon laser self oscilla1on threshold few µW
Main Problem
Avoided crossing Osen very difficult to make mode gap small enough to match 1MHz in a tabletop system.
Optomechanics for Gravitational Wave Detection
David Blair Australian Interna1onal
Gravita1onal Research Centre University Of Western Australia
Les Houches August 2015
Lecture 4
Lecture 4
Optomechanical devices for improved GW detectors. a) Review of predicted mprovements b) Narrow band cavi1es for frequency
dependent squeezing c) White light cavi1es d) Approach to thermal noise free
optomechanical devices
Bea1ng Quantum Noise
Conven1onal detector
Frequency-‐dependent squeezed vacuum injec1on
Phase-‐squeezed vacuum injec1on
White-‐light cavity
138
[2]H. J. Kimble et al. 2001, Conversion of conven1onal gravita1onal-‐wave interferometers into quantum nondemoli1on interferometers by modifying their input and/or output op1cs Phys. Rev. D 65, 022002 (2001).
Squeezing
Phase or Amplitude squeezing (Any direc1on)
Phase squeezed vacuum fluctua1ons input reduces noise at output
• Based on an OPO pumped with green light
Vacuum Squeezer
Sensi1vity Improvement from Squeezing at GEO
Losses and Phase noise cause squeezing reduc1on from 10dB to 3.7dB
Enhanced sensi1vity of LIGO with squeezed vacuum
Nature Photonics 21 July 2013
Quantum shot noise suppressed by squeezing the vacuum quantum fluctuations
Signal Recycling Tuning the signal recycling cavity length tunes the op1mum frequency Tuning the signal recycling mirror reflec1vity determines the gain and bandwidth. Note the usual nexus: more gain = less bandwidth
Figures courtesy Emil Schreiber, GEO
Optomechanical systems enable new device concepts
• When photons and phonons interact strongly with low losses, they lose their iden1ty.
• Such systems allow – Very narrow acous1c lines to be imposed on an op1cal spectrum….ie ultra-‐narrow filter cavi1es
– Nega1ve dispersion to create broadband resonant amplifica1on
To be effec4ve all of the above need thermal-‐noise free optomechanical devices at room temperature
Bea1ng Quantum Noise
Conven1onal detector
Frequency-‐dependent squeezed vacuum injec1on
Phase-‐squeezed vacuum injec1on
White-‐light cavity
146
[2]H. J. Kimble et al. 2001, Conversion of conven1onal gravita1onal-‐wave interferometers into quantum nondemoli1on interferometers by modifying their input and/or output op1cs Phys. Rev. D 65, 022002 (2001).
Opto-‐mechanical devices
• Minimum external coupling: Low op1cal loss, mm-‐scale for low diffrac1on losses
• Ultra-‐low thermal noise: thermal noise dilu1on to less than 1 phonon
Our approach: Three parallel developments • Develop balanced op1cal springs for thermal
noise dilu1on • Demonstrate optomechanics in classical regime • Develop suitable resonators
• Narrowband Filter cavity to change the phase of the squeezed light without adding noise or losses.
• Nega1ve dispersion cavity: Change signal resonance for broadband signal enhancement: white light cavity.
First Demonstra1on of Classical Frequency Dependent Squeezing
Requirement: Ultra-‐narrow band low loss op?cal filter cavi?es Two possible approaches a) Kilometer scale Fabry-‐Perot cavi1es b) Opto-‐mechanically induced transparency OMIT
OMIT allows the bandwidth of an acous4c resonator to be transferred to the op4cal frequency Advantages of OMIT: • Narrow bandwidth << 100 Hz with small scale cavi1es. • Tunable bandwidth for op1mizing sensi1vity for different GW sources.
[3]S. Weis et al.2010, Optomechanical Induced Transparency,Science 330, 1520(2010)
Narrow-‐band optomechanical filters
⎪ 149
Red detuned pump beam creates optomechanical interac1on such that the mechanical resonator response curve is embedded into the op1cal cavity spectrum.
Demonstra1ng optomechanical filter cavity
J. Qin, et al., PRA 89, 041802(R) (2014)
⎪ 150
Opto-‐mechanically induced transparency creates ultra-‐narrow band cavity
• Q-‐factor ~ 2 x 1014 Smallest
bandwidth achieved 2.6Hz
Observed Squeeze Angle Rota1on in Classical Domain (squashed light)
OMIT cavity has phase response of conven1onal cavity: phase shis across resonance.
First demonstra1on of frequency dependent squeezing of light.
White-‐light cavity
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ω
Nega1ve dispersion
Nega4ve dispersion makes the cavity “longer” for longer wavelengths so all frequencies are simultaneously resonant
WLC breaks the nexus between bandwidth and amplitude build up.
Nega1ve dispersion cancels the normal cavity round trip phase lag
Normal cavity round-‐trip phase lag: Phase cancela1on requirement:
⎪ 154
Double blue detuned opto-‐mechanical cavity creates nega1ve dispersion
In principle this system can have low noise and low losses
Nega1ve dispersion experiment
⎪ 156
Opto-‐mechanical nega1ve dispersion -‐ theory and experiment
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1
2
3
4
5
Frequency (kHz)
Ampli
tude
2δ0=3.7 kHz
2δ0=2.7 kHz
2δ0=1.7 kHz
2δ0=0.7 kHz
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−50
0
50
Frequency (kHz)
Phas
e (De
g.)
Theore1cal responses Experimental demonstra1on by our student Jiayi Qin
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−50
0
50
Phas
e =D
eg.)
Frequency =kHz)
376 376.5 377 377.5 378 378.5 379 379.5 380 380.5 381 381.5
1
2
3
4Tr
anm
issivi
ty a
mpl
itude
=a.u
)
Frequency =kHz)
2δ0=3.7 kHz
2δ0=2.7 kHz
2δ0=1.7 kHz
2δ0=0.7 kHz
Jiayi Qin et al
Nega1ve Dispersion Performance
⎪ 158
White-‐light cavity enhanced GW detector
⎪ 159
• Signal extrac1on mirror resonates the signal sidebands • Optomechanical cavity provide nega1ve dispersion • Broad range of frequencies enhanced • Hence broadband sensi1vity enhancement
Op1cal Dilu1on for Thermal Noise Free Optomechanics
• Thermal noise makes both of the above devices vastly too noisy for use in a real detector.
• Can Q-‐factors be achieved to drop thermal noise to zero at 300K?
Mul1-‐frequency pumping of opto-‐mechanical cavity
• T. Corbid et al., “Op1cal Dilu1on and Feedback Cooling of a Gram-‐Scale Oscillator to 6.9 mK”, Phys. Rev. Led. 99, 160801 (2007)
- D. E. Chang, K.-‐K. Ni, O. Painter and H. J. Kimble, “Ultrahigh-‐Q mechanical oscillators through op1cal trapping”, New J. Phys. 14, 045002 (2012).
Filter cavity pumping scheme
Op1cal Spring
Mechanical Resonator
Resonator with minimal restoring force
• Radia1on presure provides noise free restoring forces.
• Minimise mechanical restoring force Collabora4on with Shiuh Chao, Na4onal TsingHua University • Silicon cat-‐flap pendulum with very thin
Si-‐N hinge • Expect good Q-‐factor because of nm
membrane thickness and proven Q-‐factor • Design configuara1ons to prevent added quantum noise
Op1cal dilu1on
Quantum destruc1ve interference cancels quantum noise and cancels op1cal damping
163
Cat-‐flap resonators
Cat-‐flap resonator Op1cal dilu1on with
instability cancella1on
• Intrinsic (gravity-‐free) frequencies: - silicon nitride ~20Hz : graphene : 0.2 Hz.
• Op1cal spring frequency: 200kHz. - Dilu1on factors: ~108 (SiN); ~1012 (graphene).
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Cat-‐flap resonator cut from Silicon Wafer
165
Prac1cal op1cal design
Sources of Loss
• Accelera1on losses: Q =Qint. (ωint/ωos)2
• Reduce using distributed mirror with equal light reflec1on per stage: r1<r2<r3 etc
• Suspension modes: minimise excita1on by centre of
perrcussion tuning
• Suspension modes frequency: high tension from graphene, Si-‐N or nanotube suspension
r1 r1
r2
rn
Basic Concept • The arm cavity is equivalent to a single cavity with
1lted mirrors; • For small 1lt angles (𝜃 ∼ ℎ× ≪ 1) it is equivalent to
laser beam jider with GW frequency; • GW beam jider eqivalent to pumping of the cavity
with two carriers, 𝜔0 and 𝜔1 = 𝜔0 + ΩGW • Radia1on pressure force of the beat note between
two modes induces the torsional op1cal spring • When op1cal spring frequency is equal to the GW
frequency, the GW induced mirror 1lt mo1on will be amplified and hence increase the sensi1vity.
History of Optomechanics
Sapphire Oscillators