Tests of QED with Intense Lasers

Abstract

We have seen in the previous chapters that many materials respond nonlinearly to an externally applied electric field. On the other hand, Maxwell’s equations for the electromagnetic (em) field in vacuum are absolutely linear. This conclusion is not valid any more if we include quantum-mechanical effects, such as the production of particles from the vacuum, in the description of the em field. The particles need not be real but can be virtually produced and reabsorbed (in a time interval t) as long as the uncertainty relation E t ’ h holds. Such processes are at the center of all calculations in quantum electrodynamics (QED) and also endow the vacuum with nonlinear properties. That the vacuum would exhibit nonlinear behavior in the presence of em fields was recognized over 70 years ago [1, 2, 3] and since then QED has been developed into a highly accurate theory in perfect agreement with all observations. However, it is only recently that direct experimental evidence was obtained on the nonlinear behavior of the vacuum in the production of eþe pairs in photon–photon collisions. One expects to observe such nonlinear effects in the presence of strong em fields. Indeed, the interaction of electrons with the intense fields at the focus of short laser pulses has been considered by many authors. Some typical early work is that of refs. [4, 5, 6, 7, 8]. The scattering of visible light from a free electron can be understood classically and leads to the well-known Thomson cross-section. However, in an intense field the motion of the electron can become relativistic and this results in the emission of higher harmonics of the incident light. This nonlinear effect is particularly pronounced in the interaction of intense lasers with atomic electrons. An early observation of harmonic generation in laser free electron scattering was reported in [9]. A more recent and detailed study of nonlinear Thomson scattering of an intense laser from quasi-free electrons is given in [10].