Introduction to Nanomechanics (Spring 2012) Martino Poggio

Cooling Mechanical Resonators Achieve ultimate force resolution Approach the quantum regime Measure mechanical superpositions and coherences Introduction to Nanomechanics2

Superposition & Coherence? Introduction to Nanomechanics

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

Introduction to Nanomechanics5 T (K) x rms (x zp )

“Brute Force” Introduction to Nanomechanics

Real Numbers (T = 1 K) Top-down doubly clamped beams (Schwab) m = kg  = 2  x 10 MHz x th = 2 x m x zp = 3 x m Introduction to Nanomechanics

Real Numbers (T = 1 K) Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = kg  = 2  x 500 MHz x th = 4 x m x zp = 4 x m Introduction to Nanomechanics

Real Numbers (T = 1 K) Top-down doubly clamped beams (Schwab) m = kg  = 2  x 10 MHz x th = 2 x m x zp = 3 x m Bottom-up doubly clamped “clean” nanotubes (Steele/Delft) m = kg  = 2  x 500 MHz x th = 4 x m x zp = 4 x m Introduction to Nanomechanics

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

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

Introduction to Nanomechanics

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

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

fiber interferometer spectrum analyzer piezo cantilever Usual Cantilever Motion Detection

fiber interferometer spectrum analyzer damping piezo cantilever Simple Electronic Damping

Frequency (Hz) E-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

Frequency (Hz) E-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

Frequency (Hz) E-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

Frequency (Hz) E-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

Frequency (Hz) E-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

Frequency (Hz) E-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

Frequency (Hz) E-3 1E-4 1E-5 T mode = mK Q eff = 15 Sprectral density (Å 2 /Hz) Cooling (damping) of a cantilever - T = 4.2K g = 3043 Interferometer shot noise level

Frequency (Hz) 4250 Sprectral density (Å 2 /Hz) E-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

fiber interferometer spectrum analyzer damping piezo cantilever Experimental setup measurement noise

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

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

Frequency (Hz) 4250 Spectral density (Å 2 /Hz) E-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

g 3000 T mode (mK) T = 4.2 K Q 0 = 45,660 Theoretical Limit T mode, min = 4.6 mK Q eff = 36 Cooling (damping) of a cantilever – model and experiment

Theoretical Limit g T mode (K) 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