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Interferometer as a New F ield of a Quantum P hysics - the Macroscopic Quantum System - . Nobuyuki Matsumoto Tsubono lab University of Tokyo. Elites Thermal Noise Workshop @ University of Jena Aug 21, 2012. - PowerPoint PPT Presentation
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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
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
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!
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)
Outline
I. IntroductionII. Effect of a radiation pressure forceIII. Radiation Pressure InterferometerIV. Prior ResearchV. Our ProposalVI. Summary
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)
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
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) ↑
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
II. Effect of a radiation pressure force
• Optical spring effect Fixed mirror
Movable mirror
Spring effect
PHYSICAL REVIEW A 69, 051801(R) (2004)
II. Effect of a radiation pressure force
• Siddles-Sigg Instability (anti-spring effect)
PHYSICAL REVIEW D 81, 064023 (2010)
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
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
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
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
IV. Prior Research
• MEMSwidth
Mass ~ 100 ngQ ~ 10^6-10^7
PHYSICAL REVIEW A 81, 033849 (2010)
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
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
V. Our Proposal
Frequency [Hz]
Disp
lace
men
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
20Circulating power is 800 W
V-I. Triangular Cavity
• Triangular cavityCan use a flat mirror!
Angular (yaw) stability
Angular (pitch) instability
- : align- : misalign
mirror
V-I. Triangular Cavity
95.0053.02,5521
5521
2222//1
/12222
RLLl
Rl
LcP
RdRLRLL
cPI 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
↓
V-I. Triangular Cavity
• Pitch instabilitySimilar to the linear FPNo reverse of the coordinate axis
bb RRd
RLR
02020
0)(2
95.0053.0
2)1(
22
RL
dRLR
cPI wirecirc 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
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
Suspended mirror
Photo-detector
Sound-proofing
Doughnut-shaped Neodymium magnetΦ8×Φ4×5
Cylindrical Oxygen-Free CopperΦ2×3
Piezo mounted mirror
Eddy current dumping
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)
V-III. Aerogel Mirror
• How to make the aerogel?Supercritical drying technique
Natural drying ↑Meniscus
↑phase diagram
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 -
V-III. Aerogel Mirror
• Structurea. Colloidal gel
b. Polymeric gel
V-III. Aerogel Mirror
• Mechanical quality factor of silica aerogel
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
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
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