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 applicable to time-dependent tunneling problems, such as appear in many other contexts in particle and nuclear physics, condensed matter physics, atomic physics, chemical physics, and gravitational physics.
The recent developments of high intensity ultra-short laser pulses have raised the hopes of observing Schwinger vacuum pair production which is one of the important non-perturbative phenomena in Quantum electrodynamics (QED). The quantitative analysis of realistic high intensity laser pulses is vital for understanding the effect of the field parameters on the momentum spectrum of the produced particles. In this study, we analyze chirped laser pulses with a sub-cycle structure, and investigate the effects of the chirp parameter on the momentum spectrum of the produced particles. The combined ef…
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 Schwing…
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 time evolution of the adiabatic particle number in both time-dependent electric fields and in de Sitter spaces, and define a super-adiabatic particle number in which the (divergent) adiabatic expansion is truncated at optimal order. In this super-adiabatic basis, the particle number evolves smoothly in time, according to Berry's universal adiabatic smoothing of the Stokes phenomenon. This super-adiabatic basis also illustrates clearly the quantum interference effects associated with particle production, in particular for sequences of time-dependent electric field pulses, and in…
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 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.
We study the Schwinger electron-positron pair production by a strong electromagnetic field of two colliding e-polarized laser pulses with a relative phase shift $Ψ$. The spatio-temporal distribution of created pairs is very sensitive to this phase shift and to polarization of the pulses. We study this dependence in detail and demonstrate how it can be explained in terms of the underlying invariant field structure of the counterpropagating focused pulses.
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…
While the Sauter-Schwinger effect describes nonperturbative electron-positron pair creation from vacuum by a strong and slowly varying electric field $E_{\mathrm{strong}}$ via tunneling, the dynamically assisted Sauter-Schwinger effect corresponds to a strong (exponential) enhancement of the pair-creation probability by an additional weak and fast electric or electromagnetic pulse $E_{\mathrm{weak}}$. Using the WKB and worldline instanton method, we find that this enhancement mechanism strongly depends on the shape of the fast pulse. For the Sauter profile $1/\cosh^2(ωt)$ considered previously…
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 …
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.
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…
We propose a new catalysis mechanism for non-perturbative vacuum electron-positron pair production, by superimposing a plane-wave X-ray probe beam with a strongly focused optical laser pulse, such as is planned at the Extreme Light Infrastructure (ELI) facility. We compute the absorption coefficient arising from vacuum polarization effects for photons below threshold in a strong electric field. This set-up should facilitate the (first) observation of this non-perturbative QED effect with planned light sources such as ELI yielding an envisioned intensity of order 10^{26}W/cm^2.
The Schwinger process in strong electric fields creates particles and antiparticles that are entangled. The entropy of entanglement between particles and antiparticles has been found to be equal to the statistical Gibbs entropy of the produced system. Here we study the effect of quantum interference in sequences of electric pulses, and show that quantum interference suppresses the entanglement entropy of the created quantum state. This is potentially relevant to quantum-enhanced classical communications. Our results can be extended to a wide variety of two-level quantum systems.
Sequences of alternating-sign time-dependent electric field pulses lead to coherent interference effects in Schwinger vacuum pair production, producing a Ramsey interferometer, an all-optical time-domain realization of the multiple-slit interference effect, directly from the quantum vacuum. The interference, obeying fermionic quantum statistics, is manifest in the momentum dependence of the number of produced electrons and positrons along the linearly polarized electric field. The central value grows like $N^2$ for $N$ pulses [i.e., $N$ "slits"], and the functional form is well-described by a …
Quantum entanglement is the characteristic quantum correlation. Here we use this concept to analyze the quantum entanglement generated by Schwinger production of particle-antiparticle pairs in an electric field, as well as the change of mode entanglement as a consequence of the electric field effect on an entangled pair of particles. The system is partitioned by using momentum modes. Various kinds of pairwise mode entanglement are calculated as functions of the electric field. Both constant and pulsed electric fields are considered. The use of entanglement exposes information beyond that in pa…
Dykhne-Davis-Pechukas (DDP) method is a common approximation scheme for the transition probability in two-level quantum systems, as realized in the Landau-Zener effect, leading to an exponentially damping form comparable to the Schwinger pair production rate. We analyze the foundation of the DDP method using a modern complex technique inspired by the Lefschetz-thimble method. We derive an alternative and more adaptive formula that is useful even when the DDP method is inapplicable. As a benchmark, we study the modified Landau-Zener model and compare results from the DDP and our methods. We the…
Recently it has been found that the superposition of a strong and slow electric field with a weaker and faster pulse can significantly enhance the probability for non-perturbative electron-positron pair creation out of the vacuum -- the dynamically assisted Sauter-Schwinger effect. Via the WKB method, we estimate the momentum dependence of the pair creation probability and compare it to existing numerical results. Besides the theoretical interest, a better understanding of this pair creation mechanism should be helpful for the planned experiments aiming at its detection.
Via the worldline instanton method, we study electron-positron pair creation by a strong electric field of the profile $E/\cosh^2(kx)$ superimposed by a weaker pulse $E'/\cosh^2(ωt)$. If the temporal Keldysh parameter $γ_ω=mω/(qE)$ exceeds a threshold value $γ_ω^{\rm crit}$ which depends on the spatial Keldysh parameter $γ_k=mk/(qE)$, we find a drastic enhancement of the pair creation probability -- reporting on what we believe to be the first analytic non-perturbative result for the interplay between temporal and spatial field dependences $E(t,x)$ in the Sauter-Schwinger effect.
The Sauter--Schwinger effect predicts the creation of electron--positron pairs from the vacuum due to a quasiconstant electric field $E_{\mathrm{strong}}$. The pair-creation yield can be exponentially enhanced without destroying the tunneling-like nature of this mechanism by adding a weaker temporal Sauter pulse $E_{\mathrm{weak}}/\cosh^{2}(ωt)$ with $ω$ above a certain threshold $ω_{\mathrm{crit}}$. In this original form of the so-called dynamically assisted Sauter--Schwinger effect, $ω_{\mathrm{crit}}$ is independent of $E_{\mathrm{weak}}\ll E_{\mathrm{strong}}$. Via the semiclassical soluti…
In the framework of quantum electrodynamics (QED) in external potentials, we introduce a method to compute the time-dependence of the expectation value of the current density for time-dependent homogeneous external electric fields. We apply it to the so-called Sauter pulse. For late times, our results agree with the asymptotic value due to electron-positron pair production. We correct, and compare to, a general expression derived by Serber for the linearization in the external field. Based on the properties of the current density, we argue that the appearance of enhanced quasi-particle densiti…
Using Lewis-Riesenfeld theory, we derive an exact non-adiabatic master equation describing the time evolution of the QED Schwinger pair production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov type integral equation, or as a third-order differential equation. In the last version it relates to the KdV equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of time-like delta function pulse fields is also shortly considered. We compare wi…
The quantum vacuum is unstable under the influence of an external electric field and decays into pairs of charged particles, a process which is known as the Schwinger pair production. We propose and demonstrate that this electric field can generate entanglement. Using the Schwinger pair production for constant and pulsed electric fields, we study entanglement for scalar particles with zero spins and Dirac fermions. One can observe the variation of the entanglement produced for bosonic and fermionic modes with respect to different parameters.
The probability of creating an electron-positron pair out of the quantum vacuum by a strong electric field can be enhanced tremendously via an additional weaker time-dependent field. This dynamically assisted Sauter-Schwinger effect has already been studied in several works. It has been found that the enhancement mechanism depends on the shape of the weaker field. For example, a Sauter pulse $1/\cosh(ωt)^2$ and a Gaussian profile $\exp(-ω^2 t^2)$ exhibit significant, qualitative differences. However, so far most of the analytical studies were focused on the exponent entering the pair-creation …
This work covers electron positron pair production in spatially homogeneous electric (and magnetic) fields. Different field configurations are looked at in order to study various phenomena including multiphoton pair production, Sauter-Schwinger pair production and dynamically assisted pair production. The main focus lies on pulsed, rotating fields with one main frequency component which are called rotating Sauter pulses. The results are obtained via two numerical methods, that rest on different theoretical approaches. A generic method is derived from the Dirac-Heisenberg-Wigner (DHW) formalism…
At strong-coupling and weak-field limit, the scalar Schwinger effect is studied by the field-theoretical method of worldline instantons for dynamic fields of single-pulse and sinusoidal types. By examining the Wilson loop along the closed instanton path, corrections to the results obtained from weak-coupling approximations are discovered. They show that this part of contribution for production rate becomes dominant as Keldysh parameter increases, it makes the consideration at strong coupling turn out to be indispensable for dynamic fields. Moreover a breaking of weak-field condition similar to…
