Phonon spectrum measured in a 1D Yukawa chain John Goree & Bin Liu

Modes in 1-D chains Colloids: Polymer microspheres trapped by counter- propagating laser beams Lowest-order modes (sloshing & breathing modes) observed experimentally Tatarkova, et al., PRL 2002Cvitas and Siber, PRB 2003 Carbon nanotubes: Xe atoms trapped on a tube Theory: phonon spectrum

Transverse mode Modes in a 1-D chain Longitudinal 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 Medium is low density: gas instead of a solvent microspheres are underdamped Suspension is very soft: shear modulus of a 3D crystal is  smaller,  as compared to metals What’s special about plasma: Temperature can be varied: not in this talk

Microspheres Melamine formaldehyde diameter 8.09  m introduced into plasma by shaking a dispenser

Pair potential Particles suspended as a monolayer interact with a repulsive Yukawa potential: In this experiment: chargeQ e screening  length D 0.86 mm spacing a 0.80 mm  >> particle radius 4  m

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

Setup: Ar laser beam 1

Making a one-dimensional chain

“Channel” on substrate to confine a chain Microspheres are trapped above the groove Groove-shaped channel in lower electrode shapes the E field that confines particles 0.1 Hz 3 Hz 15 Hz resonant frequency groove

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 momentum imparted to microsphere incident laser beam

Experiment: Natural motion of a 1-D chain (no manipulation) central portion of a 28-particle chain 1 mm

Measuring phonon spectrum Method: Video microscopy Particle tracking  x(t) & v(t): Calculate current correlation function C(q,t) Fourier transform  C(q,  )

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 Wave propagates to two ends of chain modulated beam -I 0 ( 1 + sin  t ) continuous beam I0I0 Net force  I 0 sin  t 1 mm

Dispersion relation - natural & externally excited longitudinaltransverse ○ excited  natural ○ excited  natural N = 28

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 & GoreePRL 2003 Liu & Goree PRE 2005

Images of one-dimensional chains

scanning mirror Modulating the laser power Ar laser beam

Experiment result wave: is excited in the middle of chain propagates to two ends of chain Argon laser beam

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: