Nonlinear single Compton scattering has been thoroughly investigated in the literature under the assumption that initially the electron has a definite momentum.Here, we study a more general initial state, and consider the electron as a wavepacket. In particular, we investigate the energy spectrum of the emitted radiation and show that in typical experimental situations some features of the spectra shown in previous works are almost completely washed out. Moreover, we show that at comparable relative uncertainties, the one in the momentum of the incoming electron has a larger impact on the photon spectra at a fixed observation direction than the one on the laser frequency. I. INTRODUCTIONAccording to classical electrodynamics a charged particle (an electron, for definiteness) accelerated by a background electromagnetic field emits radiation [1]. In the underlying quantum theory, QED, the radiation process is rather described as the emission of photons by the electron [2,3]. Due to energy-momentum conservation a free electron is stable and cannot emit photons. The scattering of an electron with a single photon is known as (linear) Compton scattering. In general, the simultaneous interaction of an electron with many photons is suppressed by the appearance in the interaction probabilities of a corresponding power of the fine-structure constant α QED ≈ 1/137 1. However, if the electron interacts with a coherent collection of photons, like those in a laser beam, the effective coupling strength appearing in perturbative expansions is not just α QED , but it also depends on the typical amplitude and angular frequency of the laser field [4]. Qualitatively it is clear that a laser field characterized by an amplitude E and by an angular frequency ω is able to transfer

Accelerated charges emit electromagnetic radiation. According to classical electrodynamics, if the charges move along sufficiently close trajectories they emit coherently; i.e., their emitted energy scales quadratically with their number rather than linearly. By investigating the emission by a two-electron wave packet in the presence of an electromagnetic plane wave within strong-field QED, we show that quantum effects deteriorate the coherence predicted by classical electrodynamics even if the typical quantum nonlinearity parameter of the system is much smaller than unity. We explain this result by observing that coherence effects are also controlled by a new quantum parameter which relates the recoil undergone by the electron to the width of its wave packet in momentum space.

In the realm of laser-plasma interactions, if the laser intensity is strong enough, quantum effects play a significant role. Due to the large separation between the length scale at which quantum electrodynamic processes form and both the typical separation between particles in a plasma and the wavelength of optical lasers, it is possible in many situations of interest to take into account quantum electrodynamic processes in a fairly straightforward way. If one considers plasmas of increasingly large densities, the presence of many particles can render potentially unavoidable a full quantum treatment of the dynamics. Here, two kinds of multi-particle effects are discussed within strong-field Quantum Electrodynamics. First, we show how a correct description of coherence effects in the radiation emitted by a two-electron wave packet in a strong laser field requires a quantum treatment also if the quantum nonlinearity parameter of the system is much smaller than unity. Secondly, we indicate that at solid-state densities the presence of several particles within the formation region of radiation by an electron in a strong electromagnetic field may alter the emission probability itself, such that in general it is not possible to disentangle collective effects from quantum effects.

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