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 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

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

Finite-Element Simulation of the Collective Mode back

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

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

Low Order Mode T mix = 60 mK

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

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

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

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

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

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.

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.

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