1. 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

2. 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

3. 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!

4. 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)

5. Outline I.Introduction II.Effect of a radiation pressure force III.Radiation Pressure Interferometer IV.Prior Research V.Our Proposal VI.Summary

6. 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 noise ΔX2:fluctuations of the phase quadrature → induce a shot noise ΔX1=ΔX2 (vacuum state)ΔX1 or ΔX2 <1 (squeezed state)

7. 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

8. 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) ↑

9. 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

10. II. Effect of a radiation pressure force Optical spring effect Fixed mirror Movable mirror Spring effect PHYSICAL REVIEW A 69, 051801(R) (2004)

11. II. Effect of a radiation pressure force Siddles-Sigg Instability (anti-spring effect) PHYSICAL REVIEW D 81, 064023 (2010)

12. II. Summary of the review Opt-mechanical effects Classical effects i.Spring effect ii.Instability iii.Cooling And so on ・・・ Quantum effects i.Squeezing ii.Entanglement iii.QND And so on ・・・ Measured Not measured No one see even QRPF

13. 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 Technical trade-off Sensitivity vs Instability configuration

14. 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

15. 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

16. IV. Prior Research MEMS width Mass ~ 100 ng Q ~ 10^6-10^7 PHYSICAL REVIEW A 81, 033849 (2010)

17. IV. Prior Research TypeMassResonant frequency instabilityMechanical quality factor Suspended mirror ~10 mg~1 HzInsufficient tolerance ~7.5e5 with 300 K Membrane~100 ng~100 kHzMuch tolerance~10^6~10^7 with 1 K Suspended mirror vs membrane

18. 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

19. V. Our Proposal Frequency [Hz] Displacement fluctuations induced by QRPF [m/Hz^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=23 mg, Q=1e5) 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=2.3 mg, Q=1e4) Can not observe with 300 K (P_circ~100 mW, m=23 mg, Q=1e5) 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) SN~4 with 300 K (aerogel, m=0.23 mg Q=300) Linear FP cavity Triangular cavity Membrane(MEMS) ↓ Next, in detail

20. 20 Circulating power is 800 W

21. V-I. Triangular Cavity Triangular cavity Can use a flat mirror! Angular (yaw) stability Angular (pitch) instability - : align - : misalign mirror

22. V-I. Triangular Cavity Yaw stability Reverse of the coordinate axis Equations of motion Stability condition commondifferential - : align - : misalign Demonstration of the stability. a → movable b,c → fixed ↓

23. V-I. Triangular Cavity Pitch instability Similar to the linear FP No reverse of the coordinate axis 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

24. V-II. Demonstration Tungsten Φ20 um L=2 cm Κ=1.25e-7 N m Flat Φ12.7 mm h=6.35 mm M=1.77 g I=2.41e-8 kg m^2 Resonance frequency is 365 mHz Round trip length ～ 10 cm Finesse ～ 250 Power gain ～ 100 Round trip loss ～ 0.007 Mode match ～ 0.8 Input power ～ 1 W

25. Suspended mirror Photo-detector Sound-proofing

26. Doughnut-shaped Neodymium magnet Φ8×Φ4×5 Cylindrical Oxygen-Free Copper Φ2×3 Piezo mounted mirror Eddy current dumping

29. 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)

30. V-III. Aerogel Mirror How to make the aerogel? Supercritical drying technique Natural drying ↑Meniscus ↑phase diagram

31. V-III. Aerogel Mirror Physical property Silica aerogelSilicaUnit Density3~5002000Kg/m^3 Poisson’s ratio0.17 - Young’s modulus1e-3~100e-372.4GPa Coefficient of thermal expansion4e-65.5e-71/K Specific heat capacity840670J/kg/K Thermal conductivity0.017~0.0211.4J/m/s/K Mechanical quality factor~1000@100 g/cm^31e5-

32. V-III. Aerogel Mirror Structure a.Colloidal gel b.Polymeric gel

33. V-III. Aerogel Mirror Mechanical quality factor of silica aerogel

34. 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

35. V-III. Aerogel Mirror Physical property of aerogel ⇒ density 100 kg/m 3, Young’s modulus 30 MPa, Q factor300 35 10 -11 10 -12 10 -13 10 -14 Q factor 2000 Q factor 300

36. 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