Involved institute: Theoretical Physics (from 2018)
Year 2020-2022
Public type of publication: Articles ref. in Journals
"Online First" included

Dynamically assisted tunneling in the impulse regime

Kohlfürst, C.; Queißer, F.; Schützhold, R.

We study the enhancement of tunneling through a potential barrier V(x) by a time-dependent electric field with special emphasis on pulse-shaped vector potentials such as A(t)=A0/cosh^2(ωt). In addition to the known effects of pre-acceleration and potential deformation already present in the adiabatic regime, as well as energy mixing in analogy to the Franz-Keldysh effect in the non-adiabatic (impulse) regime, the pulse A(t) can enhance tunneling by ``pushing'' part of the wave-function out of the rear end of the barrier. Besides the natural applications in condensed matter and atomic physics, these findings could be relevant for nuclear fusion, where pulses A(t) with ω=1 keV and peak field strengths of 10^16 V/m might enhance tunneling rates significantly.

Keywords: Tunneling & traversal time; Nuclear fusion; Schroedinger equation

Trident process in laser pulses

Dinu, V.; Torgrimsson, G.

We study the trident process in laser pulses. We provide exact numerical results for all contributions, including the difficult exchange term. We show that all terms are in general important for a short pulse. For a long pulse, we identify a term that gives the dominant contribution even if the intensity is only moderately high, a0≳1, which is an experimentally important regime where the standard locally constant field (LCF) approximation cannot be used. We show that the spectrum has a richer structure at a0∼1, compared to the LCF regime a0≫1. We study the convergence to LCF as a0 increases and how this convergence depends on the momentum of the initial electron. We also identify the terms that dominate at high energy.

Approximating higher-order nonlinear QED processes with first-order building blocks

Dinu, V.; Torgrimsson, G.

Higher-order tree-level processes in strong laser fields, i.e., cascades, are in general extremely difficult to calculate, but in some regimes the dominant contribution comes from a sequence of first-order processes, i.e., nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. At high intensity the field can be treated as locally constant, which is the basis for standard particle-in-cell codes. However, the locally-constant-field (LCF) approximation and these particle-in-cell codes cannot be used when the intensity is only moderately high, which is a regime that is experimentally relevant. We have shown that one can still use a sequence of first-order processes to estimate higher orders at moderate intensities provided the field is sufficiently long. An important aspect of our new “gluing” approach is the role of the spin and polarization of intermediate particles, which is more nontrivial compared to the LCF regime.

Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field and resummations

Torgrimsson, G.

We study nonlinear trident in laser pulses in the high-energy limit, where the initial electron experiences, in its rest frame, an electromagnetic field strength above Schwinger’s critical field. At lower energies the dominant contribution comes from the “two-step” part, but in the high-energy limit the dominant contribution comes instead from the one-step term. We obtain new approximations that explain the relation between the high-energy limit of trident and pair production by a Coulomb field, as well as the role of the Weizsäcker-Williams approximation and why it does not agree with the high-χ limit of the locally-constant-field approximation. We also show that the next-to-leading order in the large-a0 expansion is, in the high-energy limit, nonlocal and is numerically very important even for quite large a0. We show that the small-a0 perturbation series has a finite radius of convergence, but using Padé-conformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the large-a0 approximation. We use Borel-Padé-conformal methods to resum the small-χ expansion and obtain a high precision up to very large χ. We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions.

Nonlinear photon trident versus double Compton scattering and resummation of one-step terms

Torgrimsson, G.

We study the photon trident process, where an initial photon turns into an electron-positron pair and a final photon under a nonlinear interaction with a strong plane-wave background field. We show that this process is very similar to double Compton scattering, where an electron interacts with the background field and emits two photons. We also show how the one-step terms can be obtained by resumming the small- and large-\chiχ expansions. We consider a couple of different resummation methods, and also propose new resummations (involving Meijer-G functions) which have the correct type of expansions at both small and large \chiχ. These new resummations require relatively few terms to give good precision.

Loops and polarization in strong-field QED

Torgrimsson, G.

In a previous paper we showed how higher-order strong-field-QED processes in long laser pulses can be approximated by multiplying sequences of ‘strong-field Mueller matrices’. We obtained expressions that are valid for arbitrary field shape and polarization. In this paper we derive practical approximations of these Mueller matrices in the locally-constant- and the locally-monochromatic-field regimes. The spin and polarization can also change due to loop contributions (the mass operator for electrons and the polarization operator for photons). We derive Mueller matrices for these as well, for arbitrary laser polarization and arbitrarily polarized initial and final particles.

Resummation of Quantum Radiation Reaction in Plane Waves

Torgrimsson, G.

We propose a new approach to obtain the momentum expectation value of an electron in a high-intensity laser, including multiple photon emissions and loops. We find a recursive formula that allows us to obtain the O(αn) term from O(αn-1), which can also be expressed as an integro-differential equation. In the classical limit we obtain the solution to the Landau-Lifshitz equation to all orders. We show how spin-dependent quantum radiation reaction can be obtained by resumming both the energy expansion as well as the α expansion.

Resummation of quantum radiation reaction and induced polarization

Torgrimsson, G.

In a previous paper we proposed a new method based on resummations for studying radiation reaction of an electron in a plane-wave electromagnetic field. In this paper we use this method to study the electron momentum expectation value for a circularly polarized monochromatic field with a0=1, for which standard locally constant-field methods cannot be used. We also find that radiation reaction has a significant effect on the induced polarization, as compared to the results without radiation reaction, i.e., the Sokolov-Ternov formula for a constant field, or the zero result for a circularly monochromatic field. We also study the Abraham-Lorentz-Dirac equation using Borel-Padé resummations.

Generalized Landau-Khalatnikov-Fradkin transformations for arbitrary N-point fermion correlators

Ahmadiniaz, N.; Edwards, J. P.; Nicasio, J.; Schubert, C.

We examine the nonperturbative gauge dependence of arbitrary configuration space fermion correlators in quantum electrodynamics (QED). First, we study the dressed electron propagator (allowing for emission or absorption of any number of photons along a fermion line) using the first quantized approach to quantum field theory and analyze its gauge transformation properties induced by virtual photon exchange. This is then extended to the N-point functions where we derive an exact, generalized version of the fully nonperturbative Landau-Khalatnikov-Fradkin (LKF) transformation for these correlators. We discuss some general aspects of the application in perturbation theory and investigate the structure of the LKF factor aboutD¼2dimensions

Keywords: LKFT; Worldline formalism; Non-perturbative QED

Observability of Coulomb-assisted quantum vacuum birefringence

Ahmadiniaz, N.; Bussmann, M.; Cowan, T.; Debus, A.; Kluge, T.; Schützhold, R.

We consider the scattering of an x-ray free-electron laser (XFEL) beam on the superposition of
a strong magnetic field $\bf{B}_{\rm ext}$ with the Coulomb field $\bf{E}_{\rm ext}$
of a nucleus with charge number $Z$. In contrast to Delbr\"uck scattering
(Coulomb field only), the magnetic field $\bf{B}_{\rm ext}$
introduces an asymmetry (i.e., polarization dependence) and renders the effective interaction volume quite
large, while the nuclear Coulomb field facilitates a significant momentum transfer $\Delta\bf k$.
For a field strength of $B_{\rm ext}=10^6 T$ (corresponding to an intensity of order $10^{22}~\rm W/cm^2$)
and an XFEL frequency of 24~keV, we find a differential cross section
$d\sigma/d\Omega\sim10^{-25}~Z^2/(\Delta{\bf k})^2$ in forward direction for one nucleus.
Thus, this effect might be observable in the near future at facilities such as the
Helmholtz International Beamline for Extreme Fields (HIBEF) at the European XFEL.


Superradiant many-qubit absorption refrigerator

Kloc, M.; Meier, K.; Hadjikyriakos, K.; Schaller, G.

We show that the lower levels of a large-spin network with a collective anti-ferromagnetic interaction and collective couplings to three reservoirs may function as a quantum absorption refrigerator. In appropriate regimes, the steady-state cooling current of this refrigerator scales quadratically with the size of the working medium, i.e., the number of spins. The same scaling is observed for the noise and the entropy production rate.

Keywords: open quantum systems; collective interactions; quantum heat engine; quantum absorbtion refrigerator; Dicke superradiance


Broadband frequency filters with quantum dot chains

Ehrlich, T.; Schaller, G.

Two-terminal electronic transport systems with a rectangular transmission can violate standard thermodynamic uncertainty relations. This is possible beyond the linear response regime and for parameters that are not accessible with rate equations obeying detailed-balance. Looser bounds originating from fluctuation theorem symmetries alone remain respected. We demonstrate that optimal finite-sized quantum dot chains can implement rectangular transmission functions with high accuracy and discuss the resulting violations of standard thermodynamic uncertainty relations as well as heat engine performance.

Keywords: fluctuation theorems; thermodynamic uncertainty relation; Levitov-Lesovik formula; transmission; reaction-coordinate mapping

Related publications


Coarse-graining master equation for periodically driven systems

Hotz, R.; Schaller, Gernot

We analyze Lindblad-Gorini-Kossakowski-Sudarshan-type generators for selected periodically driven open quantum systems. All these generators can be obtained by temporal coarse-graining procedures, and we compare different coarse-graining schemes. Similar to for undriven systems, we find that a dynamically adapted coarse-graining time, effectively yielding non-Markovian dynamics by interpolating through a series of different but invididually Markovian solutions, yields the best results among the different coarse-graining schemes, albeit at highest computational cost.

Keywords: open quantum systems; Floquet theory; periodic driving; Lindblad master equation


Autonomous implementation of thermodynamic cycles at the nanoscale

Strasberg, P.; Wächtler, C. W.; Schaller, G.

There are two paradigms to study nanoscale engines in stochastic and quantum thermodynamics.
Autonomous models, which do not rely on any external time-dependence, and models that make use of time-dependent control fields, often combined with dividing the control protocol into idealized strokes of a thermodynamic cycle. While the latter paradigm offers theoretical simplifications, its utility in practice has been questioned due to the involved approximations. Here, we bridge the two paradigms by constructing an autonomous model, which implements a thermodynamic cycle in a certain parameter regime. This effect is made possible by self-oscillations, realized in our model by the well studied electron shuttling mechanism. Based on experimentally realistic values, we find that a thermodynamic cycle analysis for a single-electron working fluid is unrealistic, but already a few-electron working fluid could suffice to justify it. We also briefly discuss additional open challenges to autonomously implement the more studied Carnot and Otto cycles.

Keywords: thermodynamic cycle; self-oscillation; autonomous control; electron shuttle


Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes

Ahmadiniaz, N.; Guzman, V. M. B.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.

In the firrst-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics (QED) in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons in configuration as well as in momentum space.

Keywords: Worlline formalism; QED; Scattering Amplitudes; Gauge Symmetry


Trapped-ion toolkit for studies of quantum harmonic oscillators under extreme conditions

Wittemer, M.; Schröder, J.-P.; Hakelberg, F.; Kiefer, P.; Fey, C.; Schützhold, R.; Warring, U.; Schaetz, T.

Many phenomena described in relativistic quantum field theory are inaccessible to direct observations, but analogue processes studied under well-defined laboratory conditions can present an alternative perspective. Recently, we demonstrated an analogy of particle creation using an intrinsically robust motional mode of two trapped atomic ions. Here, we substantially extend our classical control techniques by implementing machine-learning strategies in our platform and, consequently, increase the accessible parameter regime. As a proof of methodology, we present experimental results of multiple quenches and parametric modulation of an unprotected motional mode of a single ion, demonstrating the increased level of real-time control. In combination with previous results, we enable future experiments that may yield entanglement generation using a process in analogy to Hawking radiation. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.

Keywords: Trapped Ions; Qubits; Ion Traps (Instrumentation)

Heisenberg limit for detecting vacuum birefringence

Ahmadiniaz, N.; Cowan, T.; Sauerbrey, R.; Schramm, U.; Schlenvoigt, H.-P.; Schützhold, R.

Quantum electrodynamics predicts the vacuum to behave as a nonlinear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly nonlinear measurement schemes--while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.

Keywords: Quantum Electrodynamics; Vacuum birefringence; Heisenberg limit


Quantum radiation in dielectric media with dispersion and dissipation

Lang, S.; Schützhold, R.; Unruh, W.

By a generalization of the Hopfield model, we construct a microscopic Lagrangian describing a dielectric medium with dispersion and dissipation. This facilitates a well-defined and unambiguous ab initio treatment of quantum electrodynamics in such media, even in time-dependent backgrounds. As an example, we calculate the number of photons created by switching on and off dissipation in dependence on the temporal switching function. This effect may be stronger than quantum radiation produced by variations of the refractive index Δn(t) since the latter are typically very small and yield photon numbers of order (Δn)². As another difference, we find that the partner particles of the created medium photons are not other medium photons but excitations of the environment field causing the dissipation (which is switched on and off).

Off-shell Ward identities for N-gluon amplitudes

Ahmadiniaz, N.; Schubert, C.

Off-shell Ward identities in non-abelian gauge theory continue to be a subject of active research, since they are, in general, inhomogeneous and their form depends on the chosen gauge-fixing procedure. For the three-gluon and four-gluon vertices, it is known that a relatively simple form of the Ward identity can be achieved using the pinch technique or, equivalently, the background-field method with quantum Feynman gauge. The latter is also the gauge-fixing underlying the string-inspired formalism, and here we use this formalism to derive the corresponding form of the Ward identity for the one-loop N - gluon amplitudes.


Pair production in temporally and spatially oscillating fields

Aleksandrov, I. A.; Kohlfürst, C.

Electron-positron pair production for inhomogeneous electric and magnetic fields oscillating in space and time is investigated. By employing accurate numerical methods (Furry-picture quantization and quantum kinetic theory), final particle momentum spectra are calculated and analyzed in terms of effective models. Furthermore, criteria for the applicability of approximate methods are derived and discussed. In this context, special focus is placed on the local density approximation, where fields are assumed to be locally homogeneous in space. Eventually, we apply our findings to the multiphoton regime. Special emphasis is on the importance of linear momentum conservation and the effect of its absence in momentum spectra within approximations based on local homogeneity of the fields.

On the effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron-positron pair production

Kohlfürst, C.

Electron-positron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the Dirac-Heisenberg-Wigner formalism (quantum kinetic theory) through computing the corresponding Wigner functions. The focus is on discussing the particle momentum spectrum regarding signatures of Schwinger and multiphoton pair production. Special emphasis is put on studying the impact of a strong dynamical magnetic field on the particle distribution functions. As the equal-time Wigner approach is formulated in terms of partial integro-differential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.

Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation

Schützhold, R.; Kleinherbers, E.; Szpak, N.; König, J.

We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbard model that is induced by fermionic baths. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the reduced density matrix. An improvement on the commonly-used secular approximation, referred to as coherent approximation, is presented. We analyze the spectrum of relaxation rates and identify different time scales that are involved in the equilibration of the Hubbard dimer after a quantum quench.

Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice

Queißer, F.; Schützhold, R.; Schreiber, S.; Kratzer, P.

Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium.The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z-expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation time scales strongly depend on the type of excitations (particles or holes or both) that are initially present.

Compton-like scattering of a scalar particle with N photons and one graviton

Ahmadiniaz, N.; Balli, F. M.; Corradini, O.; Dávila, J. M.; Schubert, C.

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a tree replacement rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N.

Keywords: Scattering amplitudes; gravitons; Ward identities