Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators

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Evidence for Quantized Displacement in
Macroscopic Nanomechanical Oscillators

• CHEN, MU

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Discrete Response at Millikelvin Temperatures in
Nanomechanical Oscillators

• ANTENNA OSCILLATOR
• single crystal silicon
• coupled cantilevers
• l lt 1 mm
• high frequency
• mechanical modes
• f gt GHz
• low mode stiffness
• keff lt 1000 N/m
• millikelvin temperatures
• T ? kB / h f

0.2 mm
10.7 mm
0.5 mm
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Finite Element Modal Simulation
low frequency ( f 10 MHz ) resonance modes
cantilevers inactive
fundamental
torsional
second harmonic
high frequency ( f gt 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
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Magnetomotive Measurement
PNA
50 ??
Tmix 110 mK
L 10.7 mm
sample 4
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Magnetomotive Measurement
Linear Harmonic Oscillator
Hookes Law
B2 dependence
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Low Order Mode
Tmix 60 mK
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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
HOOKES LAW drive force range gt 2 orders of
magnitude in power nonlinear at higher drives
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expected freq shift with temperature discrete
transtions of response peak between two states,
(A and D) linear Lorentzian response jump size
Vemf 500 nV
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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
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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
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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)

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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.

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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/
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THE END Thank You _