Interferometer as a New Field of a Quantum

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. 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 ΔX 1: fluctuations of the amplitude quadrature → induce a radiation pressure noise ΔX 2: fluctuations of the phase quadrature → induce a shot noise ΔX 1=ΔX 2 (vacuum state) ↓　　　　　　 Standard quantum limit 　　　 (SQL) →ultimate limit ΔX 1 or ΔX 2 <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 ↓ ↓ → classical effect radiation pressure of light → DC power → 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 Ø 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) Φ 30 mm Width 1. 5 mm Q ~ 7. 5 e 5 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. 5 e 5 with 300 K Membrane ~100 ng ~100 k. Hz Much tolerance ~10^6~10^7 with 1 K

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 k. W, m=2. 3 mg, Q=1 e 4) SN~10 with 300 K (P_circ~1 k. W, m=23 mg, Q=1 e 5) Can not observe with 300 K (P_circ~100 m. W, m=23 mg, Q=1 e 5) 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 Demonstration of the stability. a → movable 　　　　b, c → fixed ↓ Equations of motion Stability condition common differential - : align - : misalign

V-I. Triangular Cavity • Pitch instability Similar to the linear FP No reverse of the coordinate axis a → movable 　　　　b, c → fixed ↓ Equations of motion Stability condition ～ 4 e-7 N m (23 mg mirror) ↑ ↓ ～ 4 e-7 N m (100 W, R=1 m, L=10 cm)

V-II. Demonstration Tungsten Φ 20 um L=2 cm Κ=1. 25 e-7 N m Resonance frequency is 365 m. Hz Flat Φ 12. 7 mm h=6. 35 mm M=1. 77 g I=2. 41 e-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 Φ 2× 3 Eddy current dumping Doughnut-shaped Neodymium magnet Φ 8×Φ 4× 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 - Young’s modulus 1 e-3~100 e-3 72. 4 GPa Coefficient of thermal expansion 4 e-6 5. 5 e-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 1 e 5 -

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 35 Physical property of aerogel ⇒ density 100 kg/m 3 , Young’s modulus 30 MPa , Q 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