Canonical Density Matrices from Eigenstates of Mixed Systems

One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. For individual eigenstates, it has been shown that local observables show thermal properties provided the eigenstate thermalization hypothesis holds, which requires the system to be quantum-chaotic. In the present paper, we study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Specifically, we study the emergence of the canonical density matrix of an impurity upon reduction from isolated energy eigenstates of a large but finite quantum system the impurity is embedded in. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos and corresponds in between to a system with mixed quantum phase space. We show that the probability for finding a canonical density matrix when reducing the ensemble of energy eigenstates of the finite many-body system can be quantitatively controlled and tuned by the degree of quantum chaos present. For the transition from quantum integrability to quantum chaos, we find a continuous and universal (i.e., size-independent) relation between the fraction of canonical eigenstates and the degree of chaoticity as measured by the Brody parameter or the Shannon entropy.

The speed limit of optoelectronics

Light-field driven charge motion links semiconductor technology to electric fields with attosecond temporal control. Motivated by ultimate-speed electron-based signal processing, strong-field excitation has been identified viable for the ultrafast manipulation of a solid's electronic properties but found to evoke perplexing post-excitation dynamics. Here, we report on single-photon-populating the conduction band of a wide-gap dielectric within approximately one femtosecond. We control the subsequent Bloch wavepacket motion with the electric field of visible light. The resulting current allows sampling optical fields and tracking charge motion driven by optical signals. Our approach utilizes a large fraction of the conduction-band bandwidth to maximize operating speed. We identify population transfer to adjacent bands and the associated group velocity inversion as the mechanism ultimately limiting how fast electric currents can be controlled in solids. Our results imply a fundamental limit for classical signal processing and suggest the feasibility of solid-state optoelectronics up to 1 PHz frequency.

Magnetic-Field Effect in High-Order Above-Threshold Ionization

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the 2U_{p} classical cutoff is found to be vastly different from that below this cutoff, where U_{p} is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

Theory of Subcycle Linear Momentum Transfer in Strong-Field Tunneling Ionization

Interaction of a strong laser pulse with matter transfers not only energy but also linear momentum of the photons. Recent experimental advances have made it possible to detect the small amount of linear momentum delivered to the photoelectrons in strong-field ionization of atoms. We present numerical simulations as well as an analytical description of the subcycle phase (or time) resolved momentum transfer to an atom accessible by an attoclock protocol. We show that the light-field-induced momentum transfer is remarkably sensitive to properties of the ultrashort laser pulse such as its carrier-envelope phase and ellipticity. Moreover, we show that the subcycle-resolved linear momentum transfer can provide novel insights into the interplay between nonadiabatic and nondipole effects in strong-field ionization. This work paves the way towards the investigation of the so-far unexplored time-resolved nondipole nonadiabatic tunneling dynamics.

Band Nesting in Two-Dimensional Crystals: An Exceptionally Sensitive Probe of Strain

Band nesting occurs when conduction and valence bands are approximately equispaced over regions in the Brillouin zone. In two-dimensional materials, band nesting results in singularities of the joint density of states and thus in a strongly enhanced optical response at resonant frequencies. We exploit the high sensitivity of such resonances to small changes in the band structure to sensitively probe strain in semiconducting transition metal dichalcogenides (TMDs). We measure and calculate the polarization-resolved optical second harmonic generation (SHG) at the band nesting energies and present the first measurements of the energy-dependent nonlinear photoelastic effect in atomically thin TMDs (MoS₂, MoSe₂, WS₂, and WSe₂) combined with a theoretical analysis of the underlying processes. Experiment and theory are found to be in good qualitative agreement displaying a strong energy dependence of the SHG, which can be exploited to achieve exceptionally strong modulation of the SHG under strain. We attribute this sensitivity to a redistribution of the joint density of states for the optical response in the band nesting region. We predict that this exceptional strain sensitivity is a general property of all 2D materials with band nesting.

Two-Electron Interference in Strong-Field Ionization of He by a Short Intense Extreme Ultraviolet Laser Pulse

Double ionization of helium by a single intense (above 10^{18}  W/cm^{2}) linearly polarized extreme ultraviolet laser pulse is studied by numerically solving the full-dimensional time-dependent Schrödinger equation. For the laser intensities well beyond the perturbative limit, novel gridlike interference fringes are found in the correlated energy spectrum of the two photoelectrons. The interference can be traced to the multitude of two-electron wave packets emitted at different ionization times. A semianalytical model for the dressed two-photon double ionization is shown to qualitatively account for the interference patterns in the joint energy spectrum. Similar signatures of interferences between transient induced time-delayed ionization bursts are expected for other atomic and molecular multielectron systems.

Localized Intervalley Defect Excitons as Single-Photon Emitters in WSe_{2}

Single-photon emitters play a key role in present and emerging quantum technologies. Several recent measurements have established monolayer WSe_{2} as a promising candidate for a reliable single-photon source. The origin and underlying microscopic processes have remained, however, largely elusive. We present a multiscale tight-binding simulation for the optical spectra of WSe_{2} under nonuniform strain and in the presence of point defects employing the Bethe-Salpeter equation. Strain locally shifts excitonic energy levels into the band gap where they overlap with localized intragap defect states. The resulting hybridization allows for efficient filling and subsequent radiative decay of the defect states. We identify intervalley defect excitonic states as the likely candidate for antibunched single-photon emission. This proposed scenario is shown to account for a large variety of experimental observations including brightness, radiative transition rates, the variation of the excitonic energy with applied magnetic and electric fields as well as the variation of the polarization of the emitted photon with the magnetic field.

Circular Holographic Ionization-Phase Meter

We propose an attosecond extreme ultraviolet pump IR-probe photoionization protocol that employs pairs of counterrotating consecutive harmonics and angularly resolved photoelectron detection, thereby providing a direct measurement of ionization phases. The present method, which we call circular holographic ionization-phase meter, gives also access to the phase of photoemission amplitudes of even-parity continuum states from a single time-delay measurement since the relative phase of one- and two-photon ionization pathways is imprinted in the photoemission anisotropy. The method is illustrated with ab initio simulations of photoionization via autoionizing resonances in helium. The rapid phase excursion in the transition amplitude to both the dipole-allowed (2s2p)^{1}P^{o} and the dipole-forbidden (2p^{2})^{1}D^{e} states are faithfully reproduced.

Two-color phase-controlled photoemission from a zero-dimensional nanostructure

We demonstrate that multi-photon photoemission including above-threshold multiphoton orders from a nanotip can be coherently controlled with the optical phase between two light fields. By focusing 74 fs drive pulses at 1560 nm and their second harmonic at 780 nm onto the tip and changing the optical phase between the two colors, we observe an emission current modulation of up to 97.5 %. Additionally, electron energy spectra reveal a homogeneous modulation of all multiphoton orders. Hence, the electron current can be strongly increased (by a factor of 3.7) or almost completely turned off due to interference between two different quantum channels in the material. We argue that the extremely high degree of coherence evidenced by this near-unity current modulation depth is due to the confinement of the local field enhancement at the nanotip. The nano-rod effect allows to apply large DC fields, adding a further degree of freedom to investigate the modulation contrast of the photoemitted electron yield. We show that for an increasing DC electric field a non-cooperative distribution of electron emission leads to a decrease in modulation contrast.

Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts

We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Because of the Berry curvature, states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum number with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calculations.

Real-Time Reconstruction of the Strong-Field-Driven Dipole Response

The reconstruction of the full temporal dipole response of a strongly driven time-dependent system from a single absorption spectrum is demonstrated, only requiring that a sufficiently short pulse is employed to initialize the coherent excitation of the system. We apply this finding to the time-domain observation of Rabi cycling between doubly excited atomic states in the few-femtosecond regime. This allows us to pinpoint the breakdown of few-level quantum dynamics at the critical laser intensity near 2  TW/cm^{2} in doubly excited helium. The present approach unlocks single-shot real-time-resolved signal reconstruction across timescales down to attoseconds for nonequilibrium states of matter. In contrast to conventional pump-probe schemes, there is no need for scanning time delays in order to access real-time information. The potential future applications of this technique range from testing fundamental quantum dynamics in strong fields to measuring and controlling ultrafast chemical and biological reaction processes when applied to traditional transient-absorption spectroscopy.

Absolute timing of the photoelectric effect

Photoemission spectroscopy is central to understanding the inner workings of condensed matter, from simple metals and semiconductors to complex materials such as Mott insulators and superconductors¹. Most state-of-the-art knowledge about such solids stems from spectroscopic investigations, and use of subfemtosecond light pulses can provide a time-domain perspective. For example, attosecond (10^-18 seconds) metrology allows electron wave packet creation, transport and scattering to be followed on atomic length scales and on attosecond timescales^2-7. However, previous studies could not disclose the duration of these processes, because the arrival time of the photons was not known with attosecond precision. Here we show that this main source of ambiguity can be overcome by introducing the atomic chronoscope method, which references all measured timings to the moment of light-pulse arrival and therefore provides absolute timing of the processes under scrutiny. Our proof-of-principle experiment reveals that photoemission from the tungsten conduction band can proceed faster than previously anticipated. By contrast, the duration of electron emanation from core states is correctly described by semiclassical modelling. These findings highlight the necessity of treating the origin, initial excitation and transport of electrons in advanced modelling of the attosecond response of solids, and our absolute data provide a benchmark. Starting from a robustly characterized surface, we then extend attosecond spectroscopy towards isolating the emission properties of atomic adsorbates on surfaces and demonstrate that these act as photoemitters with instantaneous response. We also find that the tungsten core-electron timing remains unchanged by the adsorption of less than one monolayer of dielectric atoms, providing a starting point for the exploration of excitation and charge migration in technologically and biologically relevant adsorbate systems.

Dynamic interference as signature of atomic stabilization

We study the ionization of atoms by very intense linearly polarized pulse with moderately high frequency by numerically solving the time-dependent Schrödinger equation (TDSE). In this regime, the photon energy exceeds the ionization potential allowing for one-photon ionization which is, however, strongly influenced by strong nonlinear photon-atom interactions. We find that the onset of atomic stabilization can be monitored by the appearance of a dynamic interference pattern in the photoelectron spectrum.

Large tunable valley splitting in edge-free graphene quantum dots on boron nitride

Coherent manipulation of the binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid-state systems, whereas exploitation of the valley has only recently been started, albeit without control at the single-electron level. Here, we show that van der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunnelling microscope and demonstrate valley splitting that is tunable from -5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits.

Observing the ultrafast buildup of a Fano resonance in the time domain

Although the time-dependent buildup of asymmetric Fano line shapes in absorption spectra has been of great theoretical interest in the past decade, experimental verification of the predictions has been elusive. Here, we report the experimental observation of the emergence of a Fano resonance in the prototype system of helium by interrupting the autoionization process of a correlated two-electron excited state with a strong laser field. The tunable temporal gate between excitation and termination of the resonance allows us to follow the formation of a Fano line shape in time. The agreement with ab initio calculations validates our experimental time-gating technique for addressing an even broader range of topics, such as the emergence of electron correlation, the onset of electron-internuclear coupling, and quasi-particle formation.

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 ([Formula: see text]) and second harmonic ([Formula: see text]) 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 simulations.

Veselago lens and Klein collimator in disordered graphene

We simulate electron transport through graphene nanoribbons of realistic size containing a p-n junction patterned by electrostatic gates. For a sharp p-n interface, Klein tunneling leads to refocusing of a divergent beam forming a Veselago lens. Wider transition regions allow only electrons with near-perpendicular incidence to pass the junction, forming a Klein collimator. Using a third nearest neighbor tight binding description we explore the influence of interface roughness and bulk disorder on guiding properties. We provide bounds on disorder amplitudes and p-n junction properties to be satisfied in order to experimentally observe the focusing effect and compare our predictions to very recent realizations.

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.

Electrostatically Confined Monolayer Graphene Quantum Dots with Orbital and Valley Splittings

The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in bilayer graphene. So far, these approaches suffer from edge disorder or insufficiently controlled localization of electrons. Here we realize an alternative strategy in monolayer graphene, by combining a homogeneous magnetic field and electrostatic confinement. Using the tip of a scanning tunneling microscope, we induce a confining potential in the Landau gaps of bulk graphene without the need for physical edges. Gating the localized states toward the Fermi energy leads to regular charging sequences with more than 40 Coulomb peaks exhibiting typical addition energies of 7-20 meV. Orbital splittings of 4-10 meV and a valley splitting of about 3 meV for the first orbital state can be deduced. These experimental observations are quantitatively reproduced by tight binding calculations, which include the interactions of the graphene with the aligned hexagonal boron nitride substrate. The demonstrated confinement approach appears suitable to create quantum dots with well-defined wave function properties beyond the reach of traditional techniques.

Size quantization of Dirac fermions in graphene constrictions

Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ∼1.5 × 10(6) m s(-1) in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.

Anomalous Fano Profiles in External Fields

We show that the external control of Fano resonances in general leads to complex Fano q parameters. Fano line shapes of photoelectron and transient absorption spectra in the presence of an infrared control field are investigated. Computed transient absorption spectra are compared with a model proposed for a recent experiment [C. Ott et al., Science 340, 716 (2013)]. Control mechanisms for photoelectron spectra are exposed: control pulses applied during excitation modify the line shapes by momentum boosts of the continuum electrons. Pulses arriving after excitation generate interference fringes due to infrared two-photon transitions.

Coherent electronic wave packet motion in C(60) controlled by the waveform and polarization of few-cycle laser fields

Strong laser fields can be used to trigger an ultrafast molecular response that involves electronic excitation and ionization dynamics. Here, we report on the experimental control of the spatial localization of the electronic excitation in the C_{60} fullerene exerted by an intense few-cycle (4 fs) pulse at 720 nm. The control is achieved by tailoring the carrier-envelope phase and the polarization of the laser pulse. We find that the maxima and minima of the photoemission-asymmetry parameter along the laser-polarization axis are synchronized with the localization of the coherent electronic wave packet at around the time of ionization.

Ab initio simulation of electrical currents induced by ultrafast laser excitation of dielectric materials

We theoretically investigate the generation of ultrafast currents in insulators induced by strong few-cycle laser pulses. Ab initio simulations based on time-dependent density functional theory give insight into the atomic-scale properties of the induced current signifying a femtosecond-scale insulator-metal transition. We observe the transition from nonlinear polarization currents during the laser pulse at low intensities to tunnelinglike excitation into the conduction band at higher laser intensities. At high intensities, the current persists after the conclusion of the laser pulse considered to be the precursor of the dielectric breakdown on the femtosecond scale. We show that the transferred charge sensitively depends on the orientation of the polarization axis relative to the crystal axis, suggesting that the induced charge separation reflects the anisotropic electronic structure. We find good agreement with very recent experimental data on the intensity and carrier-envelope phase dependence [A. Schiffrin et al., Nature (London) 493, 70 (2013).

Photovoltaic effect in an electrically tunable van der Waals heterojunction

Semiconductor heterostructures form the cornerstone of many electronic and optoelectronic devices and are traditionally fabricated using epitaxial growth techniques. More recently, heterostructures have also been obtained by vertical stacking of two-dimensional crystals, such as graphene and related two-dimensional materials. These layered designer materials are held together by van der Waals forces and contain atomically sharp interfaces. Here, we report on a type-II van der Waals heterojunction made of molybdenum disulfide and tungsten diselenide monolayers. The junction is electrically tunable, and under appropriate gate bias an atomically thin diode is realized. Upon optical illumination, charge transfer occurs across the planar interface and the device exhibits a photovoltaic effect. Advances in large-scale production of two-dimensional crystals could thus lead to a new photovoltaic solar technology.

Gravity resonance spectroscopy constrains dark energy and dark matter scenarios

We report on precision resonance spectroscopy measurements of quantum states of ultracold neutrons confined above the surface of a horizontal mirror by the gravity potential of Earth. Resonant transitions between several of the lowest quantum states are observed for the first time. These measurements demonstrate that Newton's inverse square law of gravity is understood at micron distances on an energy scale of 10-14  eV. At this level of precision, we are able to provide constraints on any possible gravitylike interaction. In particular, a dark energy chameleon field is excluded for values of the coupling constant β>5.8×108 at 95% confidence level (C.L.), and an attractive (repulsive) dark matter axionlike spin-mass coupling is excluded for the coupling strength gsgp>3.7×10-16 (5.3×10-16) at a Yukawa length of λ=20  μm (95% C.L.).

Vectorial velocity filter for ultracold neutrons based on a surface-disordered mirror system

We perform classical three-dimensional Monte Carlo simulations of ultracold neutrons scattering through an absorbing-reflecting mirror system in the Earth's gravitational field. We show that the underlying mixed phase space of regular skipping motion and random motion due to disorder scattering can be exploited to realize a vectorial velocity filter for ultracold neutrons. The absorbing-reflecting mirror system proposed allows beams of ultracold neutrons with low angular divergence to be formed. The range of velocity components can be controlled by adjusting the geometric parameters of the system. First experimental tests of its performance are presented. One potential future application is the investigation of transport and scattering dynamics in confined systems downstream of the filter.

Time-resolved photoemission on the attosecond scale: opportunities and challenges

The interaction of laser pulses of sub-femtosecond duration with matter opened up the opportunity to explore electronic processes on their natural time scale. One central conceptual question posed by the observation of photoemission in real time is whether the ejection of the photoelectron wavepacket occurs instantaneously, or whether the response time to photoabsorption is finite leading to a time delay in photoemission. Recent experimental progress exploring attosecond streaking and RABBIT techniques find relative time delays between the photoemission from different atomic substates to be of the order of -20 attoseconds. We present ab initio simulations for both one- and two-electron systems which allow the determination of both absolute and relative time delays with -1 attosecond precision. We show that the intrinsic time shift of the photoionization process encoded in the Eisenbud-Wigner-Smith delay time can be unambiguously disentangled from measurement-induced time delays in a pump-probe setting when the photoionized electronic wavepacket is probed by a modestly strong infrared streaking field. We identify distinct contributions due to initial-state polarization, Coulomb-laser coupling in the final continuum state as well as final-state interaction with the entangled residual ionic state. Extensions to multi-electron systems and to the extraction of time information in the presence of decohering processes are discussed.

Semiclassical wave functions for open quantum billiards

We present a semiclassical approximation to the scattering wave function Ψ(r,k) for an open quantum billiard, which is based on the reconstruction of the Feynman path integral. We demonstrate its remarkable numerical accuracy for the open rectangular billiard and show that the convergence of the semiclassical wave function to the full quantum state is controlled by the mean path length or equivalently the dwell time for a given scattering state. In the numerical implementation a cutoff length in the maximum path length or, equivalently, a maximum dwell time τ(max) included implies a finite energy resolution ΔE~τ(max)(-1). Possible applications include leaky billiards and systems with decoherence present.

Phase diagram for nanostructuring CaF(2) surfaces by slow highly charged ions

The impact of individual slow highly charged ions (HCI) on alkaline earth halide and alkali halide surfaces creates nano-scale surface modifications. For different materials and impact energies a wide variety of topographic alterations have been observed, ranging from regularly shaped pits to nanohillocks. We present experimental evidence for the creation of thermodynamically stable defect agglomerations initially hidden after irradiation but becoming visible as pits upon subsequent etching. A well defined threshold separating regions with and without etch-pit formation is found as a function of potential and kinetic energies of the projectile. Combining this novel type of surface defects with the previously identified hillock formation, a phase diagram for HCI induced surface restructuring emerges. The simulation of the energy deposition by the HCI in the crystal provides insight into the early stages of the dynamics of the surface modification and its dependence on the kinetic and potential energies.

Multielectron transitions induced by neutron impact on helium

We explore excitation and ionization by neutron impact as a novel tool for the investigation of electron-electron correlations in helium. We present single- and double-ionization spectra calculated in accurate numerical ab initio simulations for incoming neutrons with kinetic energies of up to 150 keV. The resulting electron spectra are found to be fundamentally different from photoionization or charged particle impact due to the intrinsic many-body character of the interaction. In particular, doubly excited resonances that are strongly suppressed in electron or photon impact become prominent. The ratio of double to single ionization is found to differ significantly from those of photon and charged-particle impact.

Analysis of circular wave packets generated by pulsed electric fields

We demonstrate that circular wave packets in high Rydberg states generated by a pulsed electric field applied to extreme Stark states are characterized by a position-dependent energy gradient that leads to a correlation between the principal quantum number n and the spatial coordinate. This correlation is rather insensitive to the initial state and can be seen even in an incoherent mix of states such as is generated experimentally allowing information to be placed into, and extracted from, such wave packets. We show that detailed information on the spatial distribution of a circular wave packet can be extracted by analyzing the complex phase of its expansion coefficients.

Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields

We experimentally and theoretically demonstrate a self-referenced wave-function retrieval of a valence-electron wave packet during its creation by strong-field ionization with a sculpted laser field. Key is the control over interferences arising at different time scales. Our work shows that the measurement of subcycle electron wave-packet interference patterns can serve as a tool to retrieve the structure and dynamics of the valence-electron cloud in atoms on a sub-10-as time scale.

Attosecond streaking of correlated two-electron transitions in helium

We present fully ab initio simulations of attosecond streaking for ionization of helium accompanied by shakeup of the second electron. This process represents a prototypical case for strongly correlated electron dynamics on the attosecond time scale. We show that streaking spectroscopy can provide detailed information on the Eisenbud-Wigner-Smith time delay as well as on the infrared-field dressing of both bound and continuum states. We find a novel contribution to the streaking delay that stems from the interplay of electron-electron and infrared-field interactions in the exit channel. We quantify all the contributions with attosecond precision and provide a benchmark for future experiments.

Wave-function mapping of graphene quantum dots with soft confinement

Using low-temperature scanning tunneling spectroscopy, we map the local density of states of graphene quantum dots supported on Ir(111). Because of a band gap in the projected Ir band structure around the graphene K point, the electronic properties of the QDs are dominantly graphenelike. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moiré potential and a 10% penetration of an Ir surface resonance into the graphene layer.

Creating and transporting Trojan wave packets

Nondispersive localized Trojan wave packets with n(i) ~ 305 moving in near-circular Bohr-like orbits are created and transported to localized near-circular Trojan states of higher n, n(f) ~ 600, by driving with a linearly polarized sinusoidal electric field whose period is slowly increased. The protocol is remarkably efficient with over 80% of the initial atoms being transferred to the higher n states, a result confirmed by classical trajectory Monte Carlo simulations.

Attosecond two-photon interferometry for doubly excited states of helium

We show that the correlation dynamics in coherently excited doubly excited resonances of helium can be followed in real time by two-photon interferometry. This approach promises to map the evolution of the two-electron wave packet onto experimentally easily accessible noncoincident single-electron spectra. We analyze the interferometric signal in terms of a semianalytical model which is validated by a numerical solution of the time-dependent two-electron Schrödinger equation in its full dimensionality.

Probing decoherence through Fano resonances

We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex plane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through quantum dots. These results open up new possibilities for studying the effect of decoherence in a wide array of physical systems where Fano resonances are present.