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 < 1  m high frequency mechanical modes f > GHz low mode stiffness k eff < 1000 N/m millikelvin temperatures T  k B / h f 10.7  m 0.5  m 0.2  m

3. Finite Element Modal Simulation in phase cantilever motion strain - coupling to central beam low k eff enhanced displacement low frequency ( f ~ 10 MHz ) resonance modes – cantilevers inactive high frequency ( f > 1 GHz ) collective mode collective mode fundamentaltorsionalsecond harmonic L = 10.7  m l = 1  m

4. Finite-Element Simulation of the Collective Mode back

5. sample 4 PNA x B I (  ) F Magnetomotive Measurement L = 10.7  m T mix = 110 mK 50  z y

6. Magnetomotive Measurement Hooke’s LawB 2 dependence L x Linear Harmonic Oscillator

7. Low Order Mode T mix = 60 mK

8. 1.5 GHz Collective Mode T mix = 1000 mK B 2 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 T mix = 110 mK expected freq shift with temperature discrete transtions of response peak between two states, (A and D) linear Lorentzian response jump size: V emf ~ 500 nV

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

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

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 *^_^*