optomechanics for gravitational wave detection · 2016-11-15 · optomechanics for gravitational...

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





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

10/07/2013 Amaldi10 LIGO-‐G1300681 119

Spa1al overlap in reality

Op1cal mode TEM02 mode Mechanical mode 26 mode 1.8 MHz

Op1cal mode TEM02 mode

10/07/2013 Amaldi10 LIGO-‐G1300681 120

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

10/07/2013 Amaldi10 LIGO-‐G1300681 121

Phonon-‐laser oscilla1on observed 2013 Xu Chen et al Arxiv 2014, PRA 2015

Membrane ring-‐up 1me

10/07/2013 Amaldi10 LIGO-‐G1300681 123

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.





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


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.


⎪ 153

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

376 376.5 377 377.5 378 378.5 379 379.5 380 380.5 381 381.50

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

376 376.5 377 377.5 378 378.5 379 379.5 380 380.5 381 381.5

−50

0

50

Frequency (kHz)

Phas

e (De

g.)

Theore1cal responses Experimental demonstra1on by our student Jiayi Qin

376 376.5 377 377.5 378 378.5 379 379.5 380 380.5 381 381.5

−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).

164

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

optomechanics for gravitational wave detection · 2016-11-15 · optomechanics for gravitational...

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