Publications of Institute of Theoretical Physics - Year 2023 to 2025

Quantum path interferences occur whenever multiple equivalent and coherent transitions result in a common final state. Such interferences strongly modify the probability of a particle to be found in that final state, a key concept of quantum coherent control. When multiple nonlinear and energy-degenerate transitions occur in a system, the multitude of possible quantum path interferences is hard to disentangle experimentally. Here, we analyze quantum path interferences during the nonlinear emission of electrons from hybrid plasmonic and photonic fields using time-resolved photoemission electron microscopy.We experimentally distinguish quantum path interferences by exploiting the momentum difference between photons and plasmons and through balancing the relative contributions of their respective fields. Our work provides a fundamental understanding of the nonlinear photon–plasmon–electron
interaction. Distinguishing emission processes in momentum space, as introduced here, could allow nano-optical quantum-correlations to be studied without destroying the quantum path interferences.

We consider birefringent (i.e., polarization changing) scattering of x-ray photons at the superposition of two optical laser beams of ultrahigh intensity and study the resonant contributions of axions or axionlike particles, which could also be short lived. Applying the specifications of the Helmholtz International Beamline for Extreme Fields (HIBEF), we find that this setup can be more sensitive than previous light-bylight scattering (birefringence) or light-shining-through-wall experiments in a certain domain of parameter space. By changing the pump and probe laser orientations and frequencies, one can even scan different axion masses, i.e., chart the axion propagator.

The critical behavior of the order-disorder phase transition in the buckled dimer structure of the Si(001) surface is investigated both theoretically by means of first-principles calculations and experimentally by spot profile analysis low-energy electron diffraction (SPA-LEED). We use density functional theory (DFT) with three different functionals commonly used for Si to determine the coupling constants of an effective lattice Hamiltonian describing the dimer interactions. Experimentally, the phase transition from the low-temperature c(4×2)- to the high-temperature p(2×1)-reconstructed surface is followed through the intensity and width of the superstructure spots within the temperature range 78–400K. Near the critical temperature Tc = 190.6K, we observe universal critical behavior of spot intensities and correlation lengths, which falls into the universality class of the two-dimensional (2D) Ising model. From the ratio of correlation lengths along and across the dimer rows we determine effective nearest-neighbor couplings of an anisotropic 2D Ising model,
J = (−24.9 ± 0.9stat ± 1.3sys )meV and J⊥ = (−0.8 ± 0.1stat )meV.We find that the experimentally determined coupling constants of the Ising model can be reconciled with those of the more complex lattice Hamiltonian
from DFT when the critical behavior is of primary interest. The anisotropy of the interactions derived from the
experimental data via the 2D Ising model is best matched by DFT calculations using the PBEsol functional.
The trends in the calculated anisotropy are consistent with the surface stress anisotropy predicted by the
DFT functionals, pointing towards the role of surface stress reduction as a driving force for establishing the
c(4×2)-reconstructed ground state.

We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the commutativity of different terms in the target Hamiltonian. It allows one to realize the required four-body interactions in a nonperturbative way, attaining strong coupling and the suppression of undesired processes. In addition, we design an optimal protocol for preparing the topologically ordered ground states with high fidelity. A proof-of-principle implementation of a topological device and its use to simulate the topological phase transition are also discussed. The proposed scheme finds natural implementation in architectures of superconducting qubits with tunable couplings.

We show that there exists a generalized, universal notion of the trace anomaly for theories which are not conformally invariant at the classical level. The definition is suitable for any regularization scheme and clearly states to what extent the classical equations of motion should be used, thus resolving existing controversies surrounding previous proposals. Additionally, we exhibit the link between our definition of the anomaly and the functional Jacobian arising from a Weyl transformation.

For the Mott insulator state of the Fermi-Hubbard model in the strong-coupling limit, we study the interaction between quasi-particles in the form of doublons and holons. Comparing different methods – the hierarchy of correlations, strong-coupling perturbation theory, and exact analytic solutions for the Hubbard tetramer – we find an effective interaction between doublons and/or holons to linear order in the hopping strength which can display attractive as well as repulsive contributions, depending on the involved momenta. Finally, we speculate about the implications of our findings for high-temperature uperconductivity.

We study the interaction between gravitational waves and quantum matter such as Bose-Einstein condensates, superfluid helium, or ultracold solids, explicitly taking into account the changes of the trapping potential induced by the gravitational wave. As a possible observable, we consider the change of energy due to the gravitational wave, for which we derive rigorous bounds in terms of kinetic energy and particle number. Finally, we discuss implications for possible experimental tests.

We study how tunneling through a potential barrier V(x) can be enhanced by an additional harmonically oscillating electric field E(t)=E0 cos(ωt). To this end, we transform into the Kramers-Henneberger frame and calculate the coupled Floquet channels numerically. We find distinct signatures of resonances when the incident energy E equals the driving frequency ω=E which clearly shows the breakdown of the time-averaged potential approximation. As a simple model for experimental applications (e.g., in solid state physics), we study the rectangular potential, which can also be benchmarked with respect to analytical results. Finally, we consider the truncated Coulomb potential relevant for nuclear fusion.

A unified set of predictions for pion and kaon elastic electromagnetic and gravitational form factors is obtained using a symmetry-preserving truncation of each relevant quantum field equation. A key part of the study is a description of salient aspects of the dressed graviton + quark vertices. The calculations reveal that each meson’s mass radius is smaller than its charge radius, matching available empirical inferences; and meson core pressures are commensurate with those in neutron stars. The analysis described herein paves the way for a direct calculation of nucleon gravitational form factors.

We apply a classical mathematical problem, the moment problem, with its related mathematical achievements, to the study of the parton distribution function (PDF) in hadron physics, and propose a strategy to sieve the moments of the PDF by exploiting its properties such as continuity, unimodality, and symmetry. Through an error-inclusive sifting process, we refine three sets of PDF moments from Lattice QCD. This refinement significantly reduces the errors, particularly for higher order moments, and locates the peak of PDF simultaneously. As our strategy is universally applicable to PDF moments from any method, we strongly advocate its integration into all PDF moment calculations.

Using a reaction model that incorporates pion bound state effects and continuum results for proton parton distributions and the pion distribution amplitude, $\varphi_\pi$, we deliver parameter-free predictions for the $\mu^+$ angular distributions in $\pi N \to \mu^+ \mu^- X$ reactions on both unpolarised and polarised targets. The analysis indicates that such angular distributions are sensitive to the pointwise form of $\varphi_\pi$ and suggests that unpolarised targets are practically more favourable. The precision of extant data is insufficient for use in charting $\varphi_\pi$; hence, practical tests of this approach to charting $\varphi_\pi$ must await data with improved precision from new-generation experiments. The reaction model yields a nonzero single-spin azimuthal asymmetry, without reference to $T$-odd parton distribution functions (DFs). This may necessitate additional care when attempting to extract such $T$-odd DFs from data.

Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity of such problems, but it requires the knowledge of an invariant compatible with the Hamiltonian of the system in question. We explore the potential of a Gaussian invariant that is suitable for quadratic Hamiltonians with any given number of motional degrees of freedom for quantum optimal control problems that are inspired by current challenges in ground-state to ground-state shuttling of trapped ions.

The photon blockade effect is commonly exploited in the development of single-photon sources. While the photon blockade effect could be used to prepare high-fidelity single-photon states in idealized regimes, practical implementations in optomechanical systems suffer from an interplay of competing processes. Here we derive a control scheme that exploits destructive interference of Fock state amplitudes of more than one photon. The resulting preparation time for photon-blockaded quantum states is limited only by the optomechanical interaction strength and can thus be orders of magnitude shorter than in existing schemes that achieve photon blockade in the steady state.

We calculate the momentum spectrum of electron-positron pairs created via the Schwinger mechanism by a class of four-dimensional electromagnetic fields called e-dipole fields. To the best of our knowledge, this is the first time the momentum spectrum has been calculated for 4D, exact solutions to Maxwell’s equations. Moreover, these solutions give fields that are optimally focused, and are hence particularly relevant for future experiments. To achieve this we have developed a worldline instanton formalism where we separate the process into a formation and an acceleration region.

We investigate superradiant enhancements in the refrigeration performance in a set of N three-level systems that are collectively coupled to a hot and a cold thermal reservoir and are additionally subject to collective periodic (circular) driving. Assuming the system-reservoir coupling to be weak, we explore the regime of stronger periodic driving strengths by comparing collective weak-driving, Floquet-Lindblad, and Floquet-Redfield master equations. We identify regimes where the power injected by the periodic driving is used to pump heat from the cold to the hot reservoir and derive analytic sufficient conditions for them based on a cycle analysis of the Floquet-Lindblad master equation. In those regimes, we also argue for which parameters collective enhancements like a quadratic scaling of the cooling current with N can be expected and support our arguments by numerical simulations.

Using the external field method, {\it i.e.\/} evaluating the effective action $V_{\mathrm{eff}}$ for an arbitrarily strong constant and homogeneous field, we explore nonperturbative properties of QED allowing arbitrary gyromagnetic ratio $g$. We find a cusp at $g = 2$ in: a) The QED $b_0$-renormalization group coefficient, and in the infinite wavelength limit in b) a subclass containing the pseudoscalar ${\cal P}^{2n}= (\vec E\cdot\vec B)^{2n} $ of light-light scattering coefficients. Properties of $b_0$ imply for certain domains of $g$ asymptotic freedom in an Abelian theory.

We implement a longstanding proposal by Weisskopf to apply virtual polarization corrections to
the in/out external fields in study of the Euler-Heisenberg-Schwinger effective action. Our approach
requires distinguishing the electromagnetic and polarization fields based on mathematical tools
developed by Bia lynicki-Birula, originally for the Born-Infeld action. Our solution is expressed
as a differential equation where the one-loop effective action serves as input. As a first result of
our approach, we recover the higher-order one-cut reducible loop diagrams discovered by Gies and
Karbstein.

The coupling energies between the buckled dimers of the Si(001) surface were determined through analysis of the anisotropic critical behavior of its order-disorder phase transition. Spot profiles in high-resolution low-energy electron diffraction as a function of temperature were analyzed within the framework of the anisotropic two-dimensional Ising model. The validity of this approach is justified by the large ratio of correlation lengths, ζ +/ζ∥+=5.2 of the fluctuating c(4×2) Domains above the critical temperature Tc=(190.6±10) K. We obtain effective couplings J∥=(-24.9±1.3) meV along the dimer rows and J⊥=(-0.8±0.1) meV across the dimer rows, i.e., antiferromagneticlike coupling of the dimers with c(4×2) symmetry.

Theory suggests that in high-energy elastic hadron+hadron scattering, t-channel exchange of a family of colourless crossingodd
states – the odderon – may generate differences between pp¯ and pp cross-sections in the neighbourhood of the
diffractive minimum. Using a mathematical approach based on interpolation via continued fractions enhanced by statistical
sampling, we develop robust comparisons between pp¯ elastic differential cross-sections measured at √s=1.96 TeV by the
D0 Collaboration at the Tevatron and function-form-unbiased extrapolations to this energy of kindred pp measurements at
√s/TeV=2.76,7,8,13 by the TOTEM Collaboration at the LHC and a combination of these data with earlier cross-section
measurements at √s/GeV=23.5,30.7,44.7,52.8,62.5 made at the intersecting storage rings. Focusing on a domain that
straddles the diffractive minimum in the pp¯ and pp cross-sections, we find that these two cross-sections differ at the
(2.2−2.6)σ level; hence, supply evidence with this level of significance for the existence of the odderon. If combined with
evidence obtained through different experiment-theory comparisons, whose significance is reported to lie in the range
(3.4−4.6)σ, one arrives at a (4.0−5.2)σ signal for the odderon.

Schwinger pair creation in a purely time-dependent electric field can be reduced to an effective quantum mechanical problem using a variety of formalisms. Here we develop an approach based on the Gelfand-Dikii equation for scalar QED, and extent it to spinor QED. We discuss some solvable special cases from this point of view. It was previously shown how to use the well-known solitonic solutions of the KdV equation to construct “solitonic” electric fields that do not create scalar pairs with an arbitrary fixed momentum. We show that this construction can be adapted to the fermionic case in two inequivalent ways, both leading to the vanishing of the pair-creation rate at certain values of the P ̈oschl-Teller like index of the associated Schr ̈odinger equation. Thus for any given momentum, we can construct electric fields that create scalar particles but not spinor particles, and also the other way round. Therefore, while often spin is even neglected in Schwingerpair creation, in such cases it becomes decisive.

Electric Dipole Moments (EDM) of particles (leptons, nucleons and light nuclei) are currently deemed one of the best indicators for new physics, i.e. phenomena, which lie outside the Stand-ard Model (SM) of elementary particle physics – so called physics “Beyond-the-Standard-Model” (BSM). Since EDMs of the SM are vanishingly small, a finite permanent EDM would indicate charge-parity symmetry (CP-) violation in addition to the well-known sources of the SM and could explain the baryon asymmetry of the Universe, while an oscillating EDM would hint at a possible Dark Matter (DM) field comprising axions or axion-like particles (ALPs). A new ap-proach exploiting polarized charged particles (proton, deuteron, 3He) in precision storage rings offers the prospect to push current experimental EDM upper limits significantly further includ-ing the possibility of an EDM discovery. In this paper, we describe the scientific background and the steps towards the realization of a precision storage ring, which will make such measure-ments possible.

Motivated by recent experimental initiatives, such as at the
Helmholtz International Beamline for Extreme Fields (HIBEF)
at the European X-ray Free Electron Laser (XFEL), we calculate
the birefringent scattering of x-rays at the combined field of
two optical (or near-optical) lasers and compare various scenarios.
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In order to facilitate an experimental detection of quantum vacuum diffraction and
birefringence, special emphasis is placed on scenarios where the initial
and final x-ray photons differ not just in polarization, but also in
propagation direction (corresponding to scattering angles in the mrad regime)
and possibly energy.

In this article we consider resummed expressions for the heat-kernel's
trace of a Laplace operator, the latter including a potential and imposing Dirichlet semitransparent boundary conditions on a surface of codimension one in flat space.
We obtain resummed expressions that correspond to the first and second order expansion of the heat-kernel in powers of the potential.
We show how to apply these results to obtain the bulk and surface form factors of a scalar quantum field theory in $d=4$ with a Yukawa coupling to a background.
A characterization of the form factors in terms of pseudo-differential operators is given.

In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario.
We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one.
In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert space for the Klein--Gordon case.

We show how to use the worldline-instanton formalism to calculate the momentum spectrum of the electron-positron pairs produced by an electric field that depends on both space and time. Using the LSZ reduction formula with a worldline representation for the propagator in a spacetime field, we make use of the saddle-point method to obtain a semiclassical approximation of the pair-production spectrum. In order to check the final result, we integrate the spectrum and compare with the results obtained using a previous instanton method for the imaginary part of the effective action.

Particle production through ultra-strong electric fields is a well-studied research field. Nevertheless, despite repeated attempts to relate the production rate within the field to the formation time of a particle, the latter is still shrouded in mystery. We provide an interpretation of a particle
distribution at finite times enabling us to isolate and, therefore, identify the relevant time scales
regarding particle formation in quantum physics within and beyond perturbation theory.

We provide a novel approach to calculate the gravitational form factor of pion under the ladder approximation of the Bethe-Salpeter equation, with contact interactions. Central to this approach is a symmetry-preserving treatment of the dressed ππ amplitude, which shows explicitly the contributions from intrinsic quarks and bound states, the latter being necessary to produce the D-term of pion in the soft-pion limit. The approach we provide in this work can be applied to many processes of physical significance.

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton’s existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale invariant. Thus, if the Standard Model is truly a part of the theory of Nature, then the proton mass is an emergent feature of QCD; and emergent hadron mass (EHM) must provide the basic link between theory and observation. Nonperturbative tools are necessary if such connections are to be made; and in this context, we sketch recent progress in the application of continuum Schwinger function methods to an array of related problems in hadron and particle physics. Special emphasis is given to the three pillars of EHM – namely, the running gluon mass, process-independent effective charge, and running quark mass; their role in stabilising QCD; and their measurable expressions in a diverse array of observables.

A single qutrit with transitions selectively driven by weakly-coupled reservoirs can implement one of the world's smallest refrigerators. We analyze the performance of N such fridges that are collectively coupled to the reservoirs. We observe a quantum boost, manifest in a quadratic scaling of the steady-state cooling current with N. As N grows further, the scaling reduces to linear, since the transitions responsible for the quantum boost become energetically unfavorable. Fine-tuned inter-qutrit interactions may be used to maintain the quantum boost for all N and also for not-perfectly collective scenarios.

We discover a correspondence between the free field and the interacting states. This correspondence is firstly given from the fact that the free propagator can be converted into a tower of propagators for massive states, when expanded with the Hermite function basis. The equivalence of propagators reveals that in this particular case the duality can naturally be regarded as the equivalence of one theory on the plane wave basis to the other on the Hermite function basis. More generally, the Hermite function basis provides an alternative quantization process with the creation/annihilation operators that correspond directly to the interacting fields. Moreover, the Hermite function basis defines an exact way of dimensional reduction. As an illustration, we apply this basis on 3+1 dimensional Yang-Mills theory with three dimensional space being reduced through the Hermite function basis, and if with only the lowest order Hermite function, the equivalent action becomes the Banks-Fischler-Shenker-Susskind (BFSS) matrix model.

The QED four-photon amplitude has been well-studied by many authors, and on-shell is treated in many textbooks. However, a calculation with all four photons off-shell is presently still lacking, despite of the fact that this amplitude appears off-shell as a subprocess in many different contexts, in vacuum as well as with some photons connecting to external fields. The present paper is the first in a series of four where we use the worldline formalism to obtain this amplitude explicitly in terms of hypergeometric functions, and derivatives thereof, for both scalar and spinor QED. The formalism allows us to unify the scalar and spinor loop calculations, to avoid the usual breaking up of the amplitude into three inequivalent Feynman diagrams, and to achieve manifest transversality as well as UV finiteness at the integrand level by an optimized version of the integration-by-parts procedure originally introduced by Bern and Kosower for gluon amplitudes. The full permutation symmetry is maintained throughout, and the amplitudes get projected naturally into the basis of five tensors introduced by Costantini et al. in 1971. Since in many applications of the “four-photon box” some of the photons can be taken in the low-energy limit, and the formalism makes it easy to integrate out any such leg, apart from the case of general kinematics (part 4) we also treat the special cases of one (part 3) or two (part 2) photons taken at low energy. In this first part of the series, we summarize the application of the worldline formalism to the N-photon amplitudes and its relationto Feynman diagrams, derive the optimized tensor-decomposed integrands of the four-photon amplitudes in scalar and spinor QED, and outline the computational strategy tobe followed in parts 2 to 4. We also give an overview of the applications of the four-photon amplitudes, with an emphasis on processes that naturally involve some off-shell photons, either because external fields are involved or we use the amplitude as a building block for higher-order process. The case where all photons are taken at low energy (the “Euler-Heisenberg approximation”) is simple enough to be doable for arbitrary photon numbers,and we include it here for completeness

We study optical absorption at graphene edges in a transversal magnetic field. The magnetic field bends the trajectories of particle- and hole excitations into antipodal direction which generates a directed current. We find a rather strong amplification of the edge current by impact ionization processes. More concretely, the primary absorption and the subsequent carrier multiplication is analyzed for a graphene fold and a zigzag edge. We identify exact and approximate selection rules and discuss the dependence of the decay rates on the initial state.

The hierarchy of correlations is an analytical approximation method which allows us to study non-equilibrium phenomena in strongly interacting quantum many-body systems on lattices in higher dimensions. So far, this method was restricted to equal-time correlators ⟨A ^ μ (t)B ^ ν (t)⟩ . In this work, we generalize this method to double-time correlators ⟨A ^ μ (t)B ^ ν (t ′ )⟩ , which allows us to study effective light cones and Green functions and to incorporate finite initial temperatures.