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 < 1 m
• high frequency mechanical modes f > GHz
• low mode stiffness keff < 1000 N/m
• millikelvin temperatures T kB / 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 keff
• enhanced displacement
low frequency ( f ~ 10 MHz ) resonance modes – cantilevers inactive
high frequency ( f > 1 GHz ) collective mode
collective mode
fundamental torsional second harmonic
L = 10.7 m
l = 1 m
sample 4
PNA
x
B
I ()F
22 2 2 20 0
1 ( )
( )
emfV I LB
LB MQ
Magnetomotive Measurement
L = 10.7 m
Tmix = 110 mK
50
z
y
22 2 2 20 0
1 ( )
( )
emfV I LB
LB MQ
Magnetomotive Measurement
2 2
2( )emf
QL BV I
M
0on resonance
220
20
( )emf
QL IV B
M
2
( )emfV QI LB
LB M
2emfV B
eff
QFx
k
Hooke’s Law B2 dependence
Reemf
dxV BL BLx
dt
L
x
Linear Harmonic Oscillator
1.5 GHz Collective Mode Tmix = 1000 mK
12
1.48 GHz
Q ~ 150
188 N/m
10 m
1000 mK
eff
eff
mix
f
k
x
T
B2 DEPENDENCE:[unreliable due to small range of B]noisy at lower driveshigh driving power = - 83 dBmnon-ideal peak shape
HOOKE’S LAW:drive force range > 2 orders of magnitude in powernonlinear at higher drives
High Frequency Collective ModeTmix = 110 mK
expected freq shift with temperature
discrete transtions ofresponse peak betweentwo states, (A and D)
linear Lorentzian response
jump size: Vemf ~ 500 nV
1.49 GHz
Q ~ 150
110 mKmix
f
T
Is It a Nonlinear Switch?
23.50 23.52 23.54 23.56 23.58 23.60
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
Sweep U p
Sweep Down
Vem
f (V
)
Frequency (M Hz)
-0.02
0.00
0.02
Am
plitu
de (m
V)
20000 30000 40000 500000
2
Time (sec)
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 ModeTmix = 110 mK
reproducible transition onup and down drive sweep
possible transitions tointermediate state
prepare system in upper statehold all parameters constant
observed spontaneoustransition upper lowertime scale: minutes
no further observedtransitions lower upperwithin the measurement time
sweep upsweep down
upper state
lower state
Summary: Facts
90
th
high
0
1.5 10 Hz
N
T 100
14
0 mK
B
f
k T
h f
90
th0
low
1.5 10 Hz
N
T 11
1
0 mK
B
f
k T
h f
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)
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. http://nano.bu.edu/