Examples of genuinely relativistic phenomena

1. ICOMP VIII, Monterey, CA October 1999 Examples of genuinely relativistic phenomena R. Grobe Intense Laser Physics Theory Unit Illinois State University Undergraduatestudents Postdocs Faculty J.W. Braun B.A. Smetanko J.J. Csesznegi P.J. Peverly R.E. Wagner T. Shepherd S.M. Mandel A. Bergquist H. Wanare P. Krekora G.H. Rutherford Q. Su R. Grobe Support : National Science Foundation, Research Corporation, Illinois State www . phy . ilstu . edu / ILP

2. Tools to explore phenomena that are genuinely relativistic Dirac : Liouville:

3. A flavor of the numerical work • Discretize: r  2563 points t 103-106 points  ≈ 4 · 2563 · 106 = 1013 complex numbers • Split operator FFT technique • Supercomputer

4. Genuinely Relativistic Phenomena • Zitterbewegung J.W. Braun, Q. Su & RG, PRA59, 604 (1999) • Klein-Paradox (particle pair production) J.W. Braun, Q. Su & RG, PRA 59, 604 (1999) • Subnatural wave packet spreading Q. Su, B.A. Smetanko & RG, Opt. Exp. 2, 277 (1998) J.C. Csesznegi, G.H. Rutherford, Q. Su & RG, Las. Phys. 9, 41 (1999) • Spin-spatial coupling in magnetic fields G.H. Rutherford & RG, PRL 81, 4772 (1998) G.H. Rutherford & RG, JPA 31, 9331 (1998) • Chaos J. Kim, and H. Lee, PRE 51, 1579 (1995) • How good is Liouville? R.E. Wagner, P.J. Peverly, Q. Su & RG, PRA (subm.) • Counterintuitive enhancement of resonances R.E. Wagner, Q. Su & RG, PRL (subm.) • Cycloatoms and dephasing P.J. Peverly, R.E. Wagner, Q. Su, & RG, Las. Phys.(in press) • Scattered light spectra R.E. Wagner, Q. Su & RG, PRA 60, No.4 (1999)

5. Schrödinger’s Zitterbewegung small ∆x  neg. energy contrib.  “Zitter” J.W. Braun, Q. Su & RG, PRA59, 604 (1999). position spin Zitterbewegung real? controversial issue...

6. Time - resolved Klein Paradox J.W. Braun, Q. Su & RG, PRA59, 604 (1999). voltage > Ekin + 2c2 Interpretation still controversial ...

7. Stern-Gerlach separation possible for electrons ??? Sz Sz Sz Pauli/Bohr: Lorentz-force “washes out” separation ?? inhomog. magnetic field: Position Dirac solution : Spin separation is possible G.H. Rutherford & RG, PRL 81, 4772 (1998) and JPA 31, 9331(1998).

8. Subnatural wave packet spreading Non-relativistic: Spreading independent of the center of mass motion • Spreading is suppressed: Q. Su, B.A Smetanko and RG, Opt. Exp. 2, 277 (1998) • Spatial profile becomes asymmetrical : Q. Su, B.A. Smetanko & RG, Las. Phys. 4, 93 (1998)

9. Relativity Induces Chaos J. Kim and H. Lee, PRE 51, 1579 (1995): + relativity => chaos non-relativistic => Liouville = Schrödinger relativistic => ??? Liouville ≈ Dirac ???? Schrödinger= Newton Dirac ≈ Liouville R.E. Wagner, P.J. Peverly, Q. Su & RG, PRA (subm.) What a surprise ...

10. Maximum speed v/c for each W non- relativistic relativistic W wL Relativity enhances resonances Myth: relativity  “heavier mass”  slower motion Fact: relativity  faster motion example: electron in laser and static magnetic field  R. Wagner, Q. Su & RG, PRL (submitted)

11. Novel steady spatial states: Cycloatoms Non-relativistic Relativistic 0 75 150 y 500 x Orbits stay in phase Orbits dephase relativistically Time (in 2p/wL)

12. Relativistic dephasing model 0 75 150 500 Time replace W W + DW (V0) relativistic (exact) dephasing model

13. Steady state spatial electron distributions Multiple resonances W = 3 w W = w W = 2 w Fractional resonances W = 1/2 w W = 1/3 w Q. Su, R.E. Wagner, P.J. Peverly & RG, SPIE (in press)

14. Scattered light spectra Single orbits non-relativistic relativistic y x Corresponding spectra R.E. Wagner, Q. Su & RG, PRA 60, No.4 (1999)

15. Summary Numerical solution to the Dirac equation Relativity leads to new phenomena in the spatial and temporal dynamics • subnatural spreading • chaos • novel resonances => novel experiments • cycloatoms • dephasing • scattered light spectra www.phy.ilstu.edu/ILP