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 solution (contour integral) of the Riccati equation in 1+1 spacetime dimensions, we find that a Gaussian-shaped pulse $E_{\mathrm{weak}}\exp[-(ωt)^{2}]$ assists tunneling in a similar way but with $ω_{\mathrm{crit}}$ depending on $E_{\mathrm{weak}}$. This remarkable sensitivity to the pulse shape arises due to the different pole structures of the vector potentials for complex times. We also study dynamical assistance by an oscillation $E_{\mathrm{weak}}\cos(ωt)$ as a model for counterpropagating laser beams and find another dependence $ω_{\mathrm{crit}}(E_{\mathrm{weak}})$.
The largeness of the Schwinger limit $E_{\mathrm{crit}}^{\mathrm{QED}}\approx 10^{18}\,\mathrm{V/m}$ has rendered the observation of this nonperturbative pair-creation mechanism impossible so far. In order to facilitate a better understanding of this effect and its dynamical assistance via experiments, we propose an analog of the many-body Dirac Hamiltonian in direct-bandgap semiconductors. The nonrelativistic Bloch-electron Hamiltonian is restricted to the valence and conduction bands in reciprocal space, which correspond to the two relativistic energy continua. Similar models have been considered before---but mainly for constant external fields. [...]
The Sauter-Schwinger effect predicts the creation of electron-positron pairs out of the quantum vacuum via tunneling induced by a strong electric field. Unfortunately, as the required field strength is extremely large, this fundamental prediction of quantum field theory has not been verified experimentally yet. Here, we study under which conditions and approximations the interband tunneling in suitable semiconductors could be effectively governed by the same (Dirac) Hamiltonian, especially for electric fields which depend on space and time. This quantitative analogy would allow us to test some…
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.
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…
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 …
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 electron-positron pair creation by a strong and slowly varying electric field, assisted by a weaker and more rapidly changing field (e.g., in the keV regime) plus an additional high-energy (say MeV) photon. It turns out that this combination can yield a pair creation probability which is exponentially larger than in the case where one (or more) of the three ingredients is missing. Apart from a deeper understanding of these non-perturbative phenomena, this double enhancement may pave the way for an experimental verification of this fundamental prediction.
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 …
From the sixties a deep and surprising connection has followed the development of superconductivity and quantum field theory. The Anderson-Higgs mechanism and the similarities between the Dirac and Bogoliubov-de Gennes equations are the most intriguing examples. In this last analogy, the massive Dirac particle is identified with a quasiparticle excitation and the fermion mass energy with the superconducting gap energy. Here we follow further this parallelism and show that it predicts an outstanding phenomenon: the superconducting Schwinger effect (SSE). As in the quantum electrodynamics Schwin…
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…
A detailed analysis of electron-positron pair creation induced by a spatially nonuniform and static electric field from vacuum is presented. A typical example is provided by the Sauter potential. For this potential, we derive the analytic expressions for vacuum decay and pair production rate accounted for the entire range of spatial variations. In the limit of a sharp step, we recover the divergent result due to the singular electric field at the origin. The limit of a constant field reproduces the classical result of Euler, Heisenberg and Schwinger, if the latter is properly averaged over the…
Schwinger pair creation in a purely time-dependent electric field can be described through a quantum Vlasov equation describing the time evolution of the single-particle momentum distribution function. This equation exists in two versions, both of which can be derived by a Bogoliubov transformation, but whose equivalence is not obvious. For the spinless case, we show here that the difference between these two evolution equations corresponds to the one between the "in-out" and "in-in" formalisms. We give a simple relation between the asymptotic distribution functions generated by the two Vlasov…
The spin-3/2 elementary particle, known as Rarita-Schwinger (RS) fermion, is described by a vector-spinor field ψ_{μα}, whose number of components is larger than its independent degrees of freedom (DOF). Thus the RS equations contain nontrivial constraints to eliminate the redundant DOF. Consequently the standard procedure adopted in realizing relativistic spin-1/2 quasi-particle is not capable of creating the RS fermion in condensed matter systems. In this work, we propose a generic method to construct a Hamiltonian which implicitly contains the RS constraints, thus includes the eigenstates a…
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…
The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\vec{E}(\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial differential equations of infinite order for the sixteen irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory (QKT) is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field $E(t)=E_0$ and the Sauter-type e…
Besides tunneling in static potential landscapes, for example, the Wentzel-Kramers-Brillouin (WKB) approach is a powerful nonperturbative approximation tool to study particle creation due to time-dependent background fields, such as cosmological particle production or the Sauter-Schwinger effect, i.e., electron-positron pair creation in a strong electric field. However, our understanding of particle creation processes in background fields depending on both space and time is rather incomplete. In order to venture into this direction, we propose a generalization of the WKB method to truly spacet…
We study the Schwinger mechanism in the presence of an additional uniformly oriented, weak super Gaussian of integer order $4N+2$. Using the worldline approach, we determine the relevant critical points to compute the leading order exponential factor analytically. We show that increasing the parameter $N$ gives rise to a strong dynamical enhancement. For $N=2$, this effect turns out to be larger compared to a weak contribution of Sauter type. For higher orders, specifically, for the rectangular barrier limit, i.e. $N \rightarrow \infty$, we approach the Lorentzian case as an upper bound. Altho…
There are deep similarities between non-linear QFT studied in high-energy and non-equilibrium physics in condensed matter. Ideas such as the Schwinger mechanism and the Volkov state are deeply related to non-linear transport and photovoltaic Hall effect in condensed matter. Here, we give a review on these relations.
We investigate the Schwinger pair production phenomena in spatially homogeneous strong electric fields. We first consider scalar QED in four-dimensions and discuss the potential ambiguity in the adiabatic order assignment for the electromagnetic potential required to fix the renormalization subtractions. We argue that this ambiguity can be solved by invoking the conformal anomaly when both electric and gravitational backgrounds are present. We also extend the adiabatic regularization method for spinor QED in two-dimensions and find consistency with the chiral anomaly. We focus on the issue of …
Emergence of higher spin relativistic fermionic materials becomes a new favorite in the study of condensed matter physics. Massive Rarita-Schwinger 3/2-spinor was known owning very exotic properties, such as the superluminal fermionic modes and even being unstable in an external magnetic field. Due to the superluminal modes and the non-trivial constraints on the Rarita-Schwinger gas, we exposit anomalous properties of the Hall effects in (2+1)-dimensions which subvert the well-known quantum Hall paradigms. First, the Hall conductance of a pure Rarita-Schwinger gas is step-like but not plateau-…
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 …
In this paper we give an overview of some recent progress in using holography to study various far-from-equilibrium condensed matter systems. Non-equilibrium problems are notoriously difficult to deal with, not to mention at strong coupling and including quantum effects. Remarkably, using holographic duality one can describe and follow the real time evolution of a far-from-equilibrium systems, including those which are spatially inhomogeneous and anisotropic, by solving partial differential gravity equations (PDEs). We sample developments on two broad classes of questions which are of much rec…
The interplay of symmetry, topology, and many-body effects in the classification of possible phases of matter poses a formidable challenge that is attracting great attention in condensed-matter physics. Such many-body effects are typically induced by inter-particle interactions involving an action at a distance, such as the Coulomb interaction between electrons in a symmetry-protected topological (SPT) phase. In this work, we show that similar phenomena also appear in high-energy physics, where inter-particle interactions are mediated by gauge bosons, and constrained by a local gauge symmetry.…
