Publications
Involved institute: Theoretical Physics (from 2018)
Year 20202022
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 timedependent electric field with special emphasis on pulseshaped vector potentials such as A(t)=A0/cosh^2(ωt). In addition to the known effects of preacceleration and potential deformation already present in the adiabatic regime, as well as energy mixing in analogy to the FranzKeldysh effect in the nonadiabatic (impulse) regime, the pulse A(t) can enhance tunneling by ``pushing'' part of the wavefunction 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

Physical Review Research 3(2021), 033153
DOI: 10.1103/PhysRevResearch.3.033153
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.

Physical Review D 101(2020), 056017
DOI: 10.1103/PhysRevD.101.056017
Approximating higherorder nonlinear QED processes with firstorder building blocks
Dinu, V.; Torgrimsson, G.
Higherorder treelevel 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 firstorder processes, i.e., nonlinear Compton scattering and nonlinear BreitWheeler pair production. At high intensity the field can be treated as locally constant, which is the basis for standard particleincell codes. However, the locallyconstantfield (LCF) approximation and these particleincell 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 firstorder 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.

Physical Review D 102(2020), 016018
DOI: 10.1103/PhysRevD.102.016018
Nonlinear trident in the highenergy limit: Nonlocality, Coulomb field and resummations
Torgrimsson, G.
We study nonlinear trident in laser pulses in the highenergy 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 “twostep” part, but in the highenergy limit the dominant contribution comes instead from the onestep term. We obtain new approximations that explain the relation between the highenergy limit of trident and pair production by a Coulomb field, as well as the role of the WeizsäckerWilliams approximation and why it does not agree with the highχ limit of the locallyconstantfield approximation. We also show that the nexttoleading order in the largea0 expansion is, in the highenergy limit, nonlocal and is numerically very important even for quite large a0. We show that the smalla0 perturbation series has a finite radius of convergence, but using Padéconformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the largea0 approximation. We use BorelPadéconformal methods to resum the smallχ expansion and obtain a high precision up to very large χ. We also use newer resummation methods based on hypergeometric/MeijerG and confluent hypergeometric functions.

Physical Review D 102(2020), 096008
DOI: 10.1103/PhysRevD.102.096008
Nonlinear photon trident versus double Compton scattering and resummation of onestep terms
Torgrimsson, G.
We study the photon trident process, where an initial photon turns into an electronpositron pair and a final photon under a nonlinear interaction with a strong planewave 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 onestep 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 MeijerG 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.

Physical Review D 102(2020), 116008
DOI: 10.1103/PhysRevD.102.116008
Loops and polarization in strongfield QED
Torgrimsson, G.
In a previous paper we showed how higherorder strongfieldQED processes in long laser pulses can be approximated by multiplying sequences of ‘strongfield 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 locallyconstant and the locallymonochromaticfield 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.

New Journal of Physics 23(2021), 065001
DOI: 10.1088/13672630/abf274
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 highintensity laser, including multiple photon emissions and loops. We find a recursive formula that allows us to obtain the O(αn) term from O(αn1), which can also be expressed as an integrodifferential equation. In the classical limit we obtain the solution to the LandauLifshitz equation to all orders. We show how spindependent quantum radiation reaction can be obtained by resumming both the energy expansion as well as the α expansion.

Physical Review Letters 127(2021), 111602
DOI: 10.1103/PhysRevLett.127.111602
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 planewave 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 constantfield 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 SokolovTernov formula for a constant field, or the zero result for a circularly monochromatic field. We also study the AbrahamLorentzDirac equation using BorelPadé resummations.

Physical Review D 104(2021), 056016
DOI: 10.1103/PhysRevD.104.056016
Generalized LandauKhalatnikovFradkin transformations for arbitrary Npoint 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 Npoint functions where we derive an exact, generalized version of the fully nonperturbative LandauKhalatnikovFradkin (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; Nonperturbative QED

Physical Review D 104(2021), 025014
Online First (2021) DOI: 10.1103/PhysRevD.104.025014
Observability of Coulombassisted quantum vacuum birefringence
Ahmadiniaz, N.; Bussmann, M.; Cowan, T.; Debus, A.; Kluge, T.; Schützhold, R.
We consider the scattering of an xray freeelectron 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.

Physical Review D 104(2021), L011902
Online First (2021) DOI: 10.1103/PhysRevD.104.L011902
Downloads:
 Original PDF 625 kB Secondary publication
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Superradiant manyqubit absorption refrigerator
Kloc, M.; Meier, K.; Hadjikyriakos, K.; Schaller, G.
We show that the lower levels of a largespin network with a collective antiferromagnetic interaction and collective couplings to three reservoirs may function as a quantum absorption refrigerator. In appropriate regimes, the steadystate 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

Contribution to WWW
https://arxiv.org/abs/2106.04164 
Physical Review Applied 16(2021), 044061104406115
Online First (2021) DOI: 10.1103/PhysRevApplied.16.044061
Downloads:
 Original PDF 3,8 MB Secondary publication
Broadband frequency filters with quantum dot chains
Ehrlich, T.; Schaller, G.
Twoterminal 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 detailedbalance. Looser bounds originating from fluctuation theorem symmetries alone remain respected. We demonstrate that optimal finitesized 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; LevitovLesovik formula; transmission; reactioncoordinate mapping
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Contribution to WWW
https://arxiv.org/abs/2103.04322 
Physical Review B 104(2021), 045424
Online First (2021) DOI: 10.1103/PhysRevB.104.045424
Downloads:
 Original PDF 660 kB Secondary publication
Coarsegraining master equation for periodically driven systems
Hotz, R.; Schaller, Gernot
We analyze LindbladGoriniKossakowskiSudarshantype generators for selected periodically driven open quantum systems. All these generators can be obtained by temporal coarsegraining procedures, and we compare different coarsegraining schemes. Similar to for undriven systems, we find that a dynamically adapted coarsegraining time, effectively yielding nonMarkovian dynamics by interpolating through a series of different but invididually Markovian solutions, yields the best results among the different coarsegraining schemes, albeit at highest computational cost.
Keywords: open quantum systems; Floquet theory; periodic driving; Lindblad master equation

Contribution to WWW
arXiv:2102.03063 [quantph]: https://arxiv.org/abs/2102.03063 
Physical Review A 104(2021), 052219
Online First (2021) DOI: 10.1103/PhysRevA.104.052219
Downloads:
 Original PDF 1,2 MB Secondary publication
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 timedependence, and models that make use of timedependent 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 selfoscillations, 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 singleelectron working fluid is unrealistic, but already a fewelectron 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; selfoscillation; autonomous control; electron shuttle

Contribution to WWW
https://arxiv.org/abs/2101.05027 
Physical Review Letters 126(2021), 180605
Online First (2021) DOI: 10.1103/PhysRevLett.126.180605
Downloads:
 Original PDF 417 kB Secondary publication
 Fulltext from journals.aps.org
Worldline master formulas for the dressed electron propagator, part 1: Offshell amplitudes
Ahmadiniaz, N.; Guzman, V. M. B.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.
In the firrstquantised worldline approach to quantum field theory, a longstanding problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the welltested closedloop 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 secondorder 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 BernKosower 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

Journal of High Energy Physics 08(2020)018
Online First (2020) DOI: 10.1007/JHEP08(2020)018
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Trappedion 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 welldefined 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 machinelearning 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 realtime 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)

Philosophical Transactions of the Royal Society A 378(2020)2177, 20190230
DOI: 10.1098/rsta.2019.0230
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 schemeswhile for ordinary linearoptics 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

Physical Review D 101(2020), 116019
Online First (2020) DOI: 10.1103/PhysRevD.101.116019
Downloads:
 Original PDF 285 kB Secondary publication
 Fulltext from link.aps.org
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 welldefined and unambiguous ab initio treatment of quantum electrodynamics in such media, even in timedependent 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).

Contribution to WWW
arXiv:1912.09869: https://arxiv.org/abs/1912.09869 
Physical Review D 102(2020)12, 125020
DOI: 10.1103/PhysRevD.102.125020
Offshell Ward identities for Ngluon amplitudes
Offshell Ward identities in nonabelian gauge theory continue to be a subject of active research, since they are, in general, inhomogeneous and their form depends on the chosen gaugefixing procedure. For the threegluon and fourgluon vertices, it is known that a relatively simple form of the Ward identity can be achieved using the pinch technique or, equivalently, the backgroundfield method with quantum Feynman gauge. The latter is also the gaugefixing underlying the stringinspired formalism, and here we use this formalism to derive the corresponding form of the Ward identity for the oneloop N  gluon amplitudes.

Contribution to WWW
arXiv:2001.00885: https://arxiv.org/abs/2001.00885 
EPL  Europhysics Letters 130(2020), 41001
Online First (2020) DOI: 10.1209/02955075/130/41001
Downloads:
 Final Draft PDF 225 kB Secondary publication
 Fulltext from iopscience.iop.org
Pair production in temporally and spatially oscillating fields
Aleksandrov, I. A.; Kohlfürst, C.
Electronpositron pair production for inhomogeneous electric and magnetic fields oscillating in space and time is investigated. By employing accurate numerical methods (Furrypicture 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.

Contribution to WWW
arXiv:1912.09924: https://arxiv.org/abs/1912.09924 
Physical Review D 101(2020)9, 096009
DOI: 10.1103/PhysRevD.101.096009
On the effect of timedependent inhomogeneous magnetic fields on the particle momentum spectrum in electronpositron pair production
Electronpositron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the DiracHeisenbergWigner 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 equaltime Wigner approach is formulated in terms of partial integrodifferential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.

Contribution to WWW
arXiv:1912.09359: https://arxiv.org/abs/1912.09359 
Physical Review D 101(2020)9, 096003
DOI: 10.1103/PhysRevD.101.096003
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 stronglyinteracting twosite FermiHubbard model that is induced by fermionic baths. To derive the proper form of the Lindblad operators that enter an effective description of the systembath coupling in different temperature regimes, we employ a diagrammatic realtime technique for the reduced density matrix. An improvement on the commonlyused 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.

Contribution to WWW
arXiv:1910.04130: https://arxiv.org/abs/1910.04130 
Physical Review B 101(2020), 125131
DOI: 10.1103/PhysRevB.101.125131
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 nonequilibrium phenomena in quantum manybody 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/Zexpansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strongcoupling limit, collisions between particles and holes dominate over particleparticle and holehole 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.

Contribution to WWW
arXiv:1909.12802: https://arxiv.org/abs/1909.12802 
Physical Review B 100(2020)24, 245110
DOI: 10.1103/PhysRevB.100.245110
Comptonlike scattering of a scalar particle with N photons and one graviton
Ahmadiniaz, N.; Balli, F. M.; Corradini, O.; Dávila, J. M.; Schubert, C.
Treelevel 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 Nphoton twoscalar amplitudes where one photon line emits the graviton. We test our construction by verifying the onshell gauge and diffeomorphism Ward identities, at arbitrary N.
Keywords: Scattering amplitudes; gravitons; Ward identities

Nuclear Physics B 950(2020), 114877
DOI: 10.1016/j.nuclphysb.2019.114877