Dirac theory of ring-shaped electron distributions in atoms

Abstract

The time-dependent Dirac equation is solved numerically on a space-time grid 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 ringlike spatial probability density similar to the features that have been recently predicted ͓Wagner, Su, and Grobe, Phys. Rev. Lett. 84, 3282 ͑2000͔͒ based on a phase-space method. We further demonstrate that spin-orbit coupling for a fast-moving electron in such an atom becomes significant and the time dependence of the spin can dephase even if initially aligned parallel to the direction of the static magnetic field.

Relation between quantum tunneling times for relativistic particles

“…This should not be taken to mean that the wave packet peak traveled as a rigid entity from input to output faster than the speed of light. As a matter of fact, the peak does not travel from input to output, as has been confirmed in direct numerical simulations of relativistic wave equations [13,17,33]. The dwell time is the 1/e lifetime of particles escaping out of both ends of the barrier.…”

“…This effect has recently been explained as arising from the saturation of stored energy or number of particles under the barrier [11][12][13]. With some exceptions [14][15][16][17][18][19][20][21][22][23], most discussions of quantum tunneling time have been based on the nonrelativistic Schrödinger equation even when apparent "faster than c" effects are considered. In particular there has been no discussion of the relation between the various tunneling times for relativistic particles.…”

Relativistic high-power laser–matter interactions

“…Besides controlling the efficiency of HHG by suppression of the wave packet spreading, dynamics of an atomic electron in the presence of a moderate-intensity laser field and a strong static magnetic field has been shown recently to result in a peculiar bound-like system, called the cycloatom by its principal investigators [166,167]. An electronic charge distribution evolves from an initial atomic ground state into a ring, a Fig.…”

“…At higher intensities, however, one must come to grips with the relativistic effects [139,140,153]. An appropriate representation ought to be in terms of relativistic wavepackets as investigated in [139].…”

Quantum-electrodynamic treatment of photoemission by a single-electron wave packet

“…The precedent for this line of thinking goes back to some of the founders of quantum mechanics, including Schrödinger [5], Gordon [6], and Klein [7]. By closely paralleling the classical-field solution, this model predicts interference akin to that obtained from a classical charge current [8][9][10].…”