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]

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

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

95.0053.02,5

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

↓

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

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