Ultrarelativistic electron states in a general background electromagnetic field

The feasibility of obtaining exact analytical results in the realm of QED in the presence of a background electromagnetic field is almost exclusively limited to a few tractable cases, where the Dirac equation in the corresponding background field can be solved analytically. This circumstance has restricted, in particular, the theoretical analysis of QED processes in intense laser fields to within the plane-wave approximation even at those high intensities, achievable experimentally only by tightly focusing the laser energy in space. Here, within the Wentzel-Kramers-Brillouin (WKB) or eikonal approximation, we construct analytically single-particle electron states in the presence of a background electromagnetic field of general space-time structure in the realistic assumption that the initial energy of the electron is the largest dynamical energy scale in the problem. The relatively compact expression of these states opens, in particular, the possibility of investigating analytically strong-field QED processes in the presence of spatially focused laser beams, which is of particular relevance in view of the upcoming experimental campaigns in this field.Comment: 7 pages, 1 figur

Nonlinear Breit-Wheeler pair production in a tightly focused laser beam

The only available analytical framework for investigating QED processes in a strong laser field systematically relies on approximating the latter as a plane wave. However, realistic high-intensity laser beams feature much more complex space-time structures than plane waves. Here, we show the feasibility of an analytical framework for investigating strong-field QED processes in laser beams of arbitrary space-time structure by determining the energy spectrum of positrons produced via nonlinear Breit-Wheeler pair production as a function of the background field in the realistic assumption that the energy of the incoming photon is the largest dynamical energy in the problem. A numerical evaluation of the angular resolved positron spectrum shows significant quantitative differences with respect to the analogous result in a plane wave, such that the present results will be also important for the design of upcoming strong laser facilities aiming at measuring this process.Comment: 6 pages, 1 figur

First-order strong-field QED processes in a tightly focused laser beam

In [Phys. Rev. Lett. \textbf{117}, 213201 (2016)] we have determined the angular resolved and the total energy spectrum of a positron produced via nonlinear Breit-Wheeler pair production by a high-energy photon counterpropagating with respect to a tightly focused laser beam. Here, we first generalize the results in [Phys. Rev. Lett. \textbf{117}, 213201 (2016)] by including the possibility that the incoming photon is not exactly counterpropagating with respect to the laser field. As main focus of the present paper, we determine the photon angular resolved and total energy spectrum for the related process of nonlinear Compton scattering by an electron impinging into a tightly-focused laser beam. Analytical integral expressions are obtained under the realistic assumption that the energy of the incoming electron is the largest dynamical energy of the problem and that the electron is initially almost counterpropagating with respect to the laser field. The crossing symmetry relation between the two processes in a tightly focused laser beam is also elucidated.Comment: 24 pages, no figure

Quantum Limitation to the Coherent Emission of Accelerated Charges

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 with the width of its wave packet in momentum space.Comment: 6 + 3 SM pages, 3 figure

Ultrarelativistic quasiclassical wave functions in strong laser and atomic fields

The problem of an ultrarelativistic charge in the presence of an atomic and a plane-wave field is investigated in the quasiclassical regime by including exactly the effects of both background fields. Starting from the quasiclassical Green's function obtained in [Phys. Lett. B \textbf{717}, 224 (2012)], the corresponding in- and out-wave functions are derived in the experimentally relevant case of the particle initially counterpropagating with respect to the plane wave. The knowledge of these electron wave functions opens the possibility of investigating a variety of problems in strong-field QED, where both the atomic field and the laser field are strong enough to be taken into account exactly from the beginning in the calculations.Comment: 24 pages, no figure

Nonlinear Compton scattering in ultra-short laser pulses

A detailed analysis of the photon emission spectra of an electron scattered by a laser pulse containing only very few cycles of the carrying electromagnetic field is presented. The analysis is performed in the framework of strong-field quantum electrodynamics, with the laser field taken into account exactly in the calculations. We consider different emission regimes depending on the laser intensity, placing special emphasis on the regime of one-cycle beams and of high laser intensities, where the emission spectra depend nonperturbatively on the laser intensity. In this regime we in particular present an accurate stationary phase analysis of the integrals that are shown to determine the computed emission spectra. The emission spectra show significant differences with respect to those in a long pulsed or monochromatic laser field: the emission lines obtained here are much broader and, more important, no dressing of the electron mass is observed.Comment: 31 pages, 15 figure

Quantum electron self-interaction in a strong laser field

The quantum state of an electron in a strong laser field is altered if the interaction of the electron with its own electromagnetic field is taken into account. Starting from the Schwinger-Dirac equation, we determine the states of an electron in a plane-wave field with inclusion, at leading order, of its electromagnetic self-interaction. On the one hand, the electron states show a pure "quantum" contribution to the electron quasi-momentum, conceptually different from the conventional "classical" one arising from the quiver motion of the electron. On the other hand, the electron self-interaction induces a distinct dynamics of the electron spin, whose effects are shown to be measurable in principle with available technology.Comment: 5 pages, 2 figure

Topological soliton-polaritons in 1D systems of light and fermionic matter

Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between polaritons, which are hybrid quasi-particles mixing matter and light degrees of freedom. Here we introduce a type of polariton which is intrinsically nonlinear and emerges as the natural quasi-particle in presence quantum degenerate fermionic matter. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in a spontaneously formed crystalline structure. Each of these soliton-polaritons carries a $\textbf{Z}_2$ topological quantum number, as they create a domain wall between two crystalline regions with opposite dimerization so that the fermion is trapped in an interphase state. These composite objects are formally equivalent to those appearing in the Su-Schrieffer-Heeger (SSH) model for electrons coupled to lattice phonons.Comment: Edited version. 6+7 pages, 3 figure

Stochasticity effects in quantum radiation reaction

When an ultrarelativistic electron beam collides with a sufficiently intense laser pulse, radiation-reaction effects can strongly alter the beam dynamics. In the realm of classical electrodynamics, radiation reaction has a beneficial effect on the electron beam as it tends to reduce its energy spread. Here, we show that when quantum effects become important, radiation reaction induces the opposite effect, i.e., the electron beam spreads out after interacting with the laser pulse. We identify the physical origin of this opposite tendency in the intrinsic stochasticity of photon emission, which becomes substantial in the full quantum regime. Our numerical simulations indicated that the predicted effects of the stochasticity can be measured already with presently available lasers and electron accelerators.Comment: 5 pages, 2 figure

Macroscopic Superpositions of Phase States with Bose-Einstein Condensates

Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology