The properties of four-wave interaction via the nonlinear quantum vacuum is investigated. The effect of the quantum vacuum is to generate photons with new frequencies and wave vectors, due to elastic photon-photon scattering. An expression for the number of generated photons is derived and using state-of-the-art laser data it is found that the number of photons can reach detectable levels. In particular, the prospect of using the high repetition Astra Gemini system at the Rutherford Appleton Laboratory is discussed. The problem of noise sources is reviewed, and it is found that the noise level can be reduced well below the signal level. Thus, detection of elastic photon-photon scattering may for the first time be achieved. PACS numbers: 12.20.Fv, 42.50.Xa Classically, elastic photon-photon scattering does not take place in vacuum. However, according to quantum electrodynamics (QED), such a process may occur owing to the interaction with virtual electron-positron pairs. Several suggestions to detect photon-photon scattering have been made, for example using harmonic generation in an inhomogeneous magnetic field [1], using resonant interaction between eigenmodes in microwave cavities [2,3], using ultra-intense fields occurring in plasma channels [4], as well as many others, see e.g. Refs. [5,6,7]. Related to, but physically different from, elastic photon-photon scattering is photon splitting [8] (see also [9]) and Delbrück scattering [10], the latter being detectable using high-Z atomic targets [10]. However, no suggestions have yet led to detection of elastic scattering among real photons.In the present Letter we will investigate the possibility to detect photon-photon scattering in vacuum using four-wave mixing, where three colliding laser pulses stimulate emission in a fourth direction with a new frequency. Four-wave mixing has the advantage of not being limited by the low cross section for photon-photon scattering [11]. A similar scheme was first studied by Ref. [12], and further theoretical [13,14,15] and experimental [16] studies of QED four-wave mixing have been performed since then. However, so far the available laser technology has not been sufficiently powerful to allow for successful detection of scattering events. Moreover, even with high laser power, the laser setup and geometry in such an experiment is important. In particular, we argue that a two-dimensional (2D) setup preferred in earlier literature is unlikely to produce a detectable signal. This is in contrast to the 3D setup presented in this Letter. We have calculated the coupling coefficient for four-wave mixing as a function of incident angles and laser polarization. For given data of the laser beams, together with the coupling coefficients, the number of scattered photons can be calculated. The analysis is then used * Currently at: Department of Physics, Stockholm University, SE-106 91, Sweden to suggest a novel concrete experiment, where the parameters are chosen to fit the Astra Gemini (AG) system (operational 2007) located at the Centr...

The quantum vacuum constitutes a fascinating medium of study, in particular since near-future laser facilities will be able to probe the nonlinear nature of this vacuum. There has been a large number of proposed tests of the low-energy, high intensity regime of quantum electrodynamics (QED) where the nonlinear aspects of the electromagnetic vacuum come into play, and we will here give a short description of some of these. Such studies can shed light, not only on the validity of QED, but also on certain aspects of nonperturbative effects, and thus also give insights for quantum field theories in general.

We have considered linear kinetic theory, including the electron-spin properties in a magnetized plasma. The starting point is a mean-field Vlasov-like equation, derived from a fully quantum-mechanical treatment, where effects from the electron-spin precession and the magnetic dipole force are taken into account. The general conductivity tensor is derived, including both the free current contribution and the magnetization current associated with the spin contribution. We conclude the paper with an extensive discussion of the quantum-mechanical boundary where we list parameter conditions that must be satisfied for various quantum effects to be influential.

We derive expressions for the coupling coefficients for electromagnetic four-wave mixing in the nonlinear quantum vacuum. An experimental setup for detection of elastic photon-photon scattering is suggested, where three incoming laser pulses collide and generate a fourth wave with a new frequency and direction of propagation. An expression for the number of scattered photons is derived and, using beam parameters for the Astra Gemini system at the Rutherford Appleton Laboratory, it is found that the signal can reach detectable levels. Problems with shot-to-shot reproducibility are reviewed, and the magnitude of the noise arising from competing scattering processes is estimated. It is found that detection of elastic photon-photon scattering may be achieved

The quantum electrodynamical (QED) short wavelength correction on plasma wave propagation for a nonrelativistic quantum plasma is investigated. A general dispersion relation for a thermal multicomponent quantum plasma is derived. It is found that the classical dispersion relation for any wave mode can be modified to include quantum and short wavelength QED effects by simple substitutions of the thermal velocity and the plasma frequency. Furthermore, the dispersion relation has been modified to include QED effects of strong magnetic fields. It is found that strong magnetic fields together with the short wavelength QED correction will induce dispersion both in vacuum and in otherwise nondispersive plasma modes. Applications to laboratory and astrophysical systems are discussed.