Slide 1

Introduction to Nanomechanics(Spring 2012)Martino Poggio1Cooling Mechanical ResonatorsAchieve ultimate force resolutionApproach the quantum regimeMeasure mechanical superpositions and coherences

11.04.2012Introduction to Nanomechanics2

2Superposition & Coherence?Introduction to Nanomechanics3

11.04.20123Strategies for Cooling ResonatorsBrute force: High resonance frequencies & low reservoir temperaturesDamping mechanical motionCavity coolingIntroduction to Nanomechanics4

11.04.20124Introduction to Nanomechanics5T (K)xrms (xzp)

11.04.20125Brute ForceIntroduction to Nanomechanics6

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Real Numbers (T = 1 K)Top-down doubly clamped beams (Schwab)m = 10-15 kg = 2 x 10 MHz

xth = 2 x 10-12 mxzp= 3 x 10-14 mIntroduction to Nanomechanics711.04.20127Real 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 mxzp = 4 x 10-12 m

Introduction to Nanomechanics8

11.04.20128Real Numbers (T = 1 K)Top-down doubly clamped beams (Schwab)m = 10-15 kg = 2 x 10 MHz

xth = 2 x 10-12 mxzp= 3 x 10-14 mBottom-up doubly clamped clean nanotubes (Steele/Delft)m = 10-21 kg = 2 x 500 MHz

xth= 4 x 10-11 mxzp = 4 x 10-12 m

Introduction to Nanomechanics911.04.20129Real Numbers (T = 10 mK)Top-down doubly clamped Si beams (Schwab)m = 10-15 kg = 2 x 10 MHz

xth = 2 x 10-13 mxzp= 3 x 10-14 mBottom-up doubly clamped clean nanotubes (Steele/Delft)m = 10-21 kg = 2 x 500 MHz

xth= 4 x 10-12 mxzp = 4 x 10-12 m

Introduction to Nanomechanics1011.04.201210Technical ChallengesResonator Fabrication (high frequency, low dissipation, low mass)Displacement sensing (low measurement imprecision, i.e. low noise floor)Refrigeration (mK temperatures)

Introduction to Nanomechanics1111.04.201211Introduction to Nanomechanics12

11.04.201212Expectation vs. RealityIntroduction to Nanomechanics13T (K)Nth

11.04.201213Strategies for Cooling ResonatorsBrute force: High resonance frequencies & low reservoir temperaturesDamping mechanical motionCavity coolingIntroduction to Nanomechanics14

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fiber interferometerspectrum analyzerpiezocantileverUsual Cantilever Motion Detection15

fiber interferometerspectrum analyzerdampingpiezocantileverSimple Electronic Damping16

350037504000Frequency (Hz)425010001001010.10.011E-31E-41E-5Tmode = 3.8 KQ0 = 45,660Sprectral density (2/Hz)Cooling (damping) of a cantilever - T = 4.2Kg = 0Interferometer shot noise level17

350037504000Frequency (Hz)425010001001010.10.011E-31E-41E-5Tmode = 530 mKQeff = 5,834Sprectral density (2/Hz)Cooling (damping) of a cantilever - T = 4.2Kg = 6.8Interferometer shot noise level18

350037504000Frequency (Hz)425010001001010.10.011E-31E-41E-5Tmode = 71 mKQeff = 674Sprectral density (2/Hz)Cooling (damping) of a cantilever - T = 4.2Kg = 67Interferometer shot noise level19

350037504000Frequency (Hz)425010001001010.10.011E-31E-41E-5Tmode = 13 mKQeff = 173Sprectral density (2/Hz)Cooling (damping) of a cantilever - T = 4.2Kg = 263Interferometer shot noise level20

350037504000Frequency (Hz)425010001001010.10.011E-31E-41E-5Tmode = 5.3 mKQeff = 87Sprectral density (2/Hz)Cooling (damping) of a cantilever - T = 4.2Kg = 525Interferometer shot noise level21

350037504000Frequency (Hz)425010001001010.10.011E-31E-41E-5Tmode = 0.62 mKQ = 36Sprectral density (2/Hz)Cooling (damping) of a cantilever - T = 4.2Kg = 1267Interferometer shot noise level22

350037504000Frequency (Hz)425010001001010.10.011E-31E-41E-5Tmode = -0.25 mKQeff = 15Sprectral density (2/Hz)Cooling (damping) of a cantilever - T = 4.2Kg = 3043Interferometer shot noise level23

350037504000Frequency (Hz)4250Sprectral density (2/Hz)10001001010.10.011E-31E-41E-5Tmode = -3.0 mKQeff = 10Cooling (damping) of a cantilever - T = 4.2Kg = 4565Mechanical feedback can cancel photon shot noise!Negative mode temperature?!Interferometer shot noise level24

fiber interferometerspectrum analyzerdampingpiezocantileverExperimental setupmeasurement noise

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Measured spectral density:Effective Q with feedback:Actual cantilever spectral density:Cantilever mode temperature:Cantilever Noise Temperature with Feedback26

Measured spectral density:Effective Q with feedback:Actual cantilever spectral density:Cantilever mode temperature:For optimumfeedback gainCantilever Noise Temperature with Feedback27

350037504000Frequency (Hz)4250Spectral density (2/Hz)10001001010.10.011E-31E-41E-5T = 4.2 KTmode = 5.3 KTmode = 530 mKTmode = 73 mKTmode = 16 mKTmode = 4.6 mKTmode = 8.3 mKTmode = 5.3 mKTmode = 9.3 mKCooling (damping) of a cantilever - T = 4.2K 4.6mK28

010002000g3000Tmode (mK)0.1400050006000T = 4.2 K Q0 = 45,660Theoretical Limit110100100010000Tmode, min = 4.6 mKQeff = 36Cooling (damping) of a cantilever model and experiment29

Theoretical Limit02000gTmode (K)10110010-110-210-340006000T = 295 KTmode = 2.9 mKT = 4.2 KT = 2.2 K102Cooling (damping) of a cantilever model and experiment30