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 11.04.2012Introduction to Nanomechanics2

3. Superposition & Coherence? Introduction to Nanomechanics311.04.2012

4. Strategies for Cooling Resonators “Brute force”: High resonance frequencies & low reservoir temperatures Damping mechanical motion Cavity cooling Introduction to Nanomechanics411.04.2012

5. Introduction to Nanomechanics5 T (K) x rms (x zp ) 11.04.2012

6. “Brute Force” Introduction to Nanomechanics611.04.2012

7. Real Numbers (T = 1 K) Top-down doubly clamped beams (Schwab) m = 10 -15 kg  = 2  x 10 MHz x th = 2 x 10 -12 m x zp = 3 x 10 -14 m Introduction to Nanomechanics711.04.2012

8. Real Numbers (T = 1 K) Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = 10 -21 kg  = 2  x 500 MHz x th = 4 x 10 -11 m x zp = 4 x 10 -12 m Introduction to Nanomechanics811.04.2012

9. Real Numbers (T = 1 K) Top-down doubly clamped beams (Schwab) m = 10 -15 kg  = 2  x 10 MHz x th = 2 x 10 -12 m x zp = 3 x 10 -14 m Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = 10 -21 kg  = 2  x 500 MHz x th = 4 x 10 -11 m x zp = 4 x 10 -12 m Introduction to Nanomechanics911.04.2012

10. Real Numbers (T = 10 mK) Top-down doubly clamped Si beams (Schwab) m = 10 -15 kg  = 2  x 10 MHz x th = 2 x 10 -13 m x zp = 3 x 10 -14 m Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = 10 -21 kg  = 2  x 500 MHz x th = 4 x 10 -12 m x zp = 4 x 10 -12 m Introduction to Nanomechanics1011.04.2012

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 Nanomechanics1111.04.2012

12. Introduction to Nanomechanics1211.04.2012

13. Expectation vs. Reality Introduction to Nanomechanics13 T (K) N th 11.04.2012

14. Strategies for Cooling Resonators “Brute force”: High resonance frequencies & low reservoir temperatures Damping mechanical motion Cavity cooling Introduction to Nanomechanics1411.04.2012

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

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

17. 350037504000 Frequency (Hz) 4250 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = 3.8 K Q 0 = 45,660 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 0 Interferometer shot noise level

18. 350037504000 Frequency (Hz) 4250 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = 530 mK Q eff = 5,834 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 6.8 Interferometer shot noise level

19. 350037504000 Frequency (Hz) 4250 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = 71 mK Q eff = 674 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 67 Interferometer shot noise level

20. 350037504000 Frequency (Hz) 4250 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = 13 mK Q eff = 173 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 263 Interferometer shot noise level

21. 350037504000 Frequency (Hz) 4250 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = 5.3 mK Q eff = 87 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 525 Interferometer shot noise level

22. 350037504000 Frequency (Hz) 4250 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = 0.62 mK Q = 36 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 1267 Interferometer shot noise level

23. 350037504000 Frequency (Hz) 4250 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = -0.25 mK Q eff = 15 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 3043 Interferometer shot noise level

24. 350037504000 Frequency (Hz) 4250 Sprectral density (Å 2 /Hz) 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T mode = -3.0 mK Q eff = 10 Cooling (damping) of a cantilever - T = 4.2K g = 4565 Mechanical feedback can cancel photon shot noise! Negative mode temperature?! Interferometer shot noise level

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

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

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

28. 350037504000 Frequency (Hz) 4250 Spectral density (Å 2 /Hz) 1000 100 10 1 0.1 0.01 1E-3 1E-4 1E-5 T = 4.2 K T mode = 5.3 K T mode = 530 mK T mode = 73 mK T mode = 16 mK T mode = 4.6 mK T mode = 8.3 mK T mode = 5.3 mK T mode = 9.3 mK Cooling (damping) of a cantilever - T = 4.2K → 4.6mK

29. 01000 2000 g 3000 T mode (mK) 0.1 400050006000 T = 4.2 K Q 0 = 45,660 Theoretical Limit 1 10 100 1000 10000 T mode, min = 4.6 mK Q eff = 36 Cooling (damping) of a cantilever – model and experiment

30. Theoretical Limit 02000 g T mode (K) 10 1 10 0 10 -1 10 -2 10 -3 40006000 T = 295 K T mode = 2.9 mK T = 4.2 K T = 2.2 K 10 2 Cooling (damping) of a cantilever – model and experiment