## Relativistic electron spin motion in cycloatoms

Optics Express, Vol. 8, Issue 2, pp. 51-58 (2001)

http://dx.doi.org/10.1364/OE.8.000051

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### Abstract

We present computer movies of the classical and quantum mechanical time evolution for an atom in a strong static magnetic field and a laser field. The resonantly induced relativistic motion of the atomic electron leads to a ring-like spatial probability density called a cycloatom. We further demonstrate that spin-orbit coupling for a fast moving electron in a cycloatom becomes significant, modifying the time-dependence of the spin even if initially aligned parallel to the static magnetic field direction. We also present several movies on time-evolution of the spin-distribution as a function of the position for a relativistic quantum state. The nature of such a space resolved spin measurement is analyzed.

© Optical Society of America

**OCIS Codes**

(000.1600) General : Classical and quantum physics

(020.4180) Atomic and molecular physics : Multiphoton processes

**ToC Category:**

Focus Issue: Quantum control of photons and matter

**History**

Original Manuscript: November 6, 2000

Published: January 15, 2001

**Citation**

Qichang Su, P. Peverly, R. Wagner, P. Krekora, and Rainer Grobe, "Relativistic electron spin motion in cycloatoms," Opt. Express **8**, 51-58 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-2-51

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### References

- For a review, see e.g. Q. Su and R. Grobe, "Examples of classical and genuinely quantum relativistic phenomena," in Multiphoton Processes, eds. L.F. DiMauro, R.R. Freeman, K.C. Kulander (American Institute of Physics, Melville, New York, 2000) p.655 or the website www.phy.ilstu.edu/ILP
- Science News, "Ring around the proton," 157, 287 (2000).
- R.E. Wagner, Q. Su and R. Grobe, "Relativistic resonances in combined magnetic and laser field," Phys. Rev. Lett. 84, 3282 (2000). [CrossRef] [PubMed]
- For movies of cycloatoms see Phys. Rev. Focus, "Fast electrons on the cheap", 5, 15, 6 April (2000) at the web site: http://focus.aps.org/v5/st15.html story
- P.J. Peverly, R.E. Wagner, Q. Su and R. Grobe, "Fractional resonances in relativistic magnetic-laser-atom interactions," Laser Phys. 10, 303 (2000).
- Q. Su, R.E. Wagner, P.J. Peverly and R. Grobe, "Spatial electron clouds at fractional and multiple magneto-optical resonances," in Frontiers of Laser Physics and Quantum Optics, eds, Z. Xu, S. Xie, S.-Y. Zhu and M.O. Scully, p.117 (Springer, Berlin, 2000).
- R.E. Wagner, P.J. Peverly, Q. Su and R. Grobe, "Classical versus quantum dynamics for a driven relativistic oscillator," Phys. Rev. A 61, 35402 (2000). [CrossRef]
- V.G. Bagrov and D.M. Gitman, Exact solutions of relativistic wave equations, (Kluwer Academic, Dordrecht, 1990). [CrossRef]
- C. Bottcher and M.R. Strayer, "Relativistic theory of fermions and classical fields on a collocation lattice," Ann. Phys. NY 175, 64 (1987). [CrossRef]
- J.C. Wells, A.S. Umar, V.E. Oberacker, C. Bottcher, M.R. Strayer, J.-S. Wu, J. Drake and R. Flanery, "A numerical implementation of the Dirac equation on a hypercube multicomputer," Int. J. Mod. Phys. C 4, 459 (1993). [CrossRef]
- K. Momberger, A. Belkacem and A.H. Sorensen, "Numerical treatment of the time-dependent Dirac equation in momentum space for atomic processes in relativistic heavy-ion collisions," Phys. Rev. A 53, 1605 (1996). [CrossRef] [PubMed]
- U.W. Rathe, C.H. Keitel, M. Protopapas, and P.L. Knight, "Intense laser-atom dynamics with the two-dimensional Dirac equation," J. Phys. B 30, L531 (1997). [CrossRef]
- N.J. Kylstra, A.M. Ermolaev and C.J. Joachain, "Relativistic effects in the time evolution of a one-dimensional model atom in an intense laser field," J. Phys. B 30, L449 (1997). [CrossRef]
- C. Szymanowski, C.H. Keitel and A. Maquet, "Influence of Zitterbewegung on relativistic harmonic generation," Las. Phys. 9, 133 (1999).
- J.W. Braun, Q. Su and R. Grobe, "Numerical approach to solve the time-dependent Dirac equation," Phys. Rev. A 59, 604 (1999). [CrossRef]
- U.W. Rathe, P. Sanders, P.L. Knight,"A case study in scalability: an ADI method for the two-dimensional time-dependent Dirac equation," Parallel Computing, 25, 525 (1999). [CrossRef]
- P. Krekora, R.E. Wagner, Q. Su and R. Grobe, "Dirac theory of ring-shaped electron distributions." Phys. Rev. A, in press.
- H. Goldstein, Classical Mechanics, 2nd edition (Addison-Wesley, New York, 1980).
- B. Thaller, The Dirac Equation, (Springer, 1992).
- R.E. Wagner, Q. Su and R. Grobe, "High-order harmonic generation in relativistic ionization of magnetically dressed atoms," Phys. Rev. A, 60, 3233 (1999). [CrossRef]
- For relativistic suppression of wave packet spreading, see, Q. Su, B.A. Smetanko and R. Grobe, "Wave packet motion in relativistic electric fields," Las. Phys. 8, 93 (1998).
- Q. Su, B.A. Smetanko and R. Grobe, "Relativistic suppression of wave packet spreading," Opt. Express 2, 277 (1998), http://www.opticsexpres.org/oearchive/source/2813.htm [CrossRef] [PubMed]
- E. Lenz, M. D�rr and W. Sandner, Las. Phys., in press.
- For a review on Lorentz transformations of 4�4 spin matrices, see, e.g., J.D. Bjorken and S.D. Drell, "Relativistic quantum mechanics," (McGraw-Hill, 1964); J. Kessler, Polarized Electrons, 2nd edition (Springer Verlag, Berlin, 1985).
- For work on the Spin-Wigner function, see, e.g., I. Bialynicki-Birula, P. Gornicki and J. Rafelski," Phase-space structure of the Dirac vacuum," Phys. Rev. D 44, 1825 (1991). [CrossRef]
- G.R. Shin, I. Bialynicki-Birula and J. Rafelski, " Wigner function of relativistic spin-1/2 particles," Phys. Rev. D 46, 645 (1992).
- For the time-evolution of the spatial width, see, J.C. Csesznegi, G.H. Rutherford, Q. Su, and R. Grobe, "Dynamics of wave packets in inhomogeneous and homogeneous magnetic fields," Las. Phys. 6, 41 (1999).
- P. Krekora, Q. Su and R. Grobe, "Dynamical signature in spatial spin distributions of relativistic electrons," Phys. Rev. A, submitted.
- L.T. Thomas, Phil. Mag. 3, 1 (1927).
- J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).

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