Phonon spectrum measured in a 1D Yukawa chain

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

2. 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

3. Modes in a 1-D chain Longitudinal mode • Transverse mode

4. 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

5. Experimental system: dusty plasma • The medium is a plasma: • a low-pressure gas • partially ionized by applying high voltage

6. 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

7. Microspheres • Melamine formaldehyde • diameter 8.09 mm • introduced into plasma by shaking a dispenser

8. In this experiment: • charge Q - 7600 e • screeninglength lD 0.86 mm • spacing a 0.80 mm } >> particle radius 4 mm Pair potential Particles suspended as a monolayer interact with a repulsive Yukawa potential:

9. 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

10. Setup: Ar laser beam 1

11. Making a one-dimensional chain

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

13. particle’s x,y position measured in each video frame Image of chain in experiment

14. incident laser beam momentum imparted to microsphere Vibrational Excitation • Elastic vibrations can be excited by: • Brownian motion in gas • Laser manipulation

15. 1 mm Experiment:Natural motion of a 1-D chain (no manipulation) central portion of a 28-particle chain

16. Measuring phonon spectrum • Method: • Video microscopy • Particle tracking Þx(t) & v(t): • Calculate current correlation function C(q,t) • Fourier transform ÞC(q,w)

17. Phonon spectrum Color corresponds to energy Energy is concentrated in a band that corresponds to a dispersion relation Symbols indicate peaks

18. Phonon spectrum Color corresponds to energy Energy is concentrated in a band that corresponds to a dispersion relation Symbols indicate peaks

19. modulated beam 1 mm -I0 ( 1 + sint ) continuous beam I0 Excitation with laser manipulation Net force µI0 sint Wave propagates to two ends of chain

20. longitudinal transverse N = 28 N = 28 ○ excited Ñ natural ○ excited Ñ natural Dispersion relation - natural & externally excited

21. 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

22. Images of one-dimensional chains

23. Modulating the laser power scanning mirror Ar laser beam

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

25. 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: