2. Robert E. Wagner Sophomore Intense Laser Physics Theory Unit Illinois State University What are Cycloatoms? Support: NSF, Res. Corp., and ISU Honors Program

3. More Technical: Use RK4 to solve this Laser Magnetic field

4. Maximum speed v/c for each  non- relativistic LL 

5. Can we use classical mechanics to approximate quantum???? realization in terms of classical particles |  (r)| 2 High probability Large density

6. Can we use classical mechanics to approximate quantum???? ?

7. Summary 1. P qm (r,t=0) => P cl (r,t=0) 2. realize P cl (r,t=0) in terms of 100,000 single trajectories 3. solve time evolution of each trajectory 4. compute a “smoothed” histogram = P cl (r,t) choose  wisely:  too small  too large

8. Non-relativisticRelativistic Orbits stay in phase Orbits dephase relativistically Time (in 2  L  75 150 500 0 y x

9. Non-relativistic Movie  =  L

11. Relativistic Movie  =  L

13. relativistic (exact)dephasing model Time 75 150 500 0 Relativistic dephasing model replace   (V 0 )

14. Steady state spatial electron distributions Multiple resonances Q. Su, R.E. Wagner, P.J. Peverly & RG, SPIE (in press) Fractional resonances  = 1/2  L  = 1/3  L  =  L  = 2  L  = 3  L

15. Fractional Resonance  =1/2  L

17. Fractional Resonance  =1/3  L

19. Summary Relativity leads to new phenomena in the spatial and temporal dynamics novel resonances => novel experiments cycloatoms dephasing [1] R.E. Wagner, Q. Su and R. Grobe, Phys. Rev. Lett. (April, 2000). [2] R.E. Wagner, Q. Su, and R. Grobe, Phys. Rev. A 60, 3233, 1999. [3] P.J. Peverly, R.E. Wagner, Q.Su and R. Grobe, Las. Phys. 10, 303 ( 2000). [4] Q. Su, R.E. Wagner, P.J. Peverly, and R. Grobe, SPIE (in press). [5] R.E. Wagner, P.J. Peverly, Q. Su and R. Grobe, Phys. Rev. A (in press). www.phy.ilstu.edu/ILP