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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
Roman Schnabel, 02 / September/ 2016 University of Hamburg 4
LIGO Data of Sept. 14th, 2015
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Roman Schnabel, 02 / September/ 2016 University of Hamburg 5
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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Roman Schnabel, 02 / September/ 2016 University of Hamburg 7
• Weber bars, fres~ 1kHz
Gravitational Wave Detectors
Auriga, Italy 3 m long aluminum cylinder
2.3 tons
Roman Schnabel, 02 / September/ 2016 University of Hamburg
4 km LIGO Gravitational-Wave Detector
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Roman Schnabel, 02 / September/ 2016 University of Hamburg
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�
Roman Schnabel, 02 / September/ 2016 University of Hamburg 10
GEO-HF: - 30kW - DC readout - OMC - Tuned, broadband SR - Squeezed Light
The Gravitational-Wave Detector GEO 600
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Roman Schnabel, 02 / September/ 2016 University of Hamburg 11
�Free� Mirrors
Roman Schnabel, 02 / September/ 2016 University of Hamburg 12
Suspended Mirrors in LIGO (40 kg each)
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Roman Schnabel, 02 / September/ 2016 University of Hamburg
Laser
Gravitational-Wave Detection
Mirror 1
Mirror 2
2) Laser light |α�
~ km
3) Interference
4) Photo-electric effect
Photo diode
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Photo-electric current modulated at GW frequency
(“unbiased estimator”)
1) Quasi-free test mass mirrors
GW induced distance change
Roman Schnabel, 02 / September/ 2016 University of Hamburg
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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Roman Schnabel, 02 / September/ 2016 University of Hamburg
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!
Roman Schnabel, 02 / September/ 2016 University of Hamburg
Shot Noise
Coherent state
€
⇒ ˆ N = N = α 2=10000
Photon number N
Prob
abili
ty [r
el. u
nits
]
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€
α = 100
~ NN~ 1
N~ 1
PLaserShot-noise
Signal
N − N N + N
N
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Roman Schnabel, 02 / September/ 2016 University of Hamburg
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
Roman Schnabel, 02 / September/ 2016 University of Hamburg
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)
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GEO-HF: - 30kW - DC readout - OMC - Tuned, broadband SR - Squeezed Light
The Gravitational Wave Detector GEO 600
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Roman Schnabel, 02 / September/ 2016 University of Hamburg
Statistic of truly random Photons
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Time intervals
Pho
tons
per
tim
e in
terv
al
N
(Poissonian) Shot noise
Roman Schnabel, 02 / September/ 2016 University of Hamburg
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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Roman Schnabel, 02 / September/ 2016 University of Hamburg
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
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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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Roman Schnabel, 02 / September/ 2016 University of Hamburg
“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
Roman Schnabel, 02 / September/ 2016 University of Hamburg
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)
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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,
Roman Schnabel, 02 / September/ 2016 University of Hamburg
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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Roman Schnabel, 02 / September/ 2016 University of Hamburg
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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Roman Schnabel, 02 / September/ 2016 University of Hamburg
Transport to the GEO600 GW Detector
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Roman Schnabel, 02 / September/ 2016 University of Hamburg
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)
Roman Schnabel, 02 / September/ 2016 University of Hamburg
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!
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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)
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(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
Roman Schnabel, 02 / September/ 2016 University of Hamburg
Laser
Gravitational-Wave Detection
Mirror 1
Mirror 2
2) Laser light |α�
~ km
3) Interference
4) Photo-electric effect
Photo diode
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Photo-electric current modulated at GW frequency
(“unbiased estimator”)
1) Quasi-free test mass mirrors
GW induced distance change
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Roman Schnabel, 02 / September/ 2016 University of Hamburg
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)]
Roman Schnabel, 02 / September/ 2016 University of Hamburg
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.