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 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

Finite-Element Simulation of the Collective Mode

back

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

Low Order Mode

0 21 MHz

11000

330 N/m

60 mK

eff

mix

f

Q

k

T

Tmix = 60 mK

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/

THE END

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