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Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators

Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators. CHEN, MU. Discrete Response at Millikelvin Temperatures in Nanomechanical Oscillators. ANTENNA OSCILLATOR single crystal silicon coupled cantilevers l < 1 m m high frequency mechanical modes

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Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators

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  1. Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators CHEN, MU

  2. Discrete Response at Millikelvin Temperatures in Nanomechanical Oscillators • ANTENNA OSCILLATOR • single crystal silicon • coupled cantilevers • l < 1mm • high frequency • mechanical modes • f> GHz • low mode stiffness • keff < 1000 N/m • millikelvin temperatures • T kB / hf 0.2 mm 10.7 mm 0.5 mm

  3. Finite Element Modal Simulation low frequency ( f ~ 10 MHz ) resonance modes – cantilevers inactive fundamental torsional second harmonic high frequency ( f > 1 GHz ) collective mode collective mode • in phase cantilever motion • strain - coupling to • central beam • low keff • enhanced displacement L = 10.7 mm l = 1 mm

  4. back Finite-Element Simulation of the Collective Mode

  5. B I (w) F x y z Magnetomotive Measurement PNA 50  Tmix = 110 mK L = 10.7 mm sample 4

  6. Magnetomotive Measurement x L Linear Harmonic Oscillator Hooke’s Law B2 dependence

  7. Low Order Mode Tmix = 60 mK

  8. 1.5 GHz Collective Mode Tmix = 1000 mK B2 DEPENDENCE: [unreliable due to small range of B] noisy at lower drives high driving power = - 83 dBm non-ideal peak shape HOOKE’S LAW: drive force range > 2 orders of magnitude in power nonlinear at higher drives

  9. High Frequency Collective Mode Tmix = 110 mK expected freq shift with temperature discrete transtions of response peak between two states, (A and D) linear Lorentzian response jump size: Vemf ~ 500 nV

  10. Is It a Nonlinear Switch? a typical example of classical nonlinearity: 23 MHz at 300 mK the observed discrete response is not the standard classical nonlinearity Badzey, et al. APL 85, 3587 (2004) linear response with Lorentzian lineshape

  11. High Frequency Collective Mode Tmix = 110 mK • reproducible transition on • up and down drive sweep • possible transitions to • intermediate state • prepare system in upper state • hold all parameters constant • observed spontaneous • transition upper  lower • time scale: minutes • no further observed • transitions lower  upper • within the measurement time sweep up sweep down upper state lower state

  12. vibration Summary: Facts • 1.5 GHz resonance peak • classical magnetomotive response -- Tmix = 1000 mK • non-classical discrete response -- Tmix = 110 mK • rule out nonlinear bistability (linear Lorentizan peak) • electrical artifacts (T dep., reproducible) • magnetic drive effects (const. mag. field, vary current)

  13. Applications • This device, pushing nanotechnology forward into the realm of quantum mechanics, can help further miniaturize wireless communication devices like cell phones. • This setup shielded the experiment from unwanted vibration noise and electromagnetic radiation that could generate from outside electrical devices, such as the movement of subway trains outside the building.

  14. Reference [1] Alexei Gaidarzhy, Guiti Zolfagharkhani, Robert L. Badzey, and Pritiraj Mohanty, Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators, Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA. (Jan, 2005) [2] Research in nanotechnology, MOHANTY GROUP. http://nano.bu.edu/

  15. THE END Thank You *^_^*

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