Phonon spectrum measured in a 1D Yukawa chain

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Phonon spectrum measured in a 1D Yukawa chain
John Goree Bin Liu
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Modes in 1-D chains

• Colloids
• Polymer microspheres trapped by
  counter-propagating laser beams
• Lowest-order modes (sloshing breathing modes)
  observed experimentally

• Carbon nanotubes
• Xe atoms trapped on a tube
• Theory phonon spectrum

Tatarkova, et al., PRL 2002
Cvitas and Siber, PRB 2003
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Modes in a 1-D chain
Longitudinal mode
Transverse mode
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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

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Experimental system dusty plasma

• The medium is a plasma
• a low-pressure gas
• partially ionized by applying high voltage

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Experimental system dusty plasma
Whats 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

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Microspheres
Melamine formaldehyde diameter 8.09 mm introduced
into plasma by shaking a dispenser
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Pair potential
Particles suspended as a monolayer interact with
a repulsive Yukawa potential
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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
• ordered lattice

QE
mg
electrode substrate
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Setup
Ar laser beam 1
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Making a one-dimensional chain
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Channel on substrate to confine a chain
Groove-shaped channel in lower electrode shapes
the E field that confines particles
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Image of chain in experiment
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Vibrational Excitation

• Elastic vibrations can be excited by
• Brownian motion in gas
• Laser manipulation

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ExperimentNatural motion of a 1-D chain (no
manipulation)
central portion of a 28-particle chain
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Measuring phonon spectrum

• Method
• Video microscopy
• Particle tracking Þ x(t) v(t)
• Calculate current correlation function C(q,t)
• Fourier transform Þ C(q,w)

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Phonon spectrum
Color corresponds to energy Energy is
concentrated in a band that corresponds to a
dispersion relation Symbols indicate peaks
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Phonon spectrum
Color corresponds to energy Energy is
concentrated in a band that corresponds to a
dispersion relation Symbols indicate peaks
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Excitation with laser manipulation
Net force µ I0 sin?t
Wave propagates to two ends of chain
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Dispersion relation - natural externally excited
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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
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Images of one-dimensional chains
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Modulating the laser power
scanning mirror
Ar laser beam
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Experiment result

• wave
• is excited in the middle of chain
• propagates to two ends of chain

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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