We suggest an experiment to observe vacuum birefringence induced by intense laser fields. A high-intensity laser pulse is focused to ultra-relativistic intensity and polarizes the vacuum which then acts like a birefringent medium. The latter is probed by a linearly polarized x-ray pulse. We calculate the resulting ellipticity signal within strong-field QED assuming Gaussian beams. The laser technology required for detecting the signal will be available within the next three years. The interactions of light and matter are described by quantum electrodynamics (QED), at present the bestestablished theory in physics. The QED Lagrangian couples photons to charged Dirac particles in a gauge invariant way. At photon energies small compared to the electron mass, ω ≪ m e , electrons (and positrons) will generically not be produced as real particles. Nevertheless, as already stated by Heisenberg and Euler, "...even in situations where the [photon] energy is not sufficient for matter production, its virtual possibility will result in a 'polarization of the vacuum' and hence in an alteration of Maxwell's equations" [1]. These authors were the first to explicitly derive the nonlinear terms induced by QED for small photon energies but arbitrary intensities (see also [2]).The most spectacular process resulting from these modifications presumably is pair production in a constant electric field. This is an absorptive process as photons disappear by disintegration into matter pairs. It can occur for field strengths larger than the critical one given by [3,4] In this electric field an electron gains an energy m e upon travelling a distance equal to its Compton wavelength, λ e = 1/m e . The associated intensity is I c = E 2 c ≃ 4.4 × 10 29 W/cm 2 such that both field strength and intensity * Electronic address: theinzl@plymouth.ac.uk

Vacuum birefringence is governed by the amplitude for a photon to flip helicity or polarisation state in an external field. Here we calculate the flip and non-flip amplitudes in arbitrary plane wave backgrounds, along with the induced spacetime-dependent refractive indices of the vacuum. We compare the behaviour of the amplitudes in the low energy and high energy regimes, and analyse the impact of pulse shape and energy. We also provide the first lightfront-QED derivation of the coefficients in the Heisenberg-Euler effective action.

We review known and discuss new signatures of high-intensity Compton scattering assuming a scenario where a high-power laser is brought into collision with an electron beam. At high intensities one expects to see a substantial redshift of the usual kinematic Compton edge of the photon spectrum caused by the large, intensity-dependent effective mass of the electrons within the laser beam. Emission rates acquire their global maximum at this edge while neighboring smaller peaks signal higher harmonics. In addition, we find that the notion of the center-of-mass frame for a given harmonic becomes intensity dependent. Tuning the intensity then effectively amounts to changing the frame of reference, going continuously from inverse to ordinary Compton scattering with the center-of-mass kinematics defining the transition point between the two.

We consider stimulated pair production employing strong-field QED in a high-intensity laser background. In an infinite plane wave, we show that light-cone quasi-momentum can only be transferred to the created pair as a multiple of the laser frequency, i.e.\ by a higher harmonic. This translates into discrete resonance conditions providing the support of the pair creation probability which becomes a delta-comb. These findings corroborate the usual interpretation of multi-photon production of pairs with an effective mass. In a pulse, the momentum transfer is continuous, leading to broadening of the resonances and sub-threshold behaviour. The peaks remain visible as long as the number of cycles per pulse exceeds unity. The resonance patterns in pulses are analogous to those of a diffraction process based on interference of the produced pairs.Comment: 7 pages, 7 EPS figures. Version 2 contains additional examples using smooth pulse envelopes. Conclusions unchange

We discuss intensity effects in collisions between beams of optical photons from a high-power laser and relativistic electrons. Our main focus are the modifications of the emission spectra due to realistic finite-beam geometries. By carefully analysing the classical limit we precisely quantify the distinction between strong-field QED Compton scattering and classical Thomson scattering.A purely classical, but fully covariant, calculation of the bremsstrahlung emitted by an electron in a plane wave laser field yields radiation into harmonics, as expected. This result is generalised to pulses of finite duration and explains the appearance of line broadening and harmonic substructure as an interference phenomenon. The ensuing numerical treatment confirms that strong focussing of the laser leads to a broad continuum while higher harmonics become visible only at moderate focussing, hence lower intensity. We present a scaling law for the backscattered photon spectral density which facilitates averaging over electron beam phase space. Finally, we propose a set of realistic parameters such that the observation of intensity induced spectral red-shift, higher harmonics, and their substructure, becomes feasible.