arXiv subjects

Michael Krüger

Publications and source records attributed to Michael Krüger.

At least 19 recordsLinked to original sources

arXiv2026

Multidimensional attosecond clocking near Dirac cones in graphite

Two-color high-harmonic spectroscopy is widely used to access sub-cycle electron dynamics and to retrieve harmonic timing information, including harmonic phases and attochirp across gases, solids, and liquids. However, the dependence of such timing observables on additional laser-control parameters remains largely unexplored. Here, we introduce driving intensity as an additional dimension of two-color harmonic spectroscopy in highly oriented pyrolytic graphite (HOPG). The retrieved attosecond two-color delays maximizing the 4th and 5th harmonic yields evolve systematically and differently with driving intensity. Semiconductor Bloch-equation calculations reproduce these trends and reveal a pronounced sensitivity of the intensity-dependent delays to the electronic band dispersion. Our results demonstrate multidimensional attosecond clocking near Dirac cones and establish intensity-dependent two-color delays as a sensitive observable for band-dispersion in quantum materials.

physics.optics↗

arXiv2026

Clocking and controlling attosecond currents in a scanning tunnelling microscope

Quantum tunnelling of electrons can be confined to the sub-cycle time scale of strong light fields, contributing decisively to the extreme time resolution of attosecond science. Because tunnelling also enables atomic-scale spatial resolution in scanning tunnelling microscopy (STM), integrating STM with light pulses has long been a key objective in ultrafast microscopy, spanning the picosecond and femtosecond domains, with first signatures of attosecond dynamics. However, while sub-cycle dynamics on the attosecond time scale are routinely controlled and determined with high precision, controlling the direction of attosecond currents and determining their duration have remained elusive in STM. Here, we induce STM tunnelling currents using two-colour laser pulses and dynamically control their direction, relying solely on the sub-cycle waveform of the pulses. Projecting our measurement data onto one-electron and many-body theory descriptions reveals a three-step transport process in the non-adiabatic tunnelling regime as the physical mechanism, with a theory-derived current burst duration of 860 as. Despite working under ambient conditions but free of thermal artifacts, we achieve sub-angström topographic sensitivity and a lateral spatial resolution of 2 nm. This unprecedented capability to directionally control attosecond bursts will enable triggering and imaging ultrafast charge dynamics at the spatio-temporal microscopy frontier of lightwave electronics.

quant-ph↗

arXiv2026

Ultrafast optically induced tunneling in narrow metallic gaps from the time dependent density functional perspective

In this work, using the time-dependent density functional theory, we address the electron tunneling triggered by short (single-cycle and several-cycle) optical pulses in narrow metallic gaps under conditions relevant for actual experiments. We identify photon-assisted tunneling with one-photon, two-photon, and higher-order photon absorption, and we discuss the effect of the tunneling barrier, applied bias, and strength of the optical field on transition from photon-assisted tunneling (weak optical fields) to the optical field emission at strong optical fields. The numerical single-electron calculations and an analytical strong-field theory model are used to gain deeper insights into the results of the time-dependent density functional theory calculations. Additionally, our parameter-free calculations allow us to retrieve and explain recent experimental results on optically induced transport in narrow metallic gaps under an applied dc bias.

physics.optics↗

arXiv2026

Two-color harmonic spectroscopy of ultrafast Dirac electron dynamics

High-harmonic generation (HHG), the hallmark effect of attosecond science, is a nonperturbative nonlinear process leading to the emission of high-harmonic light from gases and solids. In gases, extreme driving laser pulse intensities can deplete the ground state, suppressing harmonic emission during the trailing edge of the pulse. Here, we report a similar effect, pronounced ultrafast carrier saturation dynamics and harmonic emission suppression during nonperturbative harmonic generation (NPHG) in a gapless Dirac semimetal -- highly oriented pyrolytic graphite (HOPG). Remarkably, HOPG supports NPHG at laser intensities as low as $\sim 10^{10}$ W cm$^{-2}$, facilitated by its vanishing bandgap. Ultrafast carrier saturation strongly modulates the interplay between interband and intraband currents, a key characteristic of NPHG in Dirac materials. Using two-color spectroscopy, we reveal the excitation dynamics of Dirac electron-hole pairs as it affects the emission of harmonics during the presence of the driving laser pulse. The excitation of out-of-equilibrium hot carriers and the concomitant saturation near the Dirac points leads to a marked suppression of interband harmonics and induces measurable temporal shifts. These observations are supported by simulations based on semiconductor Bloch equations. Our finding reveal that field-driven carrier saturation plays a critical role in gapless solid NPHG. We demonstrate the potential of NPHG and HHG as a sensitive, all-optical probe of ultrafast carrier dynamics, offering novel opportunities for ultrafast optoelectronics in Dirac materials.

physics.optics↗

arXiv2025

Single-shot pulse retrieval of femtosecond bright squeezed vacuum

Bright squeezed vacuum (BSV) is an intense quantum state of light with zero mean electric field and huge photon number fluctuations, sufficiently intense to drive extreme nonlinear processes and imprint nonclassical statistics. However, the temporal structure of single BSV shots has not been fully characterized. Here, we retrieve the spectral and temporal pulse characteristics of a set of single-peak BSV shots. It is obtained by realizing a femtosecond BSV source at 1040 nm with a single spatial mode and perform single-shot spectral interferometry with a fully characterized coherent-state reference pulse. Our approach reveals that the group delay is consistent between the various shots, resulting in an average pulse duration of 27.2 fs, much shorter than the pump pulse, and a variation of 5.5 fs (standard deviation). We also observe a characteristic nodal structure in the spectral interferograms, demonstrating the BSV's random phase ambiguity of $π$ rad. Our approach demonstrates that BSV is a viable source of femtosecond light pulses for attosecond sub-cycle metrology of ultrafast electron dynamics.

physics.optics↗

arXiv2025

Robust strong-field theory model for ultrafast electron transport through metal-insulator-metal tunneling nanojunctions

Ultrafast science studies the dynamics of electrons in matter with extreme temporal precision, typically in the attosecond and femtosecond time domain. Recent experimental and theoretical progress has put metal-insulator-metal (MIM) tunneling nanojunctions in the spotlight of ultrafast science. Waveform-controlled laser fields can induce ultrafast currents in these junctions, opening the door to petahertz electronic operation and attosecond-scale scanning tunneling microscopy (STM). Inspired by our strong-field model for attosecond tunneling microscopy [Boyang Ma and Michael Krüger, Phys. Rev. Lett. 133, 236901 (2024)], here we generalize our model to MIM nanojunctions. We introduce several refinements and corrections, accounting for the image potential inside the gap and boundary effects. Moreover, we also find that the Keldysh parameter alone is insufficient for describing the physics in thin MIM nanojunctions. We introduce a new parameter $ζ$ that accounts for the effects of the limited size of the junction and provide several interpretations of the parameter that shed new light on the complex physics in the light-driven junction. Most strikingly, we find that for $ζ> 1$ photon-assisted tunneling is dominating the ultrafast electron transport across the junction, regardless of the value of the Keldysh parameter. Here one or more photons are absorbed and the electron undergoes static tunneling through the barrier. $ζ< 1$ is required for a regime in which the laser field and the Keldysh parameter dominate the transport. We also discuss the three-step model of electron transport across the nanojunction in the adiabatic regime, the energy cutoff of the transported electrons and the carrier-envelope phase control of the net current. Our theory model provides a rich toolbox for understanding and predicting the physics of ultrafast MIM nanojunctions.

cond-mat.mes-hall↗

arXiv2025

Measuring and controlling the birth of quantum attosecond pulses

The generation and control of extreme ultraviolet (XUV) radiation by high harmonic generation (HHG) have advanced ultrafast science, providing direct insights into electron dynamics on their natural time scale. Attosecond science has established the capability to resolve ultrafast quantum phenomena in matter by characterizing and controlling the classical properties of the high harmonics. Recent theoretical proposals have introduced novel schemes for generating and manipulating XUV HHG with distinct quantum features, paving the way to attosecond quantum optics. In this work, we transfer fundamental concepts in quantum optics into attosecond science. By driving the HHG process with a combination of an infrared bright squeezed vacuum (BSV, a non-classical state of light), and a strong coherent field, we imprint the quantum correlations of the input BSV onto both the ultrafast electron wavefunction and the harmonics' field. Performing in-situ HHG interferometry provides an insight into the underlying sub-cycle dynamics, revealing squeezing in the statistical properties of one of the most fundamental strong-field phenomena -- field induced tunneling. Our measurement allows the reconstruction of the quantum state of the harmonics through homodyne-like tomography, resolving correlated fluctuations in the harmonic field that mirror those of the input BSV. By controlling the delay between the two driving fields, we manipulate the photon statistics of the emitted attosecond pulses with sub-cycle accuracy. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.

physics.optics↗

arXiv2024

Attosecond pulses from a solid driven by a synthesized two-color field at megahertz repetition rate

Probing coherent quantum dynamics in light-matter interactions at the microscopic level requires high-repetition-rate isolated attosecond pulses (IAPs) in pump-probe experiments. To date, the generation of IAPs has been mainly limited to the kilohertz regime. In this work, we experimentally achieve attosecond control of extreme-ultraviolet (XUV) high harmonics in the wide-bandgap dielectric MgO, driven by a synthesized field of two femtosecond pulses at 800nm and 2000nm with relative phase stability. The resulting quasi-continuous harmonic plateau with ~ 9 eV spectral width centered around 16.5 eV photon energy can be tuned by the two-color phase and supports the generation of an IAP (~ 730 attoseconds), confirmed by numerical simulation based on three-band semiconductor Bloch equations. Leveraging the high-repetition-rate driver laser and the moderate intensity requirements of solid-state high-harmonic generation, we achieve IAP production at an unprecedented megahertz repetition rate, paving the way for all-solid compact XUV sources for IAP generation.

physics.optics↗

arXiv2024

Strong-field theory of attosecond tunneling microscopy

Attosecond observations of coherent electron dynamics in molecules and nanostructures can be achieved by combining conventional scanning tunneling microscopy (STM) with ultrashort femtosecond laser pulses. While experimental studies in the sub-cycle regime are underway, a robust strong-field theory description has remained elusive. Here we devise a model based on the strong-field approximation. Valid in all regimes, it provides a surprising analogy to the standard model of STM. We also show that the intuitive three-step model of attosecond science directly emerges from our model and describe the optimal conditions for attosecond STM experiments.

quant-ph↗

arXiv2024

High Harmonic Generation by Bright Squeezed Vacuum

We observe non-perturbative high harmonic generation in solids driven by a macroscopic quantum state of light, bright squeezed vacuum (BSV), which we generate in a single spatiotemporal mode. The BSV-driven process is considerably more efficient in the generation of high harmonics than classical light of the same mean intensity. Due to its broad photon-number distribution, covering states from $0$ to $2 \times 10^{13}$ photons per pulse, and sub-cycle electric field fluctuations over $\pm1\hbox{V}/\hbox{Å}$, BSV provides access to free carrier dynamics within a much broader range of peak intensities than accessible with classical light. Our findings contribute to recent developments of quantum optics with extreme intensities, moving beyond its traditional focus on low photon numbers, and providing a new method for exploring extreme nonlinearities in solids.

quant-ph↗

arXiv2023

Self-trapping of slow electrons in the energy domain

The interaction of light and swift electrons has enabled phase-coherent manipulation and acceleration of electron wavepackets. Here we investigate this interaction in a new regime where low-energy electrons (~20-200 eV) interact with a phase-matched light field. Our analytical and one-dimensional numerical study shows that slow electrons are subject to strong confinement in the energy domain due to the non-vanishing curvature of the electron dispersion. The spectral trap is tunable and an appropriate choice of light field parameters can reduce the interaction dynamics to only two energy states. The capacity to trap electrons expands the scope of electron beam physics, free-electron quantum optics and quantum simulators.

quant-ph↗

arXiv2022

High harmonic generation driven by quantum light

High harmonic generation (HHG) is an extreme nonlinear process where intense pulses of light drive matter to emit high harmonics of the driving frequency, reaching the extreme ultraviolet (XUV) and x-ray spectral ranges. So far, the HHG process was always generated by intense laser pulses that are well described as a classical electromagnetic field. Advances in the generation of intense squeezed light motivate us to revisit the fundamentals of HHG and ask how the photon statistics of light may alter this process, and more generally alter the field of extreme nonlinear optics. The role of photon statistics in non-perturbative interactions of intense light with matter has remained unexplored in both experiments and theory. Here we show that the defining spectral characteristics of HHG, such as the plateau and cutoff, are sensitive to the photon statistics of the driving light. While coherent (classical) and Fock light states induce the established HHG cutoff law, thermal and squeezed states substantially surpass it, extending the cutoff compared to classical light of the same intensity. Hence, shaping the photon statistics of light enables producing far higher harmonics in HHG. We develop the theory of extreme nonlinear optics driven by squeezed light, and more generally by arbitrary quantum states of light. Our work introduces quantum optical concepts to strong-field physics as new degrees of freedom in the creation and control of HHG, and finally shows that experiments in this field are feasible. Looking forward, HHG driven by quantum light creates quantum states of XUV and X-rays, enabling applications of quantum optics in new spectral regimes.

physics.optics↗

arXiv2018

Multi-Band Petahertz Currents Resolved via High Harmonic Generation Spectroscopy

Strong field driven electric currents in condensed matter systems open new frontiers in petahertz electronics. In this regime new challenges arise as the role of the band structure and the quantum nature of electron-hole dynamics have yet to be resolved. Here we reveal the underlying attosecond dynamics that dictates the temporal evolution of carriers in multi-band solid state systems, via high harmonic generation (HHG) spectroscopy. We demonstrate that when the electron-hole relative velocity approaches zero, enhanced quantum interference leads to the appearance of spectral caustics in the HHG spectrum. Introducing the role of the dynamical joint density of states (JDOS) we identify its direct mapping into the spectrum, exhibiting singularities at the spectral caustics. By probing these singularities, we visualize the structure of multiple unpopulated high conduction bands. Our results open a new path in the control and study of attosecond quasi-particle interactions within the field dressed band structure of crystals.

physics.optics↗

arXiv2018

Probing electronic wavefunctions by all-optical attosecond interferometry

Photoelectron spectroscopy is a powerful method that provides insight into the quantum mechanical properties of a wide range of systems. The ionized electron wavefunction carries information on the structure of the bound orbital, the ionic potential as well as the photo-ionization dynamics itself. While photoelectron spectroscopy resolves the absolute amplitude of the wavefunction, retrieving the spectral phase information has been a long-standing challenge. Here, we transfer the electron phase retrieval problem into an optical one by measuring the time-reversed process of photo-ionization -- photo-recombination -- in attosecond pulse generation. We demonstrate all-optical interferometry of two independent phase-locked attosecond light sources. This measurement enables us to directly determine the phase shift associated with electron scattering in simple quantum systems such as helium and neon, over a large energy range. In addition, the strong-field nature of attosecond pulse generation resolves the dipole phase around the Cooper minimum in argon through a single scattering angle, along with phase signatures of multi-electron effects. Our study bears the prospect of probing complex orbital phases in molecular systems as well as electron correlations through resonances subject to strong laser fields.

physics.atom-ph↗

arXiv2018

Tracing the phase of focused broadband laser pulses

Precise knowledge of the behaviour of the phase of light in a focused beam is fundamental to understanding and controlling laser-driven processes. More than a hundred years ago an axial phase anomaly for focused monochromatic light beams was discovered and is now commonly known as the Gouy phase. Recent theoretical work has brought into question the validity of applying this monochromatic phase formulation to the broadband pulses becoming ubiquitous today. Based on electron back-scattering at sharp nanometre-scale metal tips, a method is available to measure light fields with sub-wavelength spatial resolution and sub-optical cycle time resolution. Here we report such a direct, three-dimensional measurement of the spatial dependence of the optical phase of a focused, 4-fs, near-infrared laser pulse. The observed optical phase deviates substantially from the monochromatic Gouy phase - exhibiting a much more complex spatial dependence, both along the propagation axis and in the radial direction. In our measurements, these significant deviations are the rule and not the exception for focused, broadband laser pulses. Therefore, we expect wide ramifications for all broadband laser-matter interactions, such as in high-harmonic and attosecond pulse generation, femtochemistry, ophthalmological optical coherence tomography and light-wave electronics.

physics.optics↗

arXiv2017

High Visibility in Two-Color Above-Threshold Photoemission from Tungsten Nanotips in a Coherent Control Scheme

In this article we present coherent control of above-threshold photoemission from a tungsten nanotip achieving nearly perfect modulation. Depending on the pulse delay between fundamental (1560 nm) and second harmonic (780 nm) pulses of a femtosecond fiber laser at the nanotip, electron emission is significantly enhanced or depressed during temporal overlap. Electron emission is studied as a function of pulse delay, optical near-field intensities, DC bias field, and final photoelectron energy. Under optimized conditions modulation amplitudes of the electron emission of 97.5% are achieved. Experimental observations are discussed in the framework of quantum- pathway interference supported by local density of states (LDOS) simulations.

physics.optics↗

arXiv2016

Two-color coherent control of femtosecond above-threshold photoemission from a tungsten nanotip

We demonstrate coherent control of multiphoton and above-threshold photoemission from a single solid-state nanoemitter driven by a fundamental and a weak second harmonic laser pulse. Depending on the relative phase of the two pulses, electron emission is modulated with a contrast of the oscillating current signal of up to 94%. Electron spectra reveal that all observed photon orders are affected simultaneously and similarly. We confirm that photoemission takes place within 10 fs. Accompanying simulations indicate that the current modulation with its large contrast results from two interfering quantum pathways leading to electron emission.

physics.optics↗

arXiv2014

Highly coherent electron beam from a laser-triggered tungsten needle tip

We report on a quantitative measurement of the spatial coherence of electrons emitted from a sharp metal needle tip. We investigate the coherence in photoemission using near-ultraviolet laser triggering with a photon energy of 3.1 eV and compare it to DC-field emission. A carbon-nanotube is brought in close proximity to the emitter tip to act as an electrostatic biprism. From the resulting electron matter wave interference fringes we deduce an upper limit of the effective source radius both in laser-triggered and DC-field emission mode, which quantifies the spatial coherence of the emitted electron beam. We obtain $(0.80\pm 0.05)\,$nm in laser-triggered and $(0.55\pm 0.02)\,$nm in DC-field emission mode, revealing that the outstanding coherence properties of electron beams from needle tip field emitters are largely maintained in laser-induced emission. In addition, the relative coherence width of 0.36 of the photoemitted electron beam is the largest observed so far. The preservation of electronic coherence during emission as well as ramifications for time-resolved electron imaging techniques are discussed.

physics.optics↗