Science & Applications: High fields
The Quantum Vacuum and Quantum Dynamics
Photon–photon scattering is a nonclassical effect arising in quantum electrodynamics (QED) due to virtual electron–positron pairs in vacuum. Under everyday circumstances, the effect is very weak (see FIG. 1). However, under the right conditions the interaction between photons and these virtual pairs will result in what is known as photon–photon collisions. Close relatives to this effect is Delbrück scattering and photon splitting (see FIG. 2). Formulated as an effective field theory, using the Heisenberg–Euler Lagrangian (Heisenberg & Euler (1936); Schwinger (1951)), such scattering results in nonlinear corrections to Maxwell’s vacuum equations, similar in form to what is known as Kerr nonlinearities in nonlinear optics. 

FIG. 1 The crosssection for photonphoton scattering as a function of photon frequency (from Lifshitz et al.  1982) 
The effective selfinteraction term in Maxwell’s equations is small (proportional to the fine structure constant squared), which means that the field strengths need to reach appreciable values until such effects become pronounced (Marklund & Shukla (2006); Mourou et al. (2006)). However, the smallness of the photonphoton scattering cross section has been argued to be a possible window to new physics (Anoniadis (1998); Arkanihamed et al. (1998); Cheung (1999); Davoudiasl (1999)), such as weak scale quantum gravity. Physical implications, as well as possible detection techniques, of the effects of photon–photon scattering have attracted interest since the 1930’s (for surveys, see Refs. Marklund & Shukla (2006) and Mourou et al. (2006) and references therein), and the topic is hotter than ever.
FIG. 2: Three different types of interactions between photons. In the left picture an incoming photon interacts with e.g. the strong external field from an atomic nucleus, resulting in an outgoing photon with new characteristics (Delbrück scattering); in the middle picture a single photon interacts with e.g. a strong external magnetic field as to produce two lowfrequency photons (photon splitting); finally, in picture to the right two photons interacts directly via the quantum vacuum, producing two scattered photons. (Courtesy: Mattias Marklund) 
In 2006 alone, a large number of high profile papers and commentaries have been published (se e.g. Lundström et al (2006), Zavattini et al. (2006), Rabadan et al. (2006), van Tiggelen et al. (2006), Blaschke et al. (2006), Di Piazza et al. (2006), Dunne (2006), Buchanan (2006), and Brodin et al. (2007)) concerning these issues. Thus, these research topics are highly interesting to a wide community, and the event of ELI would act as catalyst and experimental probe of certain high energy phenomena as well as testing the fundamental laws of physics (AmelinoCamelia & KowalskiGlikman (2005)).
a. Nonlinear quantum vacuum effects
Photonphoton scattering
It has recently been shown that for the first time shown that detection of elastic photonphoton scattering is achievable, also when taking serious experimental constraints into account (see FIG. 3).
Such experiments on photonphoton scattering will furthermore act as benchmark experiments for high intensity laser facilities. Completely new parameter domains will be covered by facilities like the ELI, and future quantum vacuum experiments will benefit from this fundamental and clean test of the nontrivial and nonlinear properties of the quantum vacuum. Ultrahigh intensity fields naturally appear in astrophysical systems. Thus, the ELI facility would act as a new form of astrophysics laboratory. The possibility to probe the complex environments of e.g. pulsars holds an exciting perspective of bringing the stars into our laboratories, as well as probing quantum gravity effects in the low energy regime. 

FIG. 3: The geometry of the incoming laser pulses (k_{1}, k_{2}, k_{3}) and outgoing pulse (k_{4}) in the left panel. In the right panel the number of generated photons as a function of the source beam power(adapted from E. Lundström et al., Phys. Rev. Lett. 96, 083601 (2006)). We note that rapid increase in the number of stimulated photons as a function of laser power. 
FIG. 4: The production of electronpositron pairs from lowenergy electronlaser interactions. (Courtesy: Mattias Marklund) 
Gamma photon generation and electronpositron production
With the generation of highly relativistic electron beams and bunches, ELI becomes a sharp tool for studying a variety of photon scattering and pair creation processes. The generation of attosecond electron bunches is possible with the ELI facility (Naumova et al. (2004a)), creating a possibility of highly relativistic electron interactions with laser pulses. The interaction between the relativistic electrons and photons will strongly upshift the sharply focused laser pulse, thus leading to a possible coherent and polarized source of gamma photons (Naumova et al. (2004b); Nees et al. (2005)). This paves the way for a laser driven gammagamma collider, which can facilitate an efficient production of pair plasmas. Alternatively, the frequency upshifted photons may also act as the basis for a future high frequency coherent photon system.
Even at much lower electron energies, such interaction will lead to the creation of pairs through the multiphoton BreitWigner process γ+nγ' → e^{+} + e^{}(see FIG. 4) (Bula et al. (1996); Burke et al. (1997)). Such interaction will lead to the generation of intense gamma photons, something which can be utilized for diverse applications, such as coherent sourcing of laboratory gamma systems or the implementation of gammagamma collisions.
Incoherent photons, dynamical vacuum, and higher harmonic generation
A completely new possibility of doingdynamical collective vacuum physics opens up with a system such as ELI, quite distinct from the experiments done in a particle physics community. In particular, creating an intense photon gas using microcavities and an array of intense laser sources and letting this gas interact with a main laser pulse from ELI (see FIG. 5), one might be able to mimic photon propagation in the very early Universe or test the quantum electrodynamical properties of a radiation gas (Marklund et al. (2003)). In principle, the collective interaction between intense photons in vacuum will generate pulse collapse scenarios in two and three dimensions. In such a pulse collapse, the intensity of the pulse grows very large in a short time (Marklund & Shukla (2006)). Thus, one might probe the quantum vacuum using ELI in the same way as one has probed nonlinear optical systems over forty years with intense lasers.
FIG. 5: One schematic setup to probe collective and dynamical nonlinear [...] (Courtesy: Mattias Marklund) 
FIG. 6: The Generation of higher harmonics from the quantum vacuum (Courtesy: Mattias Marklund) 
Similarly, the possibility to observe higher harmonic generation through quantum vacuum interaction is within the scope of the ELI facility. Here the vacuum is excited by a nonparallel multiphoton process, such that there results a collection of photons which a frequency upshifted (see FIG. 6) (Fedotov & Narozhny (2006)). Such process have yet to be detected, and could hold surprises of nonlinear vacuum physics, much as in the laserplasma case for which unexpected higher harmonics were found.
The Schwinger limit
For electric fields E ~ mc^{2}/λ_{C }~ 10^{29} W/cm^{2}, where λ_{C} is the Compton wavelength (Schwinger (1951)), virtual electronpositron pairs will be able to separate and become real. For the case of highly relativistic attosecond electron bunches produced by the ELI laser interactiong with material targets, a secondary laser pulse would, upon interaction with these bunches, be reflected and intensified. Such a scenario could help reach the Schwinger limit, for which the vacuum becomes fully nonlinear. Fundamental issues concerning pair creation processes in space and time varying fields could then for the first time in history be experimentally investigated, a truly unique perspective.
Pseudoscalar modifications of the Standard Model
Currently, there is a regained interest in the possible modification of the Standard Model using pseudoscalar fields. This interest has its origin in several new observations and experiments (see, e.g., Zavattini et al. (2006) and references therein). The so called axion will couple to the electromagnetic field through the invariant E·B. The possibility to generate strong magnetic field through laserplasma interactions, and the subsequent use of these fields for probing the axion scale is an interesting experimental tool deriving from ELI. This could put further limits on astrophysical bounds, as well as give independent tests of these modifications to the Standard Model.
b. HawkingUnruh radiation
One of the most outstanding issues in physics today is how quantum theory, gravity, and thermodynamics are related, and the connection of these questions to black hole physics. Black holes are collapsed stars, for which the formation of event horizon signals the fact that not even light can escape such object. This is an intriguing consequence of general relativity, a classical field theory. However, when such a theory is combined with quantum field theory, new physics is introduced. Hawking showed in the early 1970’s (Hawking  1974) that such a semiclassical calculation gives rise to a thermal spectrum emitted by the black hole, so called Hawking radiation (see FIG. 6). This means that black holes are only black at the classical level, but at the quantum level they tend to loose mass in the form of a thermal radiation. The connection between this radiation, its temperature, and the entropy of black holes has deep connections to information theory, quantum gravity, and thermodynamics. Therefore the detection of such an effect would shed light on a multitude of deeply connected issues in modern physics. The temperature of this radiation is however proportional to the surface gravity at the event horizon, and for normal sized black holes, this temperature is much too low to be detected. Analogous to the Hawking effect is the so Unruh effect (Unruh  1976), in which the gravitational acceleration of the black hole is replaced by the acceleration of an observer, see FIG. 6 (this can heuristically be seen as an effect of the equivalence of gravitational and intertial mass). An observer undergoing constant acceleration would measure a nonzero temperature with respect to a zero temperature vacuum in the laboratory frame. The effect arises due to the change in the vacuum energy state in the accelerated frame. As the accelerated observer thermalizes with the background Unruh temperature, radiation would be emitted. In principle, this emission can be measured. The possible detection of this radiation is a rather longstanding experimental problem. An experimental setup based on the extreme acceleration (>10^{24} g) of an electron beam in intense counter propagating laser pulses would act as a test of the HawkingUnruh effect (see FIG. 7).
FIG. 7: The schematics of the experimental setup for Unruh radiation detection. Note than the radiation is emitted in a very particular direction as well as frequency, thus being detectable even if the background “noise” is high. (Courtesy: Mattias Marklund) 
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