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Strategies for Nanomechanics: Cooling Resonators and Achieving Quantum Regime

Dive into the world of nanomechanics to explore cooling strategies, achieve ultimate force resolution, measure mechanical superpositions, and approach the quantum regime. Learn about the technical challenges, fabrication, displacement sensing, and refrigeration techniques involved in this fascinating field. Discover the strategies for cooling resonators using high resonance frequencies, damping mechanical motion, and cavity cooling. Explore the possibilities of cold temperatures as low as millikelvin and the interplay between theoretical limits and experimental results. Join the frontier of nanomechanics and witness the convergence of expectation and reality in this cutting-edge scientific pursuit.

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Strategies for Nanomechanics: Cooling Resonators and Achieving Quantum Regime

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  1. Introduction to Nanomechanics(Spring 2012) Martino Poggio

  2. Cooling Mechanical Resonators • Achieve ultimate force resolution • Approach the quantum regime • Measure mechanical superpositions and coherences Introduction to Nanomechanics

  3. Superposition & Coherence? Introduction to Nanomechanics

  4. Strategies for Cooling Resonators • “Brute force”: High resonance frequencies & low reservoir temperatures • Damping mechanical motion • Cavity cooling Introduction to Nanomechanics

  5. xrms (xzp) T (K) Introduction to Nanomechanics

  6. “Brute Force” Introduction to Nanomechanics

  7. Real Numbers (T = 1 K) Top-down doubly clamped beams (Schwab) • m = 10-15 kg •  = 2 x 10 MHz • xth= 2 x 10-12 m • xzp= 3 x 10-14 m Introduction to Nanomechanics

  8. Real Numbers (T = 1 K) Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = 10-21 kg  = 2 x 500 MHz xth= 4 x 10-11 m xzp= 4 x 10-12 m Introduction to Nanomechanics

  9. Real Numbers (T = 1 K) Top-down doubly clamped beams (Schwab) Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = 10-21 kg  = 2 x 500 MHz xth= 4 x 10-11 m xzp= 4 x 10-12 m • m = 10-15 kg •  = 2 x 10 MHz • xth= 2 x 10-12 m • xzp= 3 x 10-14 m Introduction to Nanomechanics

  10. Real Numbers (T = 10 mK) Top-down doubly clamped Si beams (Schwab) Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = 10-21 kg  = 2 x 500 MHz xth= 4 x 10-12 m xzp= 4 x 10-12 m • m = 10-15 kg •  = 2 x 10 MHz • xth= 2 x 10-13 m • xzp= 3 x 10-14 m Introduction to Nanomechanics

  11. Technical Challenges • Resonator Fabrication (high frequency, low dissipation, low mass) • Displacement sensing (low measurement imprecision, i.e. low noise floor) • Refrigeration (mK temperatures) Introduction to Nanomechanics

  12. Introduction to Nanomechanics

  13. Expectation vs. Reality Nth T (K) Introduction to Nanomechanics

  14. Strategies for Cooling Resonators • “Brute force”: High resonance frequencies & low reservoir temperatures • Damping mechanical motion • Cavity cooling Introduction to Nanomechanics

  15. Usual Cantilever Motion Detection fiber interferometer cantilever spectrum analyzer piezo

  16. damping Simple Electronic Damping fiber interferometer cantilever spectrum analyzer piezo

  17. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 0 Tmode = 3.8 K Q0 = 45,660 100 10 1 0.1 Sprectral density (Å2/Hz) 0.01 1E-3 Interferometer shot noise level 1E-4 1E-5 3500 3750 4000 4250 Frequency (Hz)

  18. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 6.8 100 10 Tmode = 530 mK Qeff = 5,834 1 0.1 Sprectral density (Å2/Hz) 0.01 1E-3 Interferometer shot noise level 1E-4 1E-5 3500 3750 4000 4250 Frequency (Hz)

  19. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 67 100 10 1 0.1 Tmode = 71 mK Qeff = 674 Sprectral density (Å2/Hz) 0.01 1E-3 Interferometer shot noise level 1E-4 1E-5 3500 3750 4000 4250 Frequency (Hz)

  20. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 263 100 10 1 0.1 Sprectral density (Å2/Hz) 0.01 Tmode = 13 mK Qeff = 173 1E-3 Interferometer shot noise level 1E-4 1E-5 3500 3750 4000 4250 Frequency (Hz)

  21. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 525 100 10 1 0.1 Sprectral density (Å2/Hz) 0.01 Tmode = 5.3 mK Qeff = 87 1E-3 Interferometer shot noise level 1E-4 1E-5 3500 3750 4000 4250 Frequency (Hz)

  22. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 1267 100 10 1 0.1 Sprectral density (Å2/Hz) 0.01 Tmode = 0.62 mK Q = 36 1E-3 Interferometer shot noise level 1E-4 1E-5 3500 3750 4000 4250 Frequency (Hz)

  23. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 3043 100 10 1 0.1 Sprectral density (Å2/Hz) 0.01 1E-3 Interferometer shot noise level 1E-4 Tmode = -0.25 mK Qeff = 15 1E-5 3500 3750 4000 4250 Frequency (Hz)

  24. Cooling (damping) of a cantilever - T = 4.2K 1000 g = 4565 100 Mechanical feedback can cancel photon shot noise! Negative mode temperature?! 10 1 0.1 Sprectral density (Å2/Hz) 0.01 1E-3 Interferometer shot noise level 1E-4 Tmode = -3.0 mK Qeff = 10 1E-5 3500 3750 4000 4250 Frequency (Hz)

  25. damping measurement noise Experimental setup fiber interferometer cantilever spectrum analyzer piezo

  26. Cantilever Noise Temperature with Feedback Effective Q with feedback: Measured spectral density: Actual cantilever spectral density: Cantilever mode temperature:

  27. Cantilever Noise Temperature with Feedback Effective Q with feedback: Measured spectral density: Actual cantilever spectral density: Cantilever mode temperature: For optimum feedback gain

  28. Cooling (damping) of a cantilever - T = 4.2K → 4.6mK 1000 T = 4.2 K Tmode = 5.3 K 100 10 Tmode = 530 mK 1 0.1 Tmode = 73 mK Spectral density (Å2/Hz) 0.01 Tmode = 16 mK Tmode = 8.3 mK 1E-3 Tmode = 4.6 mK 1E-4 Tmode = 5.3 mK Tmode = 9.3 mK 1E-5 3500 3750 4000 4250 Frequency (Hz)

  29. Cooling (damping) of a cantilever – model and experiment 10000 T = 4.2 K Q0 = 45,660 1000 Tmode, min = 4.6 mK Qeff = 36 100 Tmode (mK) 10 Theoretical Limit 1 0.1 0 1000 3000 4000 5000 6000 2000 g

  30. Cooling (damping) of a cantilever – model and experiment 102 101 100 Tmode (K) T = 295 K 10-1 Tmode = 2.9 mK 10-2 T = 4.2 K T = 2.2 K Theoretical Limit 10-3 0 2000 4000 6000 g

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