We investigate electron-positron pair production from vacuum for short laser pulses with sub-cycle structure, in the nonperturbative regime (Schwinger pair production). We use the non-equilibrium quantum kinetic approach, and show that the momentum spectrum of the created electron-positron pairs is extremely sensitive to the sub-cycle dynamics -- depending on the laser frequency $ω$, the pulse length $τ$, and the carrier phase $ϕ$ -- and shows several distinctive new signatures. This observation could help not only in the design of laser pulses to optimize the experimental signature of Schwinger pair production, but also ultimately lead to new probes of light pulses at extremely short time scales.
We investigate non-perturbative pair production from vacuum (the Schwinger effect) in the focal region of two counter-propagating, ultra-short laser pulses with sub-cycle structure. We use the quantum kinetic formulation to calculate the momentum spectrum of created particles and show the extreme sensitivity to the laser frequency $ω$, the pulse length $τ$ and the carrier-envelope absolute phase $ϕ$. We apply this formalism to both fermions and bosons to illustrate the influence of quantum statistics in this type of electric background field.
Electron-positron pair production by the superposition of two laser pulses with different frequencies and amplitudes is analyzed as a particular realization of the assisted dynamic Schwinger effect. It is demonstrated that, within a non-perturbative kinetic equation framework, an amplification effect is conceivable for certain parameters. When both pulses have wavelengths longer than the Compton wavelength, the residual net density of produced pairs is determined by the resultant field strength. The number of pairs starts to grow rapidly if the wavelength of the high-frequency laser component …
The assistance of an intense optical laser pulse on electron-positron pair production by the Breit-Wheeler and Schwinger processes in XFEL fields is analyzed. The impact of a laser beam on high-energy photon collisions with XFEL photons consists in a phase space redistribution of the pairs emerging in the Breit-Wheeler sub-process. We provide numerical examples of the differential cross section for parameters related to the European XFEL. Analogously, the Schwinger type pair production in pulsed fields with oscillating components referring to a superposition of optical laser and XFEL frequenci…
A detector undergoing a huge acceleration measures a thermal distribution with the Unruh temperature out of the Minkowski vacuum. Though such huge accelerations occur naturally in astrophysics and gravity, one may design untraintense laser facility to detect the Unruh effect and simulate laboratory astrophysics. We derive the QED vacuum polarization and the vacuum persistence amplitude as well as the Schwinger pair creation in an accelerating frame when a constant electric field exists in the Minkowski spacetime. We advance a thermal interpretation of Schwinger pair creation in the Rindler spa…
We numerically investigate the temporal behavior and the structure of longitudinal momentum spectrum and the field polarity effect on pair production in pulsed electric fields in scalar quantum electrodynamics (QED). Using the evolution operator expressed in terms of the particle and antiparticle operators, we find the exact quantum states under the influence of electric pulses and measure the number of pairs of the Minkowski particle and antiparticle. The number of pairs, depending on the configuration of electric pulses, exhibits rich structures in the longitudinal momentum spectrum and unde…
Via a combination of analytical and numerical methods, we study electron-positron pair creation by the electromagnetic field ${\bf A}(t,{\bf r})=[f(ct-x)+f(ct+x)]{\bf e}_y$ of two colliding laser pulses. Employing a generalized WKB approach, we find that the pair creation rate along the symmetry plane $x=0$ (where one would expect the maximum contribution) displays the same exponential dependence as for a purely time-dependent electric field ${\bf A}(t)=2f(ct){\bf e}_y$. The pre-factor in front of this exponential does also contain corrections due to focusing or de-focusing effects induced by …
Recent studies of Schwinger pair production have demonstrated that the asymptotic particle spectrum is extremely sensitive to the applied field profile. We extend the idea of the dynamically assisted Schwinger effect from single pulse profiles to more realistic field configurations to be generated in an all-optical experiment searching for pair creation. We use the quantum kinetic approach to study the particle production and employ a multi-start method, combined with optimal control theory, to determine a set of parameters for which the particle yield in the forward direction in momentum spac…
We study the dynamical Schwinger effect in the vacuum excitation of the electron-positron plasma under action of a "laser pulse" of the simplest configuration: a linearly polarized, time-dependent and spatially homogeneous electric field. Methodical basis of this investigation is the kinetic equation which is an exact consequence of the basic equations of motion of QED in the considered field model. In the present work we investigate some features of the residual electron-positron plasma and the transient process of its formation.
We present simple new approximate formulas, for both scalar and spinor QED, for the number of particles produced from vacuum by a time dependent electric field, incorporating the interference effects that arise from an arbitrary number of distinct semiclassical turning points. Such interference effects are important when the temporal profile of the laser pulse has subcycle structure. We show how the resulting semiclassical intuition may be used to guide the design of temporal profiles that enhance the momentum spectrum due to interference effects. The result is easy to implement and generally …
Recent studies of the dynamically assisted Schwinger effect have shown that particle production is significantly enhanced by a proper choice of the electric field. We demonstrate that optimal control theory provides a systematic means of modifying the pulse shape in order to maximize the particle yield. We employ the quantum kinetic framework and derive the relevant optimal control equations. By means of simple examples we discuss several important issues of the optimization procedure such as constraints, initial conditions or scaling. By relating our findings to established results we demonst…
Particle production due to external fields (electric, chromo-electric or gravitational) requires evolving an initial state through an interaction with a time-dependent background, with the rate being computed from a Bogoliubov transformation between the in and out vacua. When the background fields have temporal profiles with sub-structure, a semiclassical analysis of this problem confronts the full subtlety of the Stokes phenomenon: WKB solutions are only local, while the production rate requires global information. Incorporating the Stokes phenomenon, we give a simple quantitative explanation…
We consider the possibility of experimental verification of vacuum e^+e^- pair creation at the focus of two counter-propagating optical laser beams with intensities 10^{20}-10^{22} W/cm^2, achievable with present-day petawatt lasers, and approaching the Schwinger limit: 10^{29} W/cm^2 to be reached at ELI. Our approach is based on the collisionless kinetic equation for the evolution of the e^+ and e^- distribution functions governed by a non-Markovian source term for pair production. As possible experimental signals of vacuum pair production we consider e^+e^- annihilation into gamma-pairs and…
Non-perturbative electron-positron pair creation (Schwinger effect) is studied based on the equal-time Wigner formalism in 1+1 dimensions. An ab initio calculation of the Schwinger effect in the presence of a simple space- and time-dependent electric field pulse is performed for the first time, allowing for the calculation of the time evolution of observable quantities such as the charge density, the particle number density or the total number of created particles. We predict a new self-bunching effect of charges in phase space due to the spatial and temporal structure of the pulse.
We develop a formalism to describe the particle production out of equilibrium in terms of dynamical spectral functions, i.e. Wigner transformed Pauli-Jordan's and Hadamard's functions. We take an explicit example of a spatially homogeneous scalar theory under pulsed electric fields and investigate the time evolution of the spectral functions. In the out-state we find an oscillatory peak in Hadamard's function as a result of the mixing between positive- and negative-energy waves. The strength of this peak is of the linear order of the Bogoliubov mixing coefficient, whereas the peak correspondin…
Counter-propagating and suitably polarized light (laser) beams can provide conditions for pair production. Here, we consider in more detail the following two situations: (i) In the homogeneity regions of anti-nodes of linearly polarized ultra-high intensity laser beams, the Schwinger process is dynamically assisted by a second high-frequency field, e.g. by a XFEL beam. (ii) A high-energy probe photon beam colliding with a superposition of co-propagating intense laser and XFEL beams gives rise to the laser assisted Breit-Wheeler process. Prospects of such bi-frequent field constellations with r…
The properties of the forced oscillations of electron-positron plasma (EPP) generated from vacuum under the action of a short laser pulse are considered. Calculating the density of the conduction and polarization currents within the quantum kinetic approach, we demonstrate the presence of plasma oscillations at the frequency of the external field and its odd harmonics. It is expected that radiation generated by these plasma oscillations can be observed outside the interaction region, for example, outside the focal spot of two counterpropagating laser beams, and can serve as an indicator of the…
The vacuum of quantum electrodynamics is unstable against the formation of many-body states in the presence of an external electric field, manifesting itself as the creation of electron-positron pairs (Schwinger effect). This effect has been a long-standing but still unobserved prediction as the generation of the required field strengths has not been feasible so far. However, due to the advent of a new generation of high-intensity laser systems such as the European XFEL or the Extreme Light Infrastructure (ELI), this effect might eventually become observable within the next decades. Based on t…
We investigate electron-positron pair production in pulse-shaped electric background fields using a non-Markovian quantum kinetic equation. We identify a pulse-length range for subcritical fields still in the nonperturbative regime where the number of produced pairs significantly exceeds that of a naive expectation based on the Schwinger formula. From a conceptual viewpoint, we find a remarkable quantitative agreement between the (real-time) quantum kinetic approach and the (imaginary-time) effective action approach.
The Sauter-Schwinger effect predicts the creation of electron-positron pairs out of the quantum vacuum by a strong and slowly varying electric field. This effect can be dynamically assisted by an additional weaker time-dependent field, which may drastically enhance the pair-creation probability. In previous studies, it has been found that the enhancement may crucially depend on the temporal shape of this weaker pulse, e.g., a Gaussian profile $\exp\{-(ωt)^2\}$ or a Sauter pulse $1/\cosh^2(ωt)$ behave quite differently. In order to understand this difference, we make a perturbative expansion in…
We study particle creation in a single pulse of an electric field in scalar quantum electrodynamics. We first identify parameter regions of the theory where the dynamical pair creation and Schwinger mechanism respectively dominate each other. Then, analytical expressions for the total characteristics of particle creation are determined for the case where the Schwinger mechanism dominates. We also compare our results with those produced in a constant electric field with a finite-time interval. These results coincide at a strong field regime, however they differ in general field strength. We ide…
Dynamical Sauter-Schwinger mechanism of pair creation by a time-dependent electric field comprising of $N_{\rm rep}$ identical pulses is analyzed within the framework of the spinor and scalar quantum electrodynamics. For linearly polarized pulses, both theories predict that a single eigenmode of the matter wave follows the dynamics of a two-level system. This dynamics, however, is either governed by a Hermitian (for spin 1/2 particles) or pseudo-Hermitian (for spin 0 particles) Hamiltonian. Essentially, both theories lead to a Fraunhofer-type enhancement of the momentum distributions of create…
Non-linear Compton scattering in ultra-short intense laser pulses is discussed with the focus on angular distributions of the emitted photon energy. This is an observable which is accessible easily experimentally. Asymmetries of the azimuthal distributions are predicted for both linear and circular polarization. We present a systematic survey of the influence of the laser intensity, the carrier envelope phase and the laser polarization on the emission spectra for single-cycle and few-cycle laser pulses. For linear polarization, the dominant direction of the emission changes from a perpendicula…
Recently the dynamically assisted Schwinger mechanism, i.e., electron-positron pair production from vacuum by a combination of laser pulses with different time scales has been proposed. The corresponding results, which suggest that the rate of produced pairs is significantly enhanced by dynamical effects, are verified. Employing the framework of quantum kinetic theory intrinsically enables us to additionally provide momentum space information on the generated positron spectrum.
Entropy of Schwinger pair production in time-dependent Sauter pulse electric field
Key Laboratory of Beam Technology of the Ministry of Education, and School of Physics and Astronomy, Beijing Normal University（教育部光束技术重点实验室，北京师范大学物理与天文学院）；School of Mathematics and Physics, Lanzhou Jiaotong University（兰州交通大学数学与计算机科学学院）；Institute of Radiation Technology, Beijing Academy of Science and Technology（北京市科学技术研究院辐射技术研究所）
The spectra of Compton radiation emitted during electron scattering off an intense laser beam are calculated using the framework of strong-field quantum electrodynamics. We model these intense laser beams as finite length plane-wave-fronted pulses, similar to Neville and Rohrlich [Phys. Rev. D {\bf 3}, 1692 (1971)], or as trains of such pulses. Expressions for energy and angular distributions of Compton photons are derived such that a comparison of both situations becomes meaningful. Comparing frequency distributions for both an isolated laser pulse and a laser pulse train, we find a very good…
The emission of electron-positron pairs off a probe photon propagating through a polarized short-pulsed electromagnetic (e.g.\ laser) wave field is analyzed. A significant increase of the total cross section of pair production in the subthreshold region is found for decreasing laser pulse duration even in case of moderate laser pulse intensities.
A scenario for measuring the predicted processes of vacuum elastic and inelastic photon-photon scattering with modern lasers is investigated. Numbers of measurable scattered photons are calculated for the collision of two, Gaussian-focused, pulsed lasers. We show that a single 10PW optical laser beam split into two counter-propagating pulses is sufficient for measuring the elastic process. Moreover, when these pulses are sub-cycle, our results suggest the inelastic process should be measurable too.
The $e^+e^-$ pair production by a probe photon traversing a linearly polarized laser pulse is treated as generalized nonlinear Breit-Wheeler process. For short laser pulses with very few oscillations of the electromagnetic field we find below the perturbative weak-field threshold $\sqrt{s} = 2m$ a similar enhancement of the pair production rate as for circular polarization. The strong subthreshold enhancement is traced back to the finite bandwidth of the laser pulse. A folding model is developed which accounts for the interplay of the frequency spectrum and the intensity distribution in the co…
After the clasical approach to acceleration of a charged particle by delta-form impulsive force, we consider the corresponding quantum theory based on the Volkov solution of the Dirac equation. We determine the modified Compton formula for frequency of photons generated by the scattering of the delta-form laser pulse on the electron in a rest.
Laser pulses facilitate multiphoton contributions to the trident pair production $e_L^- \to e_L^- + e_L^- + e_L^+$ , where the label $L$ indicates a laser field dressed electron ($e^-$) or positron ($e^+$). We isolate the impact of the pulse envelope in the trident S matrix element, formulated within the Furry picture, in leading order of a series expansion in the classical non-linearity parameter $a_0$. Generally, the Fourier transform of the envelope carries the information on the pulse length, which becomes an easily tractable function in the case of a $\cos^2$ pulse envelope. The transitio…
The creation of particles by two colliding strong laser beams is considered. It is found that the electron-positron pairs created in the laser field via the Schwinger mechanism may recollide after one or several oscillations in the field. Their collision can take place at high energy, which the pair gains from the field. As a result, high energy gamma quanta can be created by inelastic scattering or annihilation of the pair. Moreover, heavy particles such as muon pairs may also be created via the annihilation $e^+ + e^-\rightarrow μ^+ + μ^- $. The probability of $e^-e^+$ collision is greatly e…
The probability of electron-positron pair creation by a focused laser pulse is calculated. For description of the focused laser pulse we use a 3-dimensional model of the electromagnetic field which is based on an exact solution of Maxwell equations. There exists two types of focused waves: e- and h-polarized waves with only either electric, or magnetic vector being transverse respectively. It is shown that pair production is possible only in $e$-polarized electromagnetic wave. The dependence of the pair production probability on the intensity of the laser pulse is obtained. It is argued that t…
We present a method for determining the characteristics of an intense laser pulse by probing it with a relativistic electron beam. After an initial burst of very high-energy $γ$-radiation the electrons proceed to emit a series of attosecond duration X-ray pulses as they leave the field. These flashes provide detailed information about the interaction, allowing us to determine properties of the laser pulse: something that is currently a challenge for ultra-high intensity laser systems.
We derive the total cross section for scattering of a photon on an ultra-short laser pulse at high energies. We take into account all multi-photon interactions. We argue that the nonlinear effects due to these interactions become important at very high intensities of the laser pulse. We demonstrate however, that these intensities are significantly lower than the Schwinger critical value.
Experimental efforts toward the detection of the nonperturbative strong-field regime of the Breit-Wheeler pair creation process plan to combine incoherent sources of GeV $γ$ quanta and the coherent fields of tightly focussed optical laser pulses. This endeavour calls for a theoretical understanding of how the pair yields depend on the applied laser field profile. We provide estimates for the number of produced pairs in a setup where the high-energy radiation is generated via bremsstrahlung. Attention is paid to the role of the transversal and longitudinal focussing of the laser field, along wi…
We study the Compton scattering of x-rays off electrons that are driven by a relativistically intense short optical laser pulse. The frequency spectrum of the laser-assisted Compton radiation shows a broad plateau in the vicinity of the laser-free Compton line due to a nonlinear mixing between x-ray and laser photons. Special emphasis is placed on how the shape of the short assisting laser pulse affects the spectrum of the scattered x-rays. In particular, we observe sharp peak structures in the plateau region, whose number and locations are highly sensitive to the laser pulse shape. These stru…
