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Experimental evidence of quantum radiation reaction in aligned crystals

Quantum radiation reaction is the influence of multiple photon emissions from a charged particle on the particle's dynamics, characterized by a significant energy-momentum loss per emission. Here we report experimental radiation emission spectra from ultrarelativistic positrons in silicon in a regime where quantum radiation reaction effects dominate the positron's dynamics. Our analysis shows that while the widely used quantum approach is overall the best model, it does not completely describe all the data in this regime. Thus, these experimental findings may prompt seeking more generally valid methods to describe quantum radiation reaction. This experiment is a fundamental test of quantum electrodynamics in a regime where the dynamics of charged particles is strongly influenced not only by the external electromagnetic fields but also by the radiation field generated by the charges themselves and where each photon emission may significantly reduce the energy of the charge.

Here, u i is the positron four-velocity, s its proper-time, q = e > 0 and m its charge and mass 12 respectively, and F ij the electromagnetic field tensor of the crystal (see, for example, (2)). The 13 crystal field has been modeled starting from from the sum of Doyle-Turner string potentials (3), 14 1 centered on a regular grid according to the diamond cubic crystal structure. Once the positron 15 trajectory has been determined, the emission spectrum has been computed starting from the 16 Liénard-Wiechert potential and following the standard procedure, as described, for example, 17 in (2) and based on the expression of the differential intensity of radiation dI/dωdΩ per unit of 18 emitted radiation frequency ω and solid angle Ω: where the electron position r(t), velocity β(t) = u(t)/u 0 (t), and accelerationβ(t) = dβ(t)/dt 20 are obtained from the solution of the LL equation, and where n is the direction of observation 21 corresponding to the solid angle Ω.

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Model 2: Semiclassical plus radiation reaction model (SCRRM). In this model we partially 23 include quantum effects following an approach described, for example, in (4), where the term 24 involving the derivative of the field in supplementary Eq. (1) is neglected and the remaining 25 two are multiplied by the ratio g(χ(x)) between the quantum total emitted power and the cor-26 responding classical quantity calculated at the local value χ(x) of the quantum nonlinearity 27 parameter, where (see, for example, (5)): with K ν (·) being the modified Bessel function of order ν.

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The emission spectrum has then been evaluated as in the CRRM. This model phenomeno-30 logically takes into account that quantum effects reduce the total radiation yield but it does not 31 account for the intrinsic stochasticity of the photon emission process (see, for example, (6)).
where ε(t) and χ(t) are the positron energy and the value of the quantum parameter at time chosen sufficiently small such that the resulting single-photon emission probability is much 45 smaller than unity). In the former case, on the one hand, the photon energy is also determined 46 by sampling another random number using the procedure shown in (12), such that the emitted photons are consistently distributed in accordance with the formula for radiation emission also 48 in the CCF approximation (see, for example, (11)): where the variable u = ω/(ε − ω) is employed rather than the emitted photon energy. On probabilities within the CCF approximation are employed here (like in for example (6, 13, 14)).

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However, since the parameter ξ is in some cases only comparable to unity in the experiment, the 56 model has been improved and the straightforward kinetic approach as described, for example, 57 in (11) is insufficient. In order to see this more quantitatively, we show in supplementary figure  1 panel a) the differential probability of photon emission calculated within the CCF approxima-59 tion (green curve) and the more accurate approach using the general formula for the differential 60 intensity of radiation (see (11) and also (15-17)): with ε = ε − ω, ω = ωε/ε , and whose numerical procedure is outlined in (16). All curves thus shows that some particles are not measured due to the high rate (saturation effect).