arXiv subjects

Lars Bojer Madsen

Publications and source records attributed to Lars Bojer Madsen.

At least 19 recordsLinked to original sources

arXiv2026

Modulation of electron wave packets by scattering on time-harmonic potentials

The coherent interaction between free electrons and optical near-fields enables the active modulation of electron wave packets, a mechanism central to photon-induced near-field electron microscopy (PINEM). While existing theories effectively describe these interactions at high kinetic energies, the growing interest in low-energy ultrafast electron microscopy demands frameworks that explicitly account for finite wave packet geometries and recoil effects. In this paper, we develop a rigorous 3D quantum scattering theory for electron wave packets interacting with time-periodic potentials, capturing the case of optical near-field interaction. By mapping the time-dependent dynamics into an extended Floquet space, we formally connect the modulation process to time-independent multi-channel scattering. We evaluate the resulting scattering amplitudes using both an exact R-matrix approach and a multi-channel eikonal approximation. The latter analytical approach recovers PINEM-like probabilities weighted by the wave packet's transverse profile. Application of the theory to an oscillating potential demonstrates the generation of distinct energy sidebands, revealing that the modulation strength is sensitive to the transverse focusing of the incident electron pulse, underlining the importance of a fully 3D treatment.

quant-ph↗

arXiv2026

Roadmap on Attosecond Science

Twenty-five years have passed since the first experimental demonstration of attosecond pulses, marking the advent of our ability to resolve and control electron motion in real time. What began as a technological breakthrough - generating the shortest flashes ever produced - has evolved into a powerful approach for probing and steering electronic dynamics in atoms, molecules, and solids. This roadmap, authored by leading experts in the field, surveys the recent rapid progress in the generation and characterization of attosecond pulses, emerging attosecond measurement and control techniques, and their expanding range of applications. It reviews current and future developments in attosecond light sources, including novel laser technologies, waveform synthesizers, new schemes for high-order harmonic generation, attosecond pulse generation at free-electron lasers, and structured light. Advances in attosecond measurement methodologies are also discussed, encompassing all-attosecond pump-probe spectroscopy, attosecond four-wave mixing, attosecond microscopy, spectroscopy with light transients, and attosecond interferometry. Furthermore, the roadmap addresses applications of attosecond spectroscopy to reveal electron dynamics in molecules and condensed matter systems from both theoretical and experimental perspectives, and highlights emerging directions at the interface with quantum optics and quantum entanglement. Overall, this work aims to serve as a comprehensive resource for navigating the evolving landscape of attosecond science.

physics.optics↗

arXiv2026

Time-resolved Electron Momentum Spectroscopy with Ultrashort Electron Pulses: Confined Probing and Effects of Vacuum Dispersion

Previous theoretical studies have shown that attosecond electron dynamics can, in principle, be captured in electron momentum spectroscopy (EMS) using ultrashort electron pulses. By including further analytical considerations on the scattering probability, we here study the effect of the finite transversal extend of the projectile electron wave packet. We find that in wave packet scattering, the target momentum distribution is probed solely in a finite spatial region. This is evident from a spatially filtering Gabor transform appearing in the scattering probability, replacing the full momentum wave function appearing in the conventional plane wave treatment. In addition, by spatially shifting the target with regard to the wave packet focus, we illustrate the influence of vacuum dispersion, i.e., the spatial broadening of the wave packet as it propagates. Our findings are significant for the possibility to correctly interpret future attosecond-EMS results and the considered effects reflect fundamental aspects of wave packet scattering. The EMS setup may, therefore, constitute a useful framework for understanding scattering with finite wave packets.

physics.atom-ph↗

arXiv2026

Edge states and quantum optical high-harmonic generation from topological insulators

The strong-field process of high-harmonic generation (HHG) has, in recent years, been treated from a quantum optical perspective in the emerging research area of strong-field quantum optics. These investigations show that HHG radiation is, in general, in a nonclassical state of light. However, the quantum optical treatment of HHG from topological nontrivial materials is missing. Here, we aim to address this gap in current knowledge and consider the quantum optical HHG response from the Su-Schrieffer-Heeger model, a finite chain of atoms with both a topologically trivial and nontrivial insulating phase, the latter supporting edge states. We find that HHG from both topological phases is squeezed at the band-gap frequency. Interestingly, while the harmonic spectrum discriminates the two topological phases of the system, the degree of squeezing only discriminates the phases for smaller chain lengths. We attribute this difference to a relative increase in overlap between bulk and edge states in the topological nontrivial phase for smaller systems. Our findings reveal how the strength of dipole couplings governs the nonclassical HHG response and define new research questions on topologically protected generation of quantum light in strong-field physics.

quant-ph↗

arXiv2026

Limitations of an approximative phase-space description in strong-field quantum optics

In recent years, strong-field processes such as high-order harmonic generation (HHG) and above-threshold ionization driven by nonclassical states of light have become an increasingly popular field of study. The theoretical modeling of these processes often applies an approximate phase-space expansion of the nonclassical driving field in terms of coherent states, which has been shown to accurately predict the harmonic spectrum. However, its accuracy for the computation of quantum optical observables like the degree of squeezing and photon statistics has not been thoroughly considered. In this work, we introduce this approximative phase-space description and discuss its accuracy, and we find that it mischaracterizes the quantum optical properties of the driving laser by making it an incoherent mixture of classical states. We further show that this error in the driving field description maps onto the light emitted from HHG, as neither sub-Poissonian photon statistics nor quadrature squeezing below vacuum fluctuations can be captured by the approximative phase-space description. Lastly, to benchmark the approximative phase-space description, we consider the quantum HHG from a one-band model, which yields an exact analytical solution. Using the approximative phase-space representation with this specific model, we find a small quantitative error in the quadrature variance of the emitted field that scales with pulse duration and emitter density. Our results show that using this approximative phase-space description can mischaracterize quantum optical observables. Attributing physical meaning to such results should therefore be accompanied by a quantitative analysis of the error.

quant-ph↗

arXiv2025

High-Order Harmonic Generation with Beyond-Semiclassical Emitter Dynamics: A Strong-Field Quantum Optical Heisenberg Picture Approach

Quantum-optical descriptions of strong-field processes have attracted significant attention in recent years. Typically, the theoretical modeling has been conducted in the Schrödinger picture, where results are only obtainable under certain approximations, while, in contrast, the Heisenberg picture has remained relatively unexplored. In this work, we develop an accurately controlled perturbative expansion of the time-evolution operator in the Heisenberg picture and derive beyond-semiclassical corrections to the emitter dynamics due to the coupling to the quantized electromagnetic field, capturing effects of the quantum fluctuations present in the latter. We focus on high-order harmonic generation (HHG), where the approach is accurate in parameter regimes of current interest and it gives closed-form expressions for key observables. This formulation not only simplifies numerical calculations compared to the Schrödinger-picture approach but also provides a clear correspondence between nonclassical features of the emitted light and the underlying induced dynamics of the generating medium including quantum fluctuations. Moreover, the Heisenberg framework naturally yields scaling relations with the number of independent emitters, enabling us to assess whether nonclassical behavior should persist under typical experimental conditions involving large emitter ensembles. Interestingly, we find that the degree of squeezing increases with the number of emitters, whereas the photon statistics approaches a classical Poissonian distribution in the many-emitter limit. We also find that the beyond-semiclassical emitter dynamics significantly enhances the degree of squeezing of the emitted light. Our work advances the theoretical understanding of quantum-optical HHG and introduces an accessible and well-controlled framework to describe realistic experiments.

quant-ph↗

arXiv2025

Intense-Laser Nondipole-Induced Symmetry Breaking in Solids

High-harmonic spectroscopy in solids gives insight into the inner workings of solids, such as reconstructing band structures or probing the topological phase of materials. High-harmonic generation (HHG) is a highly non-linear phenomena and simulations guide interpretation of experimental results. These simulations often rely on the electric dipole approximation, even though the driving fields enter regimes that challenge its accuracy. Here, we investigate effects of including nondipole terms in the light-matter coupling in simulations of HHG in materials with both topologically trivial and non-trivial phases. We show how the inclusion of nondipole terms breaks dipole selection rules, allowing for new polarizations of the generated light. Specifically we find that helicity, completely absent in the dipole approximation, is induced by the nondipole extension, and that this helicity is dependent on the topological phase of the material.

quant-ph↗

arXiv2025

Scattering-asymmetry control with ultrafast electron wave packet shaping

Scattering of a tightly focused electron beam by an atom forms one of the bases of modern electron microscopy. A fundamental symmetry breaking occurs when the target atom is displaced from the beam center. This displacement results in a deflection of the beam and an asymmetric angular distribution of the scattered electrons. Here we propose a concept to control the sign and magnitude of the scattering asymmetry by shaping the incident high-energy electron wave packet in momentum space on the atto- to picosecond time scale. The shaping controls the ultrafast real-space dynamics of the wave packet, shifting the balance between two competing contributions of the impact-parameter-dependent quantum interference and the momentum distribution of the wave packet on the target. We find a strong sensitivity of the elastic scattering on the wave packet properties, an effect that will allow wave-packet and target characterization in ultrafast electron microscopy.

physics.atom-ph↗

arXiv2025

Carrier-envelope phase effects in one- and two-photon directional photoionization of non-isotropic atomic states

We study the impact of two-color ($ω$ and $2ω$) co- and counter-rotating ultrashort attosecond laser pulses on non-isotropic atomic targets through the one- and two-photon interference pattern of the photoelectron spectrum. Specifically, we take the ground state of atomic carbon, i. e., $(1s^22s^22p^2,{}^3\text{P}^\text{e})$ as a prototype. We observe and quantify the strong dependency on the relative carrier-envelope phase (CEP) of the two-color pulses and on the spatial orientation of the electronic target states. Notably, we observe that the photoelectron momentum distributions (PMDs) vary as a function of the CEP due to the interfering two-color one- and two-photon ionization paths. Besides, the PMD region corresponding to one-photon photoionization remains unaffected, with varying CEP, depending only on the ellipticity of the pulse, the central photon frequency and the magnetic quantum number of the initial state. Therefore, comparing the one-photon ionization electron ejection direction following absorption of a single ($2ω$) photon with that of the two-photon ionization channel following absorption of two photon each with energy $ω$ we may extrapolate information on the CEP difference between the two pulses.

physics.atom-ph↗

arXiv2025

Charge creation via quantum tunneling in one-dimensional Mott insulators: A numerical study of the extended Hubbard model

Charge creation via quantum tunneling, i.e. dielectric breakdown, is one of the most fundamental and significant phenomena arising from strong light(field)-matter coupling. In this work, we conduct a systematic numerical analysis of quantum tunneling in one-dimensional Mott insulators described by the extended ($U$-$V$) Hubbard model. We discuss the applicability of the analytical formula for doublon-holon (DH) pair production, previously derived for the one-dimensional Hubbard model, which highlights the relationship between the tunneling threshold, the charge gap, and the correlation length. We test the formulas ability to predict both DH pair production and energy increase rate. Using tensor-network-based approaches, we demonstrate that the formula provides accurate predictions in the absence of excitonic states facilitated by the nearest-neighbor interaction $V$. However, when excitonic states emerge, the formula more accurately describes the rate of energy increase than the DH pair creation rate and in both cases gets improved by incorporating the exciton energy as the effective gap.

cond-mat.str-el↗

arXiv2025

Excitonic Enhancement of Squeezed Light in Quantum-Optical High-Harmonic Generation From a Mott Insulator

The strong-field induced generation of nonclassical states of light is not only a subject of fundamental research but also has potential usage in quantum information science and technology. The emerging field of strong-field quantum optics has developed ways of generating nonclassical states of light from the process of high-harmonic generation (HHG) at much wider frequency ranges and intensities than is typical for quantum optics. So far, however, no clear nonclassical signal at a distinct and unambiguous frequency has been predicted. Here, we study the response from an exciton in a Mott-insulating system, using the extended Hubbard model. We find that the exciton plays a key role in the nonclassical response and generates squeezing at the exciton energy. We relate this nonclassical response to the nonvanishing time correlations of the current operator in the system. Our work defines a direction for experimental work to search for squeezed light from HHG in a spectrally confined region defined by the exciton energy.

quant-ph↗

arXiv2025

Extreme Ultraviolet High-Harmonic Interferometry of Excitation-Induced Bandgap Dynamics in Solids

Interferometry is a fundamental technique in physics, enabling precise measurements through the interference of waves. High-harmonic generation (HHG) in solids has emerged as a powerful method for probing ultrafast electronic dynamics within crystalline structures. In this study, we employed extreme ultraviolet (XUV) high-harmonic interferometry with phase-locked XUV pulse pairs to investigate excitation-induced bandgap dynamics in solids. Our experiments on amorphous SiO2 and crystalline MgO, complemented by analytical modeling and semiconductor Bloch equation simulations, reveal a correlation between transient bandgap modifications and variations in the phase of harmonic emission. These findings suggest a potential pathway for sub-cycle, all-optical control of band structure modifications, advancing prospects for petahertz-scale electronic applications and attosecond diagnostics of carrier dynamics.

physics.optics↗

arXiv2025

High-Harmonic Generation in a Crystal Driven by Quantum Light

We study intraband high-harmonic generation (HHG) in a crystal driven by quantum light. Previous theoretical studies have developed a framework based on coherent state expansions in terms of P distributions to consider nonclassical driving fields for HHG in atoms. Here, we adapt this framework to the context of solids and consider an intraband model of ZnO. We investigate the effect of the quantum optical nature of the driving field on the harmonic spectra including the cutoff and the intensity scaling of the harmonics with driving field intensity. Based on analytical calculations in the Floquet limit, we explain why driving with thermal light or bright-squeezed vacuum (BSV) produces a much higher cutoff than when driving with fields described by coherent or Fock states. Further, we derive an expression for the generated time-dependent electric field and its fluctuations and find that it inherits characteristics of the driving field. Finally, we discuss the limitations of an approximative positive P representation, which is introduced to be able to reduce the numerical complexity for Fock and BSV driving fields.

quant-ph↗

arXiv2024

Hierarchy of approximations for describing quantum light from high-harmonic generation: A Fermi-Hubbard model study

The quantum optical description of high-order harmonic generation where both the electrons of the generating medium and the driving and generated light fields are described quantum mechanically has been of significant interest in the past years. The quantum optical formulation leads to equations of motion for the generated light field in which the quantum optical field couples to the time-dependent current of the electronic medium irrespectively of the specifics of the electronic system being an atom, molecule, or solid. These equations of motion are not solvable for any realistic system and accurate and verified approximations are hence needed. In this work, we present a hierarchy of approximations for the equations of motion for the photonic state. At each level in this hierarchy, we compare it to the previous level justifying the validity using the Fermi-Hubbard model as an example of an electronic system with correlations. This model allows us to perform an accurate simulation of the electron motion of all the required states. We find that for the typical experimental situation of weak quantized-light-matter-coupling constant and at intensities well below the damage threshold, an explicit expression for the generated quantum light, referred to as the Markov-state approximation (MSA), captures the high-harmonic spectrum quantitatively and describes the single-mode quantum properties of the generated light as characterized by the Mandel-Q parameter and the degree of squeezing qualitatively.

quant-ph↗

arXiv2024

Beyond Electric-Dipole Treatment of Light-Matter Interactions in Materials: Nondipole Harmonic Generation in Bulk Si

A beyond electric-dipole light-matter theory is needed to describe emerging X-ray and THz applications for characterization and control of quantum materials but inaccessible as nondipole lattice-aperiodic terms impede on the use of Bloch's theorem. To circumvent this, we derive a formalism that captures dominant nondipole effects in intense electromagnetic fields while conserving lattice translational symmetry. Our approach enables the first accurate nondipole first-principles microscopic simulation of nonperturbative harmonic generation in Si. We reveal nondipole-induced transverse currents generating perturbative even-ordered harmonics and display the onset of nondipole high harmonic generation near the laser damage threshold.

cond-mat.mtrl-sci↗

arXiv2024

Simulating strong-field electron-hole dynamics in solids probed by attosecond transient absorption spectroscopy

We investigate the ultrafast electron dynamics of a model of a wide-bandgap material with inner, valence, and conduction bands excited by an intense few-femtosecond pump and monitored by a delayed attosecond extreme-ultraviolet probe pulse. Complementary computational methods are utilized and compared, based on the semiconductor Bloch equations (SBEs) and time-dependent density functional theory (TDDFT). TDDFT is employed to study a finite-size system, while the SBEs are utilized to investigate the corresponding solid with periodic boundary conditions imposed, with the crystal-momentum-dependent energy bands and interband couplings calculated in the parallel-transport structure gauge. The resulting strong-field electron dynamics are employed to predict experimentally accessible attosecond transient absorption spectroscopy (ATAS) signals as a function of the probe-pulse frequency and pump-probe interpulse delay. Both simulation protocols similarly capture the time-delay-dependent spectral features in the ATAS signals. The very good agreement between our TDDFT and SBE-based results allows us to interpret the ab-initio TDDFT simulations in terms of SBEs' interband couplings, validating our SBE-based model and corroborating its conclusions.

physics.optics↗

arXiv2024

Many-body effects on high-harmonic generation in Hubbard ladders

We show how many-body effects associated with background spin dynamics control the high-harmonic generation (HHG) in Mott insulators by analyzing the two-leg ladder Hubbard model. Spin dynamics activated by the interchain hopping $t_y$ drastically modifies the HHG features. When two chains are decoupled ($t_y=0$), HHG originates from the dynamics of coherent doublon-holon pairs because of spin-charge separation. With increasing $t_y$, the doublon-holon pairs lose their coherence due to their interchain hopping and resultant spin-strings. Furthermore, the HHG signal from spin-polarons -- charges dressed by spin clouds -- leads to an additional plateau in the HHG spectrum. For large $t_y$, we identify unconventional HHG processes involving $three$ elementary excitations -- two polarons and one magnon. Our results demonstrate the nontrivial nature of HHG in strongly correlated systems, and its qualitative differences to conventional semiconductors.

cond-mat.str-el↗

arXiv2024

Intra- and intercycle analysis of intraband high-order harmonic generation

We study intraband high-order harmonic generation arising from a band-gap material driven by a linearly polarized laser field. We factorize the intraband high-order harmonic-generation signal into intracycle and intercycle terms. The intracycle term uniquely determines the spectral characteristics whereas the intercycle term merely modulates the spectral features by imposing energy conservation in the long-pulse limit. Through analysis of the intracycle interference, the cutoff is identified, and the origin of the harmonic selection rules is revealed. Further, it is outlined how different components of the bandstructure contribute to different regions of the harmonic spectrum, giving rise to non-trivial intensity scaling of individual harmonics in the plateau region.

physics.optics↗