Relativistic and QED effects in ultrashort processes, and connections to high-precision spectroscopy

Full text: Relativistic electron theory and modern numerical methods allow for an ab initio description of processes which happen on very small time scales. e.g. a laser-driven relativistic electron experiences oscillations between the positive and the negative-energy continuum on time scales of 10-21 sec. These can be resolved by a numerical simulation that takes into account all relativistic effects and displays clearly the quantum and relativistic signatures of electron (and positron) motion in a laser field. In higher-harmonic generation, one primary obstacle has been the inhibition of recollisions due to radiation pressure in the high-field, relativistic domain. One obvious solution to this problem is provided by a symmetric bound system consisting of a particle and its own antiparticle, because the laser-induced motion then favors multiple recollisions even if the drift motion in the laser propagation direction is taken into account. An analytic approach to the problem, which includes a discussion of limitations due to the decay of the particles, will be presented. A last part of this talk will be concerned with the possibility of counting ultrafast oscillations in the range of 1015 Hz. Using a frequency comb, it now (almost) possible to count all 2.466 1015 cycles/second which correspond to a hydrogenic 1S-2S transition, by phase-coherent comparison to an atomic clock. Based on the measurements, limits on the temporal variation of fundamental constants can be inferred. (author)