Non-perturbative Description of Quantum Systems

Probing non-perturbative QED with electron-laser collisions

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In principle, a generalization to longer laser pulses is possible when using the attosecond lighthouse technique The dimensionless vector potential a 0 is set to , which corresponds to a peak intensity of 1. It is assumed to be fully ionized initially. The ion mass-to-charge ratio is chosen to be two times that of protons, which means that one could potentially use any fully ionized low-Z species as a target material.

The plasma profile impacts the efficiency of the generation of high harmonics and defines the requirements for the contrast of the high-power laser pulse Initially, the beam is shifted spatially so that it hits the EM attosecond pulse in its focus. The figure shows a sketch of the proposed scheme.

Perturbation theory (quantum mechanics) - Wikiwand

The plasma converts the incoming radiation into an ultraintense attosecond pulse via high harmonic generation. At this time instant, the EM field is most tightly focused in the transverse direction and it is most compressed in the longitudinal direction, leading finally to the emergence of an ultraintense and ultrashort EM pulse. A transverse and a longitudinal characterization of the pulse is given in Fig. In particular, Fig. In addition, the focused pulse appears to be very narrow on the applied length scale.

Therefore, the inset shows an enlarged picture of the main peak. One can extract a duration full width at half maximum, FWHM of roughly as from the data. Comparing this with the radiation time in Eq. At this moment in time the pulse reaches its peak value. The figure shows a characterization of the a longitudinal profile of the generated EM pulse, seen by the ultrarelativistic electron beam.

It can be seen that the electrons in the vicinity of the focal spot indeed experience such extreme conditions that one could probe the breakdown of perturbation theory. The model describes the evolution of the system in a self-consistent manner since it also takes into account the generation of secondary particles. A comparison with particle spectra obtained from simulations indicates reasonable agreement. The analytical approach is based on the distribution of particles in the phasespace. The corresponding time evolution of the system is described by the Boltzmann equations BE, for electrons, photons and positrons; see, for example Thus, the BE in a constant homogeneous magnetic field of the strength H can be used instead of using an alternating laser field.

In this regime, the differential probabilities can be written as The BE is a linear equation whose solution can be expressed in the general case with time-ordered exponentials 42 , and the dependence of these differential probabilities on the field strength H suggests the following assumption.

Prior to entering the regime of fully non-perturbative QED, experiments will surely approach a perturbative supercritical regime.

In the following, it is explained how one can identify the perturbative supercritical regime, and how one probably detect the break of perturbative QED, so enabling the determination of its range of validity. Therefore, a series of additional PIC simulations is performed in a one-dimensional geometry. This kind of pulse is subsequently referred to as a clean Gaussian pulse.

Simultaneously, the spectrum of the generated photon beam will reproduce the shape of w rad if the EM pulse is short enough, as shown in the previous section. Thus, the shape of the photon spectrum remains the same when one increases the amplitude of an ultrashort EM pulse.

This is in a good agreement with Fig. The electron beam parameters remain unchanged see the numerical modeling section for more information. One can observe that all photon spectra obey the same power-law behavior that coincides with the behavior of the first generation of the photons predicted by Eq. Thus, for ultrashort EM pulses, a change of the photon spectrum shape can indicate the entering in the regime of non-perturbative QED. This duration is used since it matches the one of the generated main pulse [see Fig. Besides, Fig. The values of the power-law indexes are given in the labels.

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It can be seen in Fig. However, note that the best power-law index for the photon distribution in Fig.

This may indicate that the photon distribution function is already influenced by further generations of secondary photons. Therefore, simulations with shorter pulses are carried out. If the EM pulse is not short enough, more generations of secondary particles should be taken into account. This can be seen, for instance, when returning to the photon spectrum that is obtained in the proposed setup [see solid lines in Fig. A deviating power-law index indicates that the analytical solution 11 and 12 is inapplicable, and hence the pre- and postpulses of the attosecond pulse have to be included in the BE, e.

This can be achieved as follows. The interaction of such a pulse with the electron beam results in particle spectra that coincide very good with the spectra obtained in the proposed setup, as can be seen from the dashed curves in Fig.

The comparison with the reference spectra in Fig. In conclusion, an experimental scheme has been proposed that might be promising for exploring a supercritical regime of radiation reaction or even a fully non-perturbative regime of QED. This scheme considers the generation of an ultraintense attosecond pulse via high harmonic generation at an over-dense plasma surface. In a second step, the EM attosecond pulse collides with a counterpropagating GeV-class electron beam in a nearly head-on geometry.

Numerical PIC simulations underline the feasibility of the proposal. An analytical treatment reveals that if the attosecond pulse is short enough, the number of secondary particles will be small and the differential probability of the photon emission can be measured directly in the proposed scheme. Based on perturbative QED, the model further indicates that in the case of relatively long attosecond pulses the most part of the resulting particle spectra can be reproduced in simple one-dimensional simulations with clean Gaussian pulses of appropriate duration.

If the Nikishov—Ritus formulas break, simple one-dimensional simulations will not be able to reproduce the experimental spectra any more, indicating the entering of the regime where high-order radiative corrections become important. Strickland, D.

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Compression of amplified chirped optical pulses. Yanovsky, V. Ultra-high intensityTW laser at 0.

Danson, C. Petawatt class lasers worldwide. Pirozhkov, A. Approaching the diffraction-limited, bandwidth-limited Petawatt.

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