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![Page 1: Interferometer as a New Field of a Quantum Physics - the Macroscopic Quantum System - Nobuyuki Matsumoto Tsubono lab University of Tokyo Elites Thermal.](https://reader030.fdocuments.net/reader030/viewer/2022032517/56649cc05503460f949876a0/html5/thumbnails/1.jpg)
Interferometer as a New Field of a Quantum Physics
- the Macroscopic Quantum System -
Nobuyuki MatsumotoTsubono lab
University of Tokyo
Elites Thermal Noise Workshop @ University of Jena Aug 21, 2012
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Tsubono Lab @ University of Tokyo
• Directed by Prof. Kimio Tsubono of department of physics at university of Tokyo
• Research on Relativity, Gravitational Wave, and Laser Interferometer
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motivation
• Interferometer can detect gravitational waves and study quantum physics because the quantum nature of the light can move to a state of the mirror via the radiation pressure of light→Macroscopic quantum physics can be studied!
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Abstract
GoalProviding a new field to study quantum physicsEx.i. Studying a quantum de-coherenceii. Generation of a macroscopic “cat state”iii. Generation of a squeezed lightRequirementObservation of a Quantum Radiation Pressure Fluctuations (QRPF)
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Outline
I. IntroductionII. Effect of a radiation pressure forceIII. Radiation Pressure InterferometerIV. Prior ResearchV. Our ProposalVI. Summary
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I. Introduction
• What is the light?Wave-particle duality ↓ Uncertainty principle
↓ ↓Standard quantum limit quantum non-demolition (SQL) measurement (QND)→ultimate limit →surpassing the SQL
ΔX1:fluctuations of the amplitude quadrature → induce a radiation pressure noiseΔX2:fluctuations of the phase quadrature → induce a shot noise
ΔX1=ΔX2 (vacuum state) ΔX1 or ΔX2 <1 (squeezed state)
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I. Introduction
• Quantum effect in a gravitational detector→quantum noise originated by the vacuum (ground state) fluctuations
Laser
PD
DC power + Vacuum Fluctuations (Quantum Sideband)
Quantum Sideband
common
differential
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I. Introduction
• Generation of the squeezed light & Reduction of shot noise our squeezed vacuum
generator via χ(2) effect↑
Optical Parametric Oscillator (OPO)
Nonlinear media (PPKTP) ↑ ↑
↓↓↓Pump, Green light (532 nm)
↓Correlated IR light
↓Down conversion (green → IR) ↑
Seed (1064 nm) ↑
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I. Introduction
• Quantum effect in an opt-mechanical system→QRPF are not noises but signals!
Fixed mirror
Movable mirror
radiation pressure of light ↓ ↓ ↓Mediation between the mechanical system and the optical system
↓↓↓↓
→ DC power → classical effect→ power fluctuations →quantum effect induced by QRPF
→opt-mechanical system
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II. Effect of a radiation pressure force
• Optical spring effect Fixed mirror
Movable mirror
Spring effect
PHYSICAL REVIEW A 69, 051801(R) (2004)
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II. Effect of a radiation pressure force
• Siddles-Sigg Instability (anti-spring effect)
PHYSICAL REVIEW D 81, 064023 (2010)
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II. Summary of the review
• Opt-mechanical effects• Classical effectsi. Spring effectii. Instabilityiii. Cooling And so on ・・・• Quantum effectsi. Squeezingii. Entanglementiii. QNDAnd so on ・・・
Measured
Not measured
No one see even QRPF
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III. Radiation Pressure Interferometer
• Interferometer to study quantum physics using a radiation pressure effect
Difficulty i. Weak force
light test masslow stiffnesshigh power beam
ii. Siddles-Sigg instabilityhigh stiffnesslow power beam
Technical trade-offSensitivity vs Instabilityconfiguration
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IV. Prior Research
• Suspended tiny mirror (linear FP)i. High susceptibility due to low stiffnessii. Do not have a much tolerance for restoring a
high power beam
• MEMS (Micro Electro Mechanical Systems)i. Light (~100 ng) but not high susceptibility due to
high stiffness ii. Have a much tolerance for restoring a high
power beam
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IV. Prior Research
• Suspended tiny mirror (linear FP)
Φ30 mm
Width 1.5 mm
Flat mirror
Q ~ 7.5e5
PHYSICAL REVIEW D 81, 064023 (2010)
C. R. Physique 12 (2011) 826–836
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IV. Prior Research
• MEMSwidth
Mass ~ 100 ngQ ~ 10^6-10^7
PHYSICAL REVIEW A 81, 033849 (2010)
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IV. Prior Research
Type Mass Resonant frequency
instability Mechanical quality factor
Suspended mirror
~10 mg ~1 Hz Insufficient tolerance
~7.5e5 with 300 K
Membrane ~100 ng ~100 kHz Much tolerance ~10^6~10^7 with 1 K
• Suspended mirror vs membrane
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V. Our Proposal
• Triangular cavitySiddels-Sigg instability of yaw motion is eliminatedwithout increasing the stiffness
• Silica aerogel mirror (low density ~ 0.1 g/cm^3)More sensitive test mass
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V. Our Proposal
Frequency [Hz]
Dis
plac
emen
t fluc
tuati
ons
indu
ced
by Q
RPF
[m/H
z^1/
2]
SN~2 with 1 K
SN~10 with 300 K(P_circ~1 kW, m=23 mg, Q=1e5)
SN~10 with 300 K(P_circ~1 kW, m=2.3 mg, Q=1e4)
Can not observe with 300 K(P_circ~100 mW, m=23 mg, Q=1e5)
SN~4 with 300 K(aerogel, m=0.23 mg Q=300)
Linear FP cavity
Triangular cavity
Membrane(MEMS)
↓Next, in detail
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20Circulating power is 800 W
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V-I. Triangular Cavity
• Triangular cavityCan use a flat mirror!
Angular (yaw) stability
Angular (pitch) instability
- : align- : misalign
mirror
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V-I. Triangular Cavity
95.0053.02,5
521
5
521
2222
//1
/1222
2
R
LLl
R
l
Lc
P
RdRL
RLL
c
PI wire
circwire
circ
• Yaw stabilityReverse of the coordinate axis
Equations of motion
Stability condition
common differential
- : align- : misalign
Demonstration of the stability.
a → movable b,c → fixed
↓
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V-I. Triangular Cavity
• Pitch instabilitySimilar to the linear FPNo reverse of the coordinate axis
bb RR
d
RLR
02
020
0)(2
95.0053.0
2)1(
2
2
R
L
d
R
LR
c
PI wire
circ Equations of motion
a → movable b,c → fixed
↓
↓~ 4e-7 N m (100 W, R=1 m, L=10 cm)
~ 4e-7 N m (23 mg mirror)↑
Stability condition
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V-II. DemonstrationTungsten Φ20 umL=2 cmΚ=1.25e-7 N m Flat
Φ12.7 mmh=6.35 mmM=1.77 gI=2.41e-8 kg m^2
Resonance frequency is 365 mHz
Round trip length ~ 10 cmFinesse ~ 250Power gain ~ 100Round trip loss ~ 0.007Mode match ~ 0.8Input power ~ 1 W
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Suspended mirror
Photo-detector
Sound-proofing
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Doughnut-shaped Neodymium magnetΦ8×Φ4×5
Cylindrical Oxygen-Free CopperΦ2×3
Piezo mounted mirror
Eddy current dumping
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V-III. Aerogel Mirror
• What is the aerogel?→materials in which the typical structure of the pores and the network is largely maintained while the pore liquid of a gel is replaced by air
The samples were prepared at university of Kyoto.(Inorganic Chemistry of Materials Laboratory)
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V-III. Aerogel Mirror
• How to make the aerogel?Supercritical drying technique
Natural drying ↑Meniscus
↑phase diagram
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V-III. Aerogel Mirror
• Physical propertySilica aerogel Silica Unit
Density 3~500 2000 Kg/m^3
Poisson’s ratio 0.17 0.17 -
Young’s modulus 1e-3~100e-3 72.4 GPa
Coefficient of thermal expansion 4e-6 5.5e-7 1/K
Specific heat capacity 840 670 J/kg/K
Thermal conductivity 0.017~0.021 1.4 J/m/s/K
Mechanical quality factor ~1000@100 g/cm^3 1e5 -
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V-III. Aerogel Mirror
• Structurea. Colloidal gel
b. Polymeric gel
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V-III. Aerogel Mirror
• Mechanical quality factor of silica aerogel
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V-III. Aerogel Mirror
• How to make a good mirror? (finesse > 1000)• Polishinghydrophilic aerogel → freon or dry nitrogen gas (`slurry’ gas, it is impossible to use water) & diamond lapping film (~0.3 um roughness) (fixed abrasive machining technique)hydrophobic aerogel → OSCAR polishing (slurry) (free abrasive machining technique)
• CoatingDielectric multilayer will be prepared by ion beam sputtering
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V-III. Aerogel Mirror
Physical property of aerogel density 100 kg/m⇒ 3 , Young’s modulus 30 MPa , Q factor30035
10-11
10-12
10-13
10-14
Q factor 2000Q factor 300
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VI. Summary
• Opt-mechanical system→interesting system to study quantum physics
• Triangular cavity→decrease the stiffness without being induced instability
• Aerogel mirror→more sensitive mirror