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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: