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.

When exposed to intense electromagnetic fields, the quantum vacuum is expected to exhibit properties of a polarizable medium akin to a weakly nonlinear dielectric material. Various schemes have been proposed to measure such vacuum polarization effects using a combination of high-power lasers. Motivated by several planned experiments, we provide an overview of experimental signatures that have been suggested to confirm this prediction of quantum electrodynamics of real photon-photon scattering.Keywords: Heisenberg-Euler; photon-photon scattering; vacuum birefringence; vacuum polarization MotivationThe increasing availability of multi-hundred TW and PW lasers [1] brings the confirmation of long-predicted phenomena of strong-field quantum electrodynamics (QED) [2,3] closer. A multitude of effects on the polarization, wavevector and frequency of photons that probe the polarization of the charged virtual pairs of the vacuum have been theoretically investigated. All of these effects can be understood in terms of the single process of 'photon-photon scattering'. The current best experimental limit on the predicted crosssection for photon-photon scattering using just high-power laser pulses lies eighteen orders of magnitude above QED [4] , but recent laser-cavity experiments such as BMV [5] and PVLAS [6] have reduced this to six and three orders of magnitude, respectively (or three orders of magnitude and a factor 50, respectively, at the level of the refractive index). Moreover, coinciding with the completion of the XFEL laser at DESY, an experiment at the HIBEF facility [7] plans to measure one manifestation of photon-photon scattering, namely the birefringence of the vacuum, using the XFEL beam and a 1 PW optical laser. This has generated much interest in vacuum polarization effects.The aims of this work are two-fold. First, the main analytical approaches used to study photon-photon scattering will be shown to be essentially equivalent for predictions of planned laser experiments. Second, an overview of the predicted signatures of real photon-photon scattering in various experimental scenarios will be provided, which is also hoped to be useful for the nonspecialist and, in particular, promote discussions between theorists and experimentalists. Introduction: vacuum polarizationVacuum polarization, depicted in the Feynman diagram of Figure 1, is a basic radiative correction that modifies the propagation of photons in vacuum through the appearance of virtual pairs in a 'fermion loop'.There are two complementary interpretations of this effect. The first is based on what is called 'old-fashioned' perturbation theory which emphasizes energy considerations at the price of manifest covariance [8] . In this interpretation, Heisenberg's uncertainty relation is invoked to show how quantum mechanics predicts energy and momentum conservation may be violated. The amount of this violation is inversely proportional to the space-time scale over which it occurs. This effect is represented by short-lived 'virtual' particles. T...

We study the feasibility of measuring vacuum birefringence by probing the focus of a high-intensity optical laser with an x-ray free electron laser (XFEL). This amounts to performing a new type of QED precision experiment, employing only laser pulses, hence space- and time-dependent fields. To set the stage, we briefly review the status of QED precision tests and then focus on the example of vacuum birefringence. Adopting a realistic laser beam model in terms of pulsed Gaussian beams we calculate the induced phase shift and translate it into an experimental signal, counting the number of photons with flipped polarization. We carefully design a detailed experiment at the European XFEL operating in self-seeded mode, supplemented by a petawatt class optical laser via the HIBEF project. Assuming all components to represent the current state of the art, in particular the x-ray polarizers, realistic estimates of signal-to-noise ratios plus ensuing acquisition times are provided. This is accompanied by a statistical analysis of the impact of poor laser focus overlap either due to timing and pointing jitter as well as limited alignment accuracy. A number of parasitic effects are analyzed together with appropriate countermeasures. We conclude that vacuum birefringence can indeed be measured upon combining an XFEL with a high-power optical laser if depolarization effects in the x-ray lenses can be controlled.

We show that the emission of soft photons via nonlinear Compton scattering in a pulsed plane wave (laser field) is in general infrared divergent. We give examples of both soft and soft-collinear divergences, and we pay particular attention to the case of crossed fields in both classical and quantum theories.