gravitational-wave detectors - desy · gravitational-wave detection mirror 1 mirror 2 ~ km photo...

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Gravitational-Wave Detectors

Roman Schnabel

Institut für Laserphysik Zentrum für Optische Quantentechnologien Universität Hamburg

Roman Schnabel, 02 / September/ 2016 University of Hamburg 2

Outline

•  Gravitational waves (GWs)

•  Resonant bar detectors

•  Laser Interferometers - Quasi-free test mass mirrors - Photo-electric detection

•  The GW detector GEO600 with squeezed light

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GW150914 Gravitational-wave Event from Colliding Black Holes

Roman Schnabel

Institut für Laserphysik Zentrum für Optische Quantentechnologien Universität Hamburg


LIGO Data of Sept. 14th, 2015

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LIGO Data of Sept. 14th, 2015

Results (numerical solution of Einstein‘s equations)

Distance from Earth: 1.3 billion light years.

Roman Schnabel, 02 / September/ 2016 University of Hamburg

Gravitational waves

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L

+Δ L Gra

vitat

iona

l wav

e

λ

Binary system

To Earth

fBS

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•  Weber bars, fres~ 1kHz

Gravitational Wave Detectors

Auriga, Italy 3 m long aluminum cylinder

2.3 tons


4 km LIGO Gravitational-Wave Detector

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5


Laser

Gravitational-Wave Detection

Mirror 1

Mirror 2

~ km

Photo diode

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1) Quasi-free test mass mirrors

GW induced distance change

•  Laser interferometers

2) Laser light |α�


GEO-HF: - 30kW - DC readout - OMC - Tuned, broadband SR - Squeezed Light

The Gravitational-Wave Detector GEO 600

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�Free� Mirrors


Suspended Mirrors in LIGO (40 kg each)

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Laser


Mirror 1

Mirror 2


~ km

3) Interference

4) Photo-electric effect

Photo diode

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Photo-electric current modulated at GW frequency

(“unbiased estimator”)




Statistic of Truly Random Photons

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Time intervals

Pho

tons

per

tim

e in

terv

al

N

Looks like a signal…

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Statistic of Truly Random Photons

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Time intervals

Pho

tons

per

tim

e in

terv

al

N

…but isn’t, just photon shot noise!


Shot Noise

Coherent state

€

⇒ ˆ N = N = α 2=10000

Photon number N

Prob

abili

ty [r

el. u

nits

]

16

€

α = 100

~ NN~ 1

N~ 1

PLaserShot-noise

Signal

N − N N + N

N

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Increasing the Light Power

High power laser

Mirror 1

Mirror 2

Photo diode

Photo-electric current

Light absorption/heating

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Power-recycling mirror


Is there a possibility to increase the signal/quantum noise–ratio without increasing the laser power?

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Yes! On the basis of squeezed light!

[Caves, Phys. Rev. D 23, 1693 (1981)]

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Introduction of „squeezed states“ of electro-magnetic fields:

H. P. Yuen, Two-photon coherent states of the radiation field, Phys. Rev. A 13, 2226–2243 (1976)


GEO-HF: - 30kW - DC readout - OMC - Tuned, broadband SR - Squeezed Light

The Gravitational Wave Detector GEO 600

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Statistic of truly random Photons

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Time intervals

Pho

tons

per

tim

e in

terv

al

N

(Poissonian) Shot noise


Statistic of quantum-correlated Photons

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Time intervals

Pho

tons

per

tim

e in

terv

al

N

Squeezed shot noise (Sub-poissonian)

A “nonclassical” effect! The semi-classical model fails:

First, light propagates and interferes as a wave and, second,

particles appear randomly During energy transfer

Paradoxical!

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Squeezing factor: 3 dB

Squeezing factor: 10 dB

“Squeezed” Counting Statistics

Photon number N

Prob

abili

ty [r

el. u

nits

]

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Noise squeezing

Paradoxical!

Poisson statistics


First generation of squeezed states of light (-7%, -0.3 dB):

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Observation of squeezed states generated by four-wave mixing in an optical cavity. Phys. Rev. Lett. 55, 2409 (1985)

First generation of squeezed states of light with PDC (-50%, -3 dB):

L.- A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520 (1986)

In terms of S/N: 3 dB squeezing = doubling the light power›

1985: First Generation of Squeezed Light

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“Squeezing” Laboratories

First squeezed light: [Slusher et al., PRL 55, 2409 (1985)]

Research labs with squeezed light (not complete):

-  Kimble (CalTech): teleportation: [Furuzawa et al., SCIENCE 282, 706 (1998)]

-  Grangier (Orsay); kitten: [Ourjoumtsev et al., SCIENCE, 312, 83 (2006)]

-  Schiller and Mlynek (Konstanz): tomography: [Nature 387, 471 (1997)]

-  Bachor and Lam (Canberra): 6dB at 1064nm [J. Opt. B 1, 469 (1999)]

-  Leuchs (Erlangen); ~7 dB pulsed [Opt. Lett. 33, 116 (2008)]

-  Polzik (Copenhagen), [Neergaard-Nielsen et al., PRL 97, 083604 (2006)]

-  Furusawa (Tokyo); 9 dB: [Takeno et al., Opt. Express 15, 4321 (2007)]

-  Fabre (Paris); Zhang, Peng (Shanxi); Andersen (Copenhagen); Mavalvala (MIT)

-  Nussenzveig (Sao Paulo); Pfister (Virginia); ...

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Squeezing at frequencies in the GW detection band (10 Hz to 10 kHz) -  Control beam as noise source identified [Bowen, RS et al., J. Opt. B 4, 421 (2002)], [RS et al., Opt. Comm. 240, 185 (2004)] -  First Audioband squeezing [McKenzie et al., PRL 93, 161105 (2004)] -  New control scheme [Vahlbruch, RS et al., PRL 97, 011101 (2006)] -  6 dB over complete band [Vahlbruch, RS et al., NJP 9, 371 (2007] Compatibility with GW detector techniques -  Power-recycling [McKenzie et al., PRL 88, 231102 (2002).] - Signal-recycling [Vahlbruch, RS et al., PRL 95, 211102 (2005)] - Suspended interferometer [Goda et al., Nat. Phys. 4, 472 (2008).] Strong continuous wave squeezing (>10 dB) at 1064nm -  [Vahlbruch, RS et al., PRL 100, 033602 (2008)] - [M. Mehmet, RS et al., PRA 81, 013814 (2010)]

Squeezing Issues for GW Detection

Squeezing at frequencies in the GW detection band (10 Hz to 10 kHz) -  Control beam as noise source identified [Bowen, RS et al., J. Opt. B 4,

421 (2002)], [RS et al., Opt. Comm. 240, 185 (2004)] -  First Audioband squeezing [McKenzie et al., PRL 93, 161105 (2004)] -  New control scheme [Vahlbruch, RS et al., PRL 97, 011101 (2006)] -  6 dB over complete band [Vahlbruch, RS et al., NJP 9, 371 (2007] Compatibility with GW detector techniques -  Power-recycling [McKenzie et al., PRL 88, 231102 (2002).] - Signal-recycling [Vahlbruch, RS et al., PRL 95, 211102 (2005)] - Suspended interferometer [Goda et al., Nat. Phys. 4, 472 (2008).] Strong continuous wave squeezing (>10 dB) at 1064nm -  [Vahlbruch, RS et al., PRL 100, 033602 (2008)] - [M. Mehmet, RS et al., PRA 81, 013814 (2010)]

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Design of the �GEO600 Squeezer�

[Henning Vahlbruch, PhD thesis, Hannover, 2008] - Gravitational Wave International Committee (GWIC) Thesis Prize 2008 - S-AMOP DPG Thesis Prize 2010


The GEO600 Squeezed Light Laser

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Alexander Khalaidovski and Henning Vahlbruch, 2009/2010 Real-time control system: Nico Lastzka and Christian Gräf

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Standing wave cavity

Generation of Squeezed Light

χ2-nonlinear crystal: MgO:LiNbO3 or PPKTP

Pump field input (cw, 532nm)

Squeezed field output (cw, 1064nm) by parametric down-conversion (PDC)


Generation of Squeezed Light

Nonlinear dielectric polarisation of matter by light (Taylor-expansion)

Pi = ε0 χ ijE j + χ ijk(2)EjEk + χ ijkl

(3)EjEkEl + hijk(2)BkEj + hijkl

(3)BkBlEj +...( )

SHG, THG, Kerr effect, Faraday effect Cotton-Mouton effect Parametric Four wave mixing down-conversion, PDC (OPO,OPA)

zyxlkji ,,,...,,, =

2nd order terms in detail:

( ) ( ) ( ) ( )∑ −=−jk

kkjjkjiijkii EEP ωωωωωχεω ,,)2(0

)2(

0=++− kji ωωω

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Parametric amplification (degenerate): Graphical description how the ground state uncertainty is converted into a squeezed vacuum [J. Bauchrowitz, T. Westphal, R.S., Am. J. Phys. 81, 767 (2013)]

The ground state uncertainty is squeezed, when the pump field shows a minimum,


Wigner Function of Squeezed Light

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Measured: - 11.5 dB / +16 dB@5MHz

[Mehmet et al., PRA 81, 013814 (2010)]

Phase-space quasi-probability

distribution of a squeezed vacuum

state

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The GEO600 Squeezed Light Laser

[H. Vahlbruch, A. Khalaidovski, N. Lastzka, C. Gräf, K. Danzmann, and R. Schnabel, The GEO600 squeezed light source, Class. Quantum Grav. 27, 084027 (2010)] Alexander Khalaidovski: Stefano Braccini Thesis Prize 2011.

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Transport to the GEO600 GW Detector

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Obse

rvator

y nois

e, ca

librat

ed to

GW

-strai

n [1/

√ Hz

]

10-22

10-21

10-20

1kFrequency [Hz]

5k4k3k2k400 800500

GEO600 Spectral Density 2010

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Photon shot noise (Poisson statistics)


GEO600: Squeezed Light in Application

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Observatory noise without squeezed light

Obse

rvator

y nois

e, ca

librat

ed to

GW

-strai

n [1/

√ Hz

]

10-22

10-21

10-20

1kFrequency [Hz]

5k4k3k2k400 800500

Obse

rvator

y nois

e, ca

librat

ed to

GW

-strai

n [1/

√ Hz

]

10-22

10-21

10-20

1kFrequency [Hz]

5k4k3k2k400 800500

Observatory noise with 10 dB squeezing

(and 38% loss) Optimum quantum approach! [Demkowicz-Dobrzanski, Banaszek, Schnabel, PRA 88, 041802(R) (2013)]

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Shot noise

squeezed

This is not just a proof of principle!

GEO600 regularly uses squeezed light during its

observational runs. [Grote et al., PRL 110, 181101

(2013)]

An application of nonclassical quantum

metrology today!


LSC, Nature Photonics 7, 613–619 (2013)

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Shot Noise and Radiation Pressure Noise

Quantum noise in phase quadrature

Standard quantum limit

(SQL)

Shot noise

Radiation pressure noise

[Caves 1981]

Squeezed shot noise, 20dB (Alternatively 100x

laser power)

X1 X2

(Both signal Normalized)


(Light power, coherent state) [Caves, Phys. Rev. D 45, 75 (1980)]

Shot Noise and Radiation Pressure Noise

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Standard Quantum Limit (SQL)

Shot noise

Radiation pressure

noise

[Jaekel, Reynaud 1990]

QND-Regime

Squeezing SN and RPN

Squeezed Light Input (8dB) €

ˆ X 1€

ˆ X 2


Laser


Mirror 1

Mirror 2


~ km

3) Interference

4) Photo-electric effect

Photo diode

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Photo-electric current modulated at GW frequency

(“unbiased estimator”)



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Calibration of Photo Diode Quantum Efficiency

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Total Efficiency: (97.5 ± 0.1)% à PD: (99.5 ± 0.5)%

(99.05 ± 0.45)%

99

.8%

[H. Vahlbruch, MM, KD, RS, Phys. Rev. Lett., accepted (2016)]


The Einstein Telescope

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•  10 km arms

•  under ground

•  Cryo-cooled silicon mirrors

•  10 dB squeezed light at 1064 nm and 1550 nm

European design study

[M. Punturo et al., Class. Quantum Grav. 084007 (2010)]

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Summary / Outlook

•  Squeezed light can be used to calibrate photo detectors

•  The GW detector GEO600 uses squeezed light in observational runs.

•  Most likely, squeezed light will be used in all future GW detectors.

•  The nonclassical (paradoxical) part of quantum mechanics will improve the detection of gravitational waves.

gravitational-wave detectors - desy · gravitational-wave detection mirror 1 mirror 2 ~ km photo...

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