Download JG-APS-Mar-05 -1D-ch..

Phonon spectrum measured in a
1D Yukawa chain
John Goree & Bin Liu
Modes in 1-D chains
Colloids:
• Polymer microspheres
trapped by counterpropagating laser beams
• Lowest-order modes
(sloshing & breathing
modes) observed
experimentally
Tatarkova, et al., PRL 2002
Carbon nanotubes:
• Xe atoms trapped on a tube
• Theory: phonon spectrum
Cvitas and Siber, PRB 2003
Modes in a 1-D chain
Longitudinal mode
Transverse mode
Experimental system: dusty plasma
Like a colloidal suspension:
• polymer microspheres
• electrically charged
• suspended in medium that
provides screening
• colloidal crystals
• optical methods include:
• direct imaging of particles
• laser manipulation
Experimental system: dusty plasma
The medium is a plasma:
• a low-pressure gas
• partially ionized by applying high voltage
Experimental system: dusty plasma
What’s special about plasma:
Medium is low density:
• gas instead of a solvent
• microspheres are underdamped
Suspension is very soft:
• shear modulus of a 3D crystal is
1019 smaller, as compared to metals
Temperature can be varied:
• not in this talk
Microspheres
Melamine formaldehyde
diameter 8.09 mm
introduced into plasma by
shaking a dispenser
Pair potential
Particles suspended as a monolayer interact with a repulsive Yukawa
potential:
In this experiment:
charge
Q
- 7600 e
screening length lD
0.86 mm
spacing
0.80 mm
a
}
>> particle radius 4 mm
Suspension of Microspheres
Microspheres :
• have no buoyancy
• levitated by electric field
a few mm above
electrode substrate
• form horizontal
monolayer
• no out-of-plane buckling
is observed
QE
• ordered lattice
mg
electrode
substrate
Setup:
video camera
(top view)
scanning
mirror
microsphere
RF
lower electrode
Ar laser beam 2
lase beam1
Ar laser
beam 1
Making a one-dimensional chain
“Channel” on substrate to confine a chain
Groove-shaped channel in lower
electrode shapes the E field that
confines particles
Microspheres are trapped
above the groove
QE
resonant frequency
0.1 Hz
3 Hz
mg
groove
groove
lower
electrode
15 Hz
Image of chain in experiment
particle’s x,y position
measured in each video frame
Vibrational Excitation
Elastic vibrations can be excited by:
• Brownian motion in gas
• Laser manipulation
incident laser
beam
momentum
imparted to
microsphere
Experiment:
Natural motion of a 1-D chain (no manipulation)
1 mm
central portion
of a 28-particle
chain
Measuring phonon spectrum
Method:
•
•
•
•
Video microscopy
Particle tracking  x(t) & v(t):
Calculate current correlation function C(q,t)
Fourier transform  C(q,w)
Phonon spectrum
Color corresponds
to energy
Energy is
concentrated in a
band that
corresponds to a
dispersion relation
Symbols indicate
peaks
Phonon spectrum
Color corresponds
to energy
Energy is
concentrated in a
band that
corresponds to a
dispersion relation
Symbols indicate
peaks
Excitation with laser manipulation
1 mm
modulated beam
-I0 ( 1 + sinwt )
continuous beam
I0
Net force  I0 sinwt
Wave propagates
to two ends of chain
Dispersion relation - natural & externally excited
longitudinal
transverse
N = 28
N = 28
○ excited
natural
○ excited
natural
Summary
• We used direct imaging
to observe particle
motion in a 1-D chain
• We characterized the
phonons by:
• Power spectra
• Dispersion relation
More details & theory:
Liu, Avinash & Goree PRL 2003
Liu & Goree
PRE 2005
Images of one-dimensional chains
Modulating
the laser
power
scanning
mirror
Ar laser beam
Experiment result
Argon laser beam
Argon laser beam
wave:
• is excited in the middle of chain
• propagates to two ends of chain
Thermal motion
Gas temperature = room temperature
Particle kinetic temperature was computed
from particle velocities
230 K from mean kinetic energy:
390K from fit of velocity distribution function: