Download 2012-8-21@Germany

Interferometer as a New Field of a
Quantum Physics
- the Macroscopic Quantum System -
Nobuyuki Matsumoto
Tsubono 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
Goal
Providing a new field to study quantum physics
Ex.
i. Studying a quantum de-coherence
ii. Generation of a macroscopic “cat state”
iii. Generation of a squeezed light
Requirement
Observation of a Quantum Radiation Pressure
Fluctuations (QRPF)
Outline
I.
II.
III.
IV.
V.
VI.
Introduction
Effect of a radiation pressure force
Radiation Pressure Interferometer
Prior Research
Our Proposal
Summary
I. Introduction
• What is the light?
Wave-particle duality
↓
Uncertainty principle
ΔX1:fluctuations of the amplitude quadrature → induce a radiation pressure noise
ΔX2:fluctuations of the phase quadrature → induce a shot noise
ΔX1=ΔX2 (vacuum state)
↓
Standard quantum limit
(SQL)
→ultimate limit
ΔX1 or ΔX2 <1 (squeezed state)
↓
quantum non-demolition
measurement (QND)
→surpassing the SQL
I. Introduction
• Quantum effect in a gravitational detector
→quantum noise originated by the vacuum
(ground state) fluctuations
DC power + Vacuum Fluctuations
(Quantum Sideband)
common
Laser
Quantum Sideband
PD
differential
I. Introduction
• Generation of the squeezed light & Reduction of
shot noise our squeezed vacuum
generator via χ(2) effect
↑
Optical Parametric Oscillator (OPO)
↓
Down conversion (green → IR)
↑
Nonlinear media (PPKTP)
Seed (1064 nm)↑
↑
↑
↓
↓
↓
Correlated IR light
↓
Pump, Green light (532 nm)
I. Introduction
• Quantum effect in an opt-mechanical system
→QRPF are not noises but signals!
Fixed mirror
→opt-mechanical system
↓
↓ Movable mirror
↓
↓
radiation pressure of light → DC power
→ classical effect
↓
→ power fluctuations →quantum effect
↓
induced by QRPF
↓
Mediation between the mechanical system and the optical system
II. Effect of a radiation pressure force
• Optical spring effect
Fixed mirror
Spring effect
PHYSICAL REVIEW A 69, 051801(R) (2004)
Movable mirror
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 effects
i. Spring effect
ii. Instability
iii. Cooling
And so on・・・
Measured
• Quantum effects
i. Squeezing
ii. Entanglement
iii. QND
And so on・・・
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 mass
low stiffness
high power beam
ii. Siddles-Sigg instability
high stiffness
low power beam
configuration
Technical trade-off
Sensitivity vs Instability
IV. Prior Research
• Suspended tiny mirror (linear FP)
i. High susceptibility due to low stiffness
ii. 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)
Flat mirror
PHYSICAL REVIEW D 81, 064023 (2010)
Φ30 mm
Width
1.5 mm
Q ~ 7.5e5
C. R. Physique 12 (2011) 826–836
IV. Prior Research
• MEMS
width
Mass ~ 100 ng
Q ~ 10^6-10^7
PHYSICAL REVIEW A 81, 033849 (2010)
IV. Prior Research
• Suspended mirror vs membrane
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
1K
V. Our Proposal
• Triangular cavity
Siddels-Sigg instability of yaw motion is eliminated
without increasing the stiffness
• Silica aerogel mirror (low density ~ 0.1 g/cm^3)
More sensitive test mass
Displacement fluctuations
induced by QRPF [m/Hz^1/2]
Linear FP cavity
V. Our Proposal
Triangular cavity
Membrane(MEMS)
SN~4 with 300 K
(aerogel, m=0.23 mg
Q=300)
↓
Next, in detail
SN~10 with 300 K
(P_circ~1 kW, m=2.3 mg, Q=1e4)
SN~10 with 300 K
(P_circ~1 kW, m=23 mg, Q=1e5)
Can not observe with 300 K
(P_circ~100 mW, m=23 mg, Q=1e5)
SN~2 with 1 K
Frequency [Hz]
Circulating power is 800 W
20
V-I. Triangular Cavity
- : align
- : misalign
• Triangular cavity
Can use a flat mirror!
mirror
Angular (yaw) stability
Angular (pitch) instability
V-I. Triangular Cavity
• Yaw stability
Reverse of the
coordinate axis
common
differential
- : align
- : misalign
Demonstration of the stability.
a → movable
b,c → fixed
↓
Equations of motion I   2 Pcirc  2 2 L  2
c 
Stability condition
1


1 L / R
2P

   wire   circ 2 2 L  2    wire
1 L / R  d / R 
c
2 5 l
2 5
L
  1
, l  2 L  0.053   0.95
5
R
5
R
V-I. Triangular Cavity
• Pitch instability
Similar to the linear FP
No reverse of the coordinate axis
a → movable
b,c → fixed
   
  
    
  
 b 

2 ( R  L)
0
 2R
↓
Equations of motion I  2 Pcirc 

c 
Stability condition 0.053  L 
R
0
 2d
0
R    


0    


R

b



～4e-7 N m (23 mg mirror)
↑
R
L
d 
(1  ) 


 wire

R
2
2
↓
0.95
～4e-7 N m (100 W, R=1 m, L=10 cm)
V-II. Demonstration
Tungsten
Φ20 um
L=2 cm
Κ=1.25e-7 N m
Resonance frequency is 365 mHz
Flat
Φ12.7 mm
h=6.35 mm
M=1.77 g
I=2.41e-8 kg m^2
Round trip length ～ 10 cm
Finesse ～250
Power gain ～100
Round trip loss ～ 0.007
Mode match ～ 0.8
Input power ～ 1 W
Sound-proofing
Suspended mirror
Photo-detector
Piezo mounted mirror
Cylindrical Oxygen-Free Copper
Φ2×3
Eddy current dumping
Doughnut-shaped Neodymium magnet
Φ8×Φ4×5
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
↑phase diagram
Natural drying
↑Meniscus
V-III. Aerogel Mirror
• Physical property
Silica 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
• Structure
a. 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)
• Polishing
hydrophilic 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)
• Coating
Dielectric multilayer will be prepared by ion beam sputtering
10-11
V-III. Aerogel Mirror
Q factor 2000
Q factor 300
10-12
10-13
10-14
Physical property of aerogel ⇒ density 100
kg/m3 ,
35
Young’s modulus 30 MPa , Q factor300
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