Publications Project 04 
Interactions of Ultrashort Field with Solid Surfaces and Nanostructures
Project Leader: Joachim Burgdörfer
Creation of Rydberg Polarons in a Bose GasF. Camargo, R. Schmidt, J. D. Whalen, R. Ding, G. Woehl, Jr., S. Yoshida, J. Burgdörfer, F. B. Dunning, H. R. Sadeghpour, E. Demler, and T. C. Killian 

We report spectroscopic observation of Rydberg polarons in an atomic Bose gas. Polarons are created by excitation of Rydberg atoms as impurities in a strontium BoseEinstein condensate. They are distinguished from previously studied polarons by macroscopic occupation of bound molecular states that arise from scattering of the weakly bound Rydberg electron from groundstate atoms. The absence of a pwave resonance in the lowenergy electronatom scattering in Sr introduces a universal behavior in the Rydberg spectral line shape and in scaling of the spectral width (narrowing) with the Rydberg principal quantum number, n. Spectral features are described with a functional determinant approach (FDA) that solves an extended Fröhlich Hamiltonian for a mobile impurity in a Bose gas. Excited states of polyatomic Rydberg molecules (trimers, tetrameters, and pentamers) are experimentally resolved and accurately reproduced with a FDA.  
Published: 20180222 Press release TU Wien, 20180226 [17/2018] 

Observing the ultrafast buildup of a Fano resonance in the time domainA. Kaldun, A. Blättermann, V. Stooß, S. Donsa, H. Wei, R. Pazourek, S. Nagele, C. Ott, C. D. Lin, J. Burgdörfer, T. Pfeifer 

Although the timedependent 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 twoelectron 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 timegating technique for addressing an even broader range of topics, such as the emergence of electron correlation, the onset of electroninternuclear coupling, and quasiparticle formation.  
Published: 20161107 Press release TU Wien, 20161111 [73/2016] 

Attosecond correlation dynamicsM. Ossiander, F. Siegrist, V. Shirvanyan, R. Pazourek, A. Sommer, T. Latka, A. Guggenmos, S. Nagele, J. Feist, J. Burgdörfer, R. Kienberger & M. Schultze 

Photoemission of an electron is commonly treated as a oneparticle phenomenon. With attosecond streaking spectroscopy we observe the breakdown of this single activeelectron approximation by recording up to six attoseconds retardation of the dislodged photoelectron due to electronic correlations. We recorded the photonenergydependent emission timing of electrons, released from the helium ground state by an extremeultraviolet photon, either leaving the ion in its ground state or exciting it into a shakeup state. We identify an optical fielddriven d.c. Stark shift of chargeasymmetric ionic states formed after the entangled photoemission as a key contribution to the observed correlation time shift. These findings enable a complete wavepacket reconstruction and are universal for all polarized initial and final states. Subattosecond agreement with quantum mechanical ab initio modelling allows us to determine the absolute zero of time in the photoelectric effect to a precision better than 1/25th of the atomic unit of time.  
Published: 20161107 Press release TU Wien, 20161107 [72/2016] 

Coincidence spectroscopy of highlying Rydberg states produced in strong field interactionS. Larimian, S. Erattupuzha, R. Maurer, C. Lemell, S. Nagele, S. Yoshida, J. Burgdörfer, A. Baltuska, M. Kitzler, X. Xie 

We demonstrate the detection of highlying Rydberg states produced in strong laser fields with coincidence spectroscopy. Electron emission after the interaction of strong laser pulses with atoms and molecules is measured together with the parent ions in coincidence measurements. These electrons originate from highlying Rydberg states with quantum numbers from n∼20 up to n≲120 formed by frustrated field ionization. Ionization rates are retrieved from the measured ionization signal of these Rydberg states. Simulations show that both tunneling ionization by a weak dc field and photoionization by blackbody radiation contribute to delayed electron emission on the nano to microsecond scale. Furthermore, the dependence of the Rydbergstate production on the ellipticity of the driving laser field indicates that such highlying Rydberg states are populated through electron recapture. The present experiment provides detailed quantitative information on Rydberg production in strongfield interaction.  
Published: 20160901 

Timedependent completeactivespace selfconsistentfield method for atoms: Application to highharmonic generationT. Sato, K. L. Ishikawa, I. Brezinova, F. Lackner, S. Nagele, J. Burgdörfer 

We present a numerical implementation of the timedependent completeactivespace selfconsistentfield (TDCASSCF) method [Phys. Rev. A 88, 023402 (2013)] for atoms driven by a strong linearly polarized laser pulse. The present implementation treats the problem in its full dimensionality and introduces a gaugeinvariant frozencore approximation, an efficient evaluation of the Coulomb mean field scaling linearly with the number of basis functions, and a splitoperator method specifically designed for stable propagation of stiff spatial derivative operators. We apply this method to highharmonic generation in helium, beryllium, and neon and explore the role of electron correlations.  
Published: 20160809 

Nonlinear response of graphene to a few cycle THz laser pulse: role of doping and disorderL. Chizhova, J. Burgdörfer, and F. Libisch 

The nonlinear response of graphene to a THz laser pulse is studied by solving the timedependent Dirac equation and the timedependent Schrödinger equation within a tightbinding approximation applied to finitesized structures. We compare predictions of these two approximations for the harmonic spectrum with the recent experiment by P. Bowlan et al. [Phys. Rev. B 89, 041408(R) (2014)]. We highlight the influence of shortrange and longrange disorder which can be accounted for within the tightbinding description on a microscopic level. We find good agreement with the experiment. Most notably, the intensity of the second harmonic offers a quantitative indicator for the amount of shortrange disorder.  
Published: 20160809 

Semiclassical twostep model for strongfield ionizationN. I. ShvetsovShilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, K. Tőkési 

We present a semiclassical twostep model for strongfield ionization that accounts for path interferences of tunnelionized electrons in the ionic potential beyond perturbation theory. Within the framework of a classical trajectory Monte Carlo representation of the phasespace dynamics, the model employs the semiclassical approximation to the phase of the full quantum propagator in the exit channel. By comparison with the exact numerical solution of the timedependent Schrödinger equation for strongfield ionization of hydrogen, we show that for suitable choices of the momentum distribution after the first tunneling step, the model yields good quantitative agreement with the full quantum simulation. The twodimensional photoelectron momentum distributions, the energy spectra, and the angular distributions are found to be in good agreement with the corresponding quantum results. Specifically, the model quantitatively reproduces the fanlike interference patterns in the lowenergy part of the twodimensional momentum distributions, as well as the modulations in the photoelectron angular distributions.  
Published: 20160719 

Size quantization of Dirac fermions in graphene constrictionsB. Terrés, L. A. Chizhova, F. Libisch, J. Peiro, D. Jörger, S. Engels, A. Girschik, K. Watanabe, T. Taniguchi, S. V. Rotkin, J. Burgdörfer, and C. Stampfer 

Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in highquality 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 sizeconfined 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 × 10⁶ m s¹ 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.  
Published: 20160520 

Trap losses induced by nearresonant Rydberg dressing of cold atomic gasesJ. A. Aman, B. J. DeSalvo, F. B. Dunning, T. C. Killian, S. Yoshida, and J. Burgdörfer 

The nearresonant dressing of cold strontium gases and BoseEinstein condensates contained in an optical dipole trap (ODT) with the 5s30s³S1 Rydberg state is investigated as a function of the effective twophoton Rabi frequency, detuning, and dressing time. The measurements demonstrate that a rapid decrease in the groundstate atom population in the ODT occurs even for weak dressing and when well detuned from resonance. This decrease is attributed to Rydberg atom excitation, which can lead to direct escape from the trap and to population of very longlived 5s5p³P0,2 metastable states. The effects of interactions between Rydberg atoms, including those populated by blackbody radiation, are analyzed. The work has important implications when considering the use of Rydberg dressing to control the interactions between dressed groundstate atoms.  
Published: 20160429 

Rydbergblockade effects in AutlerTownes spectra of ultracold strontiumB. J. DeSalvo, J. A. Aman, C. Gaul, T. Pohl, S. Yoshida, J. Burgdörfer, K. R. A. Hazzard, F. B. Dunning, and T. C. Killian 

We present a combined experimental and theoretical study of the effects of Rydberg interactions on AutlerTownes spectra of ultracold gases of atomic strontium. Realizing twophoton Rydberg excitation via a longlived triplet state allows us to probe the regime where Rydberg state decay presents the dominant decoherence mechanism. The effects of Rydberg interactions are observed in shifts, asymmetries, and broadening of the measured atomloss spectra. The experiment is analyzed within a onebody densitymatrix approach, accounting for interactioninduced level shifts and dephasing through nonlinear terms that approximately incorporate correlations due to the Rydberg blockade. This description yields good agreement with our experimental observations for short excitation times. For longer excitation times, the loss spectrum is altered qualitatively, suggesting additional dephasing mechanisms beyond the standard blockade mechanism based on pure van der Waals interactions.  
Published: 20160222 

Lifetimes of ultralongrange strontium Rydberg moleculesCamargo, F., J. D. Whalen, R. Ding, H. R. Sadeghpour, S. Yoshida, J. Burgdörfer, F. B. Dunning, and T. C. Killian 

The lifetimes of the lowerlying vibrational states of ultralongrange strontium Rydberg molecules comprising one groundstate 5s² ¹S0 atom and one Rydberg atom in the 5s38s³S1 state are reported. The molecules are created in an ultracold gas held in an optical dipole trap and their numbers determined using field ionization, the product electrons being detected by a microchannel plate. The measurements show that, in marked contrast to earlier measurements involving rubidium Rydberg molecules, the lifetimes of the lowlying molecular vibrational states are very similar to those of the parent Rydberg atoms. This results because the strong pwave resonance in lowenergy electronrubidium scattering, which strongly influences the rubidium molecular lifetimes, is not present for strontium. The absence of this resonance offers advantages for experiments involving strontium Rydberg atoms as impurities in quantum gases and for testing of theories of molecular formation and decay.  
Published: 20160204 

Controlling ultrafast currents by the nonlinear photogalvanic effectG. Wachter, S.A. Sato, I. Floss, C. Lemell, X.M. Tong, K. Yabana, J. Burgdörfer 

We investigate the effect of broken inversion symmetry on the generation and control of ultrafast currents in a transparent dielectric (SiO2) by strong femtosecond optical laser pulses. Ab initio simulations based on timedependent density functional theory predict ultrafast direct currents that can be viewed as a nonlinear photogalvanic effect. Most surprisingly, the direction of the current undergoes a sudden reversal above a critical threshold value of laser intensity of about Ic ~ 3 x 10¹³ W cm−². We trace this switching to the transition from nonlinear polarisation currents to the tunnelling excitation regime. The latter is found to be sensitive to the relative orientation between laser polarisation and chemical bonds. We demonstrate control of the ultrafast currents by the time delay between two laser pulses. While two temporally separated laser pulses lead to currents along one direction their temporal overlap can reverse the current. We find the ultrafast current control by the nonlinear photogalvanic effect to be remarkably robust and insensitive to the laserpulse shape and the carrierenvelope phase.  
Published: 20151221 

Protocol for observing molecular dipole excitations by attosecond selfstreakingG. Wachter, S. Nagele, S.A. Sato, R. Pazourek, M. Wais, C. Lemell, X.M. Tong, K. Yabana, J. Burgdörfer 

We propose a protocol to probe the ultrafast evolution and dephasing of coherent electronic excitation in molecules in the time domain by the intrinsic streaking field generated by the molecule itself. Coherent electronic motion in the endohedral fullerene Ne@C60 is initiated by a moderately intense femtosecond UVvisible pulse leading to coherent oscillations of the molecular dipole moment that persist after the end of the laser pulse. The resulting timedependent molecular near field is probed through the momentum modulation of photoemission from the central neon atom by a timedelayed attosecond XUV pulse. Our ab initio timedependent density functional theory and classical trajectory simulations predict that this selfstreaking signal accurately traces the molecular dipole oscillations in real time. We discuss the underlying processes and give an analytical model that captures the essence of our ab initio simulations.  
Published: 20151218 

Anomalous Fano Profiles in External FieldsA. Zielinski, V.P. Majety, S. Nagele, R. Pazourek, J. Burgdörfer, A. Scrinzi 

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 twophoton transitions.  
Published: 20151210 

Rydberg blockade effects at n∼300 in strontiumX. Zhang, F.B. Dunning, S. Yoshida, J. Burgdörfer 

Rydberg blockade at n∼300, is examined using strontium nF31 Rydberg atoms excited in an atomic beam in a small volume defined by two tightly focused crossed laser beams. The observation of blockade for such states is challenging due to their extreme sensitivity to stray fields and the many magnetic sublevels associated with F states which results in a high local density of states. Nonetheless, with a careful choice of laser polarization to selectively excite only a limited number of these sublevels, sizable blockade effects are observed on an ∼0.1 mm length scale extending blockade measurements into the nearmacroscopic regime and enabling study of the dynamics of strongly coupled manybody highn Rydberg systems under carefully controlled conditions.  
Published: 20151123 

Application of normconserving pseudopotentials to intense lasermatter interactionsX.M. Tong, G. Wachter, S. Sato, C. Lemell, K. Yabana, and J. Burgdörfer 

We investigate the applicability of normconserving pseudopotentials to intense lasermatter interactions by performing timedependent density functional theory simulations with an allelectron potential and with normconserving pseudopotentials. We find pseudopotentials to be reliable for the simulation of abovethreshold ionization over a broad range of laser intensities both for the total ionization probability and the photoelectron energy spectrum. For the simulation of highorderharmonic generation, pseudopotentials are shown to be applicable for lowerorder harmonics in the spectral range in which the onephoton recombination dipolematrix element can be recovered by the pseudopotential calculation.  
Published: 20151029 

Ultralongrange Rydberg molecules in a divalent atomic systemB. DeSalvo, J. Aman, F.B. Dunning, T. Killian, H. Sadeghpour, S. Yoshida, and J. Burgdörfer 

We report the creation of ultralongrange Sr2 molecules comprising one groundstate 5s2 1S0 atom and one atom in a 5sns 3S1 Rydberg state for n ranging from 29 to 36. Molecules are created in a trapped ultracold atomic gas using twophoton excitation near resonant with the 5s5p 3P1 intermediate state, and their formation is detected through groundstate atom loss from the trap. The observed molecular binding energies are reproduced with the aid of firstorder perturbation theory that utilizes a Fermi pseudopotential with effective swave and pwave scattering lengths to describe the interaction between an excited Rydberg electron and a groundstate Sr atom.  
Published: 20150928 

Time delays in correlated photoemission processesR. Pazourek, S. Nagele, and J. Burgdörfer 

We theoretically study timeresolved twophoton double ionization (TPDI) of helium as probed by attosecond streaking. We review recent advances in the understanding of the photoelectric effect in the time domain and discuss the differences between one and twophoton ionization, as well as one and twoelectron emission. We perform exact abinitio simulations for attosecond streaking experiments in the sequential TPDI regime and compare the results to the twoelectron EisenbudWignerSmith delay for the process. Our calculations directly show that the timing of the emission process sensitively depends on the energy sharing between the two outgoing electrons. In particular, we identify Fanolike interferences in the relative time delay of the two emitted electrons when the sequential ionization channel occurs via intermediate excited ionic (shakeup) states. Furthermore, we find that the photoemission time delays are only weakly dependent on the relative emission angle of the ejected electrons.  
Published: 20150907 

Signatures of tunneling and multiphoton ionization by shortlaser pulses: The partialwave distributionD. Arbó, C. Lemell, and J. Burgdörfer 

We analyze the twodimensional angular momentumenergy distribution of electrons emitted from argon by short laser pulses. We identify characteristic features of both multiphoton and tunneling ionization in the partialwave distribution for Keldysh parameters close to unity. We observe a remarkable degree of quantumclassical correspondence in the photoinization process which becomes even more pronounced after intensity averaging over the focal volume. We derive an energydependent cutoff for the highest angular momentum accessible within the framework of the strongfield approximation, which accurately reproduces the partial wave distributions found from solutions of the timedependent Schrödinger equation.  
Published: 20150907 

Attosecond chronoscopy of photoemissionR. Pazourek, S. Nagele, and J. Burgdörfer 

Recent advances in the generation of wellcharacterized subfemtosecond laser pulses have opened up unpredicted opportunities for the realtime observation of ultrafast electronic dynamics in matter. Such attosecond chronoscopy allows a novel look at a wide range of fundamental photophysical and photochemical processes in the time domain, including Auger and autoionization processes, as well as photoemission from atoms, molecules, and surfaces, complementing conventional energydomain spectroscopy. Attosecond chronoscopy raises fundamental conceptual and theoretical questions as to which novel information becomes accessible and which dynamical processes can be controlled and steered. Several of these questions, currently a matter of lively debate, are addressed in this review. The focus is placed on one prototypical case, the chronoscopy of the photoelectric effect by attosecond streaking. Is photoionization instantaneous or is there a finite response time of the electronic wave function to the photoabsorption event? Answers to this question turn out to be far more complex and multifaceted than initially thought. They touch upon fundamental issues of time and time delay as observables in quantum theory. Recent progress of our understanding of timeresolved photoemission from atoms, molecules, and solids is reviewed. Unresolved and open questions are highlighted and future directions are discussed addressing the observation and control of electronic motion in more complex nanoscale structures and in condensed matter.  
Published: 20150812 

Ionization of argon by twocolor laser pulses with coherent phase controlD. Arbó, C. Lemell, S. Nagele, N. Camus, L. Fechner, A. Krupp, T. Pfeifer, S. Lopéz, R. Moshammer, and J. Burgdörfer 

We present a joint experimental and theoretical study of ionization of argon atoms by a linearly polarized twocolor laser field (λ1=800 nm, λ2=400 nm). Changing the relative phase φ between the two colors, the forwardbackward asymmetry of the doubly differential momentum distribution of emitted electrons can be controlled. We find excellent agreement between the measurements and the solution of the timedependent Schrödinger equation in the singleactive electron approximation. Surprisingly we also find good agreement between the quantum and classical calculations of electron momentum distributions generated by lasers at optical wavelengths.  
Published: 20150803 

Large optical field enhancement for nanotips with large opening anglesS. Thomas, G. Wachter, C. Lemell, J. Burgdörfer, P. Hommelhoff 

We theoretically investigate the dependence of the enhancement of optical nearfields at nanometric tips on the shape, size, and material of the tip. We confirm the strong dependence of the field enhancement factor on the radius of curvature. In addition, we find a surprisingly strong increase of field enhancement with increasing opening angle of the nanotips. For gold and tungsten nanotips in the experimentally relevant parameter range (radius of curvature ≥5nm at 800 nm laser wavelength), we obtain field enhancement factors of up to ~35 for Au and ~12 for W for large opening angles. We confirm this strong dependence on the opening angle for many other materials featuring a wide variety in their dielectric response. For dielectrics, the opening angle dependence is traced back to the electrostatic force of the induced surface charge at the tip shank. For metals, the plasmonic response strongly increases the field enhancement and shifts the maximum field enhancement to smaller opening angles.  
Published: 20150610 

Realtime observation of collective excitations in photoemissionC. Lemell, S. Neppl, G. Wachter, K. Tökési, R. Ernstorfer, P. Feulner, R. Kienberger, J. Burgdörfer 

Ejection of an electron by absorption of an extreme ultraviolet (xuv) photon probes the manyelectron response of a solid well beyond the singleparticle picture. Photoemission spectra feature complex correlation satellite structures signifying the simultaneous excitation of single or multiple plasmons. The time delay of the plasmon satellites relative to the main line can be resolved in attosecond streaking experiments. Timeresolved photoemission thus provides the key to discriminate between intrinsic and extrinsic plasmon excitation. We demonstrate the determination of the branching ratio between intrinsic and extrinsic plasmon generation for simple metals.  
Published: 20150603 

Coherent Electronic Wave Packet Motion in C60 Controlled by the Waveform and Polarization of FewCycle Laser FieldsH. Li, B. Mignolet, G. Wachter, S. Skruszewitcz, S. Zherebtsov, F. Suessmann, A. Kessel, S. Trushin, N. Kling, M. Kuebel, B. Ahn, D. Kim, I. BenItzhak, C. Cocke, T. Fennel, J. Tiggesbaeumker, K. MeiwesBroer, C. Lemell, J. Burgdörfer, R. Levine, F. Remacle, M. Kling 

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 C60 fullerene exerted by an intense fewcycle (4 fs) pulse at 720 nm. The control is achieved by tailoring the carrierenvelope phase and the polarization of the laser pulse. We find that the maxima and minima of the photoemissionasymmetry parameter along the laserpolarization axis are synchronized with the localization of the coherent electronic wave packet at around the time of ionization.  
Published: 20150327 

Probing timeordering in twophoton double ionization of helium on the attosecond time scaleR. Pazourek, S. Nagele, and J. Burgdörfer 

We show that time ordering underlying timedependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of timeresolved twophoton double ionization of helium by an attosecond XUV pulse. The Eisenbud–Wigner–Smith time delay for the emission of a twoelectron wavepacket and the time interval between subsequent emission events can be unambiguously determined by attosecond streaking. The delay between the two emission events sensitively depends on the energy, pulse duration, and angular distribution of the emitted electron pair. Our fullydimensional ab initio quantum mechanical simulations provide benchmark data for experimentally accessible observables.  
Published: 20150304 

Propagating twoparticle reduced density matrices without wave functionsF. Lackner, I. Brezinova, T. Sato, K. L. Ishikawa, and J. Burgdörfer 

Describing timedependent manybody systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a timedependent manybody theory that is based on the twoparticle reduced density matrix (2RDM). We present a closed equation of motion for the 2RDM by developing a reconstruction functional for the threeparticle reduced density matrix (3RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing Nrepresentability during time evolution is essential for achieving stable solutions. As a prototypical test case which features longrange Coulomb interactions we employ the onedimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both oneparticle observables such as the timedependent dipole moment and twoparticle observables such as the pair density and mean electronelectron interaction energy. Our results are in very good agreement with numerically exact solutions for the Nelectron wave function obtained from the multiconfigurational timedependent HartreeFock method.  
Published: 20150211 

Direct observation of electron propagation and dielectric screening on the atomic length scaleS. Neppl, R. Ernstorfer, A. Cavalieri, C. Lemell, G. Wachter, E. Magerl, E. Bothschafter, M. Jobst, M. Hofstetter, U. Kleineberg, J. Barth, D. Menzel, J. Burgdörfer, P. Feulner, F. Krausz, and R. Kienberger 

The propagation and transport of electrons in crystals is a fundamental process pertaining to the functioning of most electronic devices. Microscopic theories describe this phenomenon as being based on the motion of Bloch wave packets. These wave packets are superpositions of individual Bloch states with the group velocity determined by the dispersion of the electronic band structure near the central wavevector in momentum space. This concept has been verified experimentally in artificial superlattices by the observation of Bloch oscillations—periodic oscillations of electrons in real and momentum space. Here we present a direct observation of electron wave packet motion in a realspace and realtime experiment, on length and time scales shorter than the Bloch oscillation amplitude and period. We show that attosecond metrology (1 as = 10−18 seconds) now enables quantitative insight into weakly disturbed electron wave packet propagation on the atomic length scale without being hampered by scattering effects, which inevitably occur over macroscopic propagation length scales. We use subfemtosecond (less than 10−15 seconds) extremeultraviolet light pulses to launch photoelectron wave packets inside a tungsten crystal that is covered by magnesium films of varied, welldefined thicknesses of a few ångströms. Probing the moment of arrival of the wave packets at the surface with attosecond precision reveals freeelectronlike, ballistic propagation behaviour inside the magnesium adlayer—constituting the semiclassical limit of Bloch wave packet motion. Realtime access to electron transport through atomic layers and interfaces promises unprecedented insight into phenomena that may enable the scaling of electronic and photonic circuits to atomic dimensions. In addition, this experiment allows us to determine the penetration depth of electrical fields at optical frequencies at solid interfaces on the atomic scale.  
Published: 20150115 

Formation of verylowenergy states crossing the ionization threshold of argon atoms in strong midinfrared fieldsB. Wolter, C. Lemell, M. Baudisch, M.G. Pullen, X.M. Tong, M. Hemmer, A. Senftleben, C.D. Schröter, J. Ullrich, R. Moshammer, J. Biegert, J. Burgdörfer 

Atomic ionization by intense midinfrared (midIR) pulses produces lowelectronenergy features that the strongfield approximation, which is expected to be valid in the tunneling ionization regime characterized by small Keldysh parameters (γ≪1), cannot describe. These features include the lowenergy structure (LES), the verylowenergy structure (VLES), and the more recently found zeroenergy structure (ZES). They result from the interplay between the laser electric field and the atomic Coulomb field which controls the lowenergy spectrum also for small γ. In the present joint experimental and theoretical study we investigate the vectorial momentum spectrum of photoelectrons emitted from an Ar gas target at very low energies. Using a reaction microscope optimized for the detection of verylowenergy electrons, we have performed a thorough study of the threedimensional momentum spectrum well below 1 eV. Our measurements are complemented by quantum and classical simulations, which allow for an interpretation of the LES and VLES and of the ZES in terms of twodimensional Coulomb focusing and recapture into Rydberg states, respectively.  
Published: 20141222 

Ionization of helium by slow antiproton impact: Total and differential cross sectionsS. Borbély, J. Feist, K. Tökési, S. Nagele, L. Nagy, J. Burgdörfer 

We investigate theoretically the single and double ionization of the He atom by antiproton impact for projectile energies ranging from 3 keV up to 1000 keV. We obtain accurate total cross sections by directly solving the fully correlated twoelectron timedependent Schrödinger equation. The cross sections are in excellent agreement with the available experimental data. We also present fully ab initio doubly differential data for single ionization at 10 and 100 keV impact energies and compare to classicaltrajectory Monte Carlo calculations. In these differential cross sections we identify the binaryencounter peak along with the anticusp minimum. Furthermore, we also point out the importance of the postcollisional electronprojectile interaction at low antiproton energies, which significantly suppresses electron emission in the forward direction.  
Published: 20141110 

Ab Initio Simulation of Electrical Currents Induced by Ultrafast Laser Excitation of Dielectric MaterialsG. Wachter, C. Lemell, J. Burgdörfer 

We theoretically investigate the generation of ultrafast currents in insulators induced by strong fewcycle laser pulses. Ab initio simulations based on timedependent density functional theory give insight into the atomicscale properties of the induced current signifying a femtosecondscale insulatormetal 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 carrierenvelope phase dependence [A. Schiffrin et al., Nature (London) 493, 70 (2013)].  
Published: 20140818 

Attosecond streaking of CohenFano interferences in the photoionization of H2^{+}Q.C. Ning, L.Y. Peng, S.N. Song, W.C. Jiang, S. Nagele, R. Pazourek, J. Burgdörfer, Q. Gong 

We present a numerical abinitio simulation of the time delay in the photoionization of the simplest diatomic molecule H_{2}^{+} as observed by attosecond streaking. We show that the strong variation of the EisenbudWignerSmith time delay t_{EWS} as a function of energy and emission angle becomes observable in the streaking time shift t_{S} provided laser field induced components are accounted for. The strongly enhanced photoemission time shifts are traced to destructive CohenFano (or twocenter) interferences. Signatures of these interferences in the streaking trace are shown to be enhanced when the ionic fragments are detected in coincidence.  
Published: 20140730 

Efficient threephoton excitation of quasionedimensional strontium Rydberg atoms with n~300S. Ye, X. Zhang, F.B. Dunning, S. Yoshida, M. Hiller, J. Burgdörfer 

The efficient production of veryhighn, n∼300, quasionedimensional (quasi1D) strontium Rydberg atoms through threephoton excitation of extreme Stark states in the presence of a weak dc field is demonstrated using a crossed laseratom beam geometry. Strongly polarized quasi1D states with large permanent dipole moments ∼1.2n^{2} a.u. can be created in the beam at densities (∼10^{6} cm^{−3}) where dipole blockade effects should become important. A further advantage of threephoton excitation is that the product F states are sensitive to the presence of external fields, allowing stray fields to be reduced to very small values. The experimental data are analyzed using quantum calculations based on a twoactiveelectron model together with classical trajectory Monte Carlo simulations. These allow determination of the atomic dipole moments and confirm that stray fields can be reduced to ≤25 μV cm^{−1}.  
Published: 20140701 

Interference of electron wave packets in atomic ionization by subcycle sculpted laser pulsesD.G. Arbó, S. Nagele, X.M. Tong, X. Xie, M. Kitzler, J. Burgdörfer 

We present a theoretical analysis of the atomic photoelectron emission spectra produced by a linearly polarized sculpted laser pulse of two colors with frequencies ω and 2ω. The spectrum of the “direct” electrons with intermediate energies prominently features both intracycle and intercycle interferences. We derive a simple analytic expression for this spectral range based on a semiclassical approximation of the timedependent distorted wave strongfield approximation generalized to strongfield ionization by a twocolor pulse. We verify its applicability to approximately represent the intricate interference patterns by comparison with the exact solutions of the timedependent Schr¨odinger equation and with the strongfield approximation.We show that the interference patterns can be tuned and its contrast enhanced by the additional “knob” available, the relative phase between the two frequency components. The present results confirm that twocolor ionization allows resolving interference structures originating from trajectories launched within a time interval of less than 100 as [X. Xie et al., Phys. Rev. Lett. 108, 193004 (2012)].  
Published: 20140416 

Timeresolved photoemission using attosecond streakingS. Nagele, R. Pazourek, M. Wais, G. Wachter, J. Burgdörfer 

We theoretically study timeresolved photoemission in atoms as probed by attosecond streaking. We review recent advances in the study of the photoelectric effect in the time domain and show that the experimentally accessible time shifts can be decomposed into distinct contributions that stem from the fieldfree photoionization process itself and from probefield induced corrections. We perform accurate quantummechanical as well as classical simulations of attosecond streaking for effective oneelectron systems and determine all relevant contributions to the time delay with attosecond precision. In particular, we investigate the properties and limitations of attosecond streaking for the transition from shortranged potentials (photodetachment) to longranged Coulomb potentials (photoionization). As an example for a more complex system, we study timeresolved photoionization for endohedral fullerenes A@C_{60} and discuss how streaking time shifts are modified due to the interaction of the C_{60} cage with the probing infrared streaking field.  
Published: 20140410 

Electron rescattering at metal nanotips induced by ultrashort laser pulsesG. Wachter, C. Lemell, J. Burgdörfer 

We theoretically investigate the interaction of moderate intensity nearinfrared few cycle laser pulses with nanoscale metal tips. Local eld enhancement in a nanometric region around the tip apex triggers coherent electron emission on the nanometer length and femtosecond time scale. The quantum dynamics at the surface are simulated with timedependent density functional theory (TDDFT) and interpreted based on the simple man's model. We investigate the dependence of the emitted electron spectra on the laser wavelength.  
Published: 20140410 

Time delays for attosecond streaking in photoionization of neonJ. Feist, O. Zatsarinny, S. Nagele, R. Pazourek, J. Burgdörfer, X. Guan, K. Bartschat, B.I. Schneider 

We revisit the timeresolved photoemission in neon atoms as probed by attosecond streaking. We calculate streaking time shifts for the emission of 2p and 2s electrons and compare the relative delay as measured in a recent experiment by Schultze et al. [Science 328, 1658 (2010)]. The Bspline Rmatrix method is employed to calculate accurate EisenbudWignerSmith time delays from multielectron dipole transition matrix elements for photoionization. The additional laser fieldinduced time shifts in the exit channel are obtained from separate, timedependent simulations of a full streaking process by solving the timedependent Schr¨odinger equation on the singleactiveelectron level. The resulting accurate total relative streaking time shifts between 2s and 2p emission lie well below the experimental data. We identify the presence of unresolved shakeup satellites in the experiment as a potential source of error in the determination of streaking time shifts.  
Published: 20140314 

What will it take to observe processes in real time?S.R. Leone, C.W. McCurdy, J. Burgdörfer, L.S. Cederbaum, Z. Chang, N. Dudovich, J. Feist, C.H. Greene, M. Ivanov, R. Kienberger, U. Keller, M.F. Kling, Z.H. Loh, T. Pfeifer, A.N. Pfeiffer, R. Santra, K. Schafer, A. Stolow, U. Thumm, M.J.J. Vrakking 

Even for simple systems, the interpretations of new attosecond measurements are complicated and provide only a glimpse of their potential. Nonetheless, the lasting impact will be the revelation of how shorttime dynamics can determine the electronic properties of more complex systems.  
Published: 201403 

Characterizing highn quasionedimensional strontium Rydberg atomsM. Hiller, S. Yoshida, J. Burgdörfer, S. Ye, X. Zhang, F.B. Dunning 

The production of highn, n∼300, quasionedimensional (quasi1D) strontium Rydberg atoms through twophoton excitation of selected extreme Stark states in the presence of a weak dc field is examined using a crossed laseratom beam geometry. The dipolar polarization of the electron wave function in the product states is probed using two independent techniques. The experimental data are analyzed with a classical trajectory Monte Carlo simulation employing initial ensembles that are obtained with the aid of quantum calculations based on a twoactiveelectron model. Comparisons between theory and experiment highlight different characteristics of the product quasi1D states, in particular, their large permanent dipole moments, ∼1.0 to 1.2n^{2}ea_{0}, where e is the electronic charge and a_{0} is the Bohr radius. Such states can be engineered using pulsed electric fields to create a wide variety of target states.  
Published: 20140221 Physical Review A 89, 023426 (2014) DOI: 10.1103/PhysRevA.89.023426 

Probing the influence of the Coulomb field on atomic ionization by sculpted twocolor laser fieldsX.H. Xie, S. Roither, S. Gräfe, D. Kartashov, E. Persson, C. Lemell, L. Zhang, M. S. Schöffler, A. Baltuška, J. Burgdörfer, M. Kitzler 

Interpretation of electron or photon spectra obtained with strong laser pulses that may carry attosecond dynamical and Ångström structural information about atoms or molecules usually relies on variants of the strongfield approximation (SFA) within which the influence of the Coulomb potential on the electron trajectory is neglected.We employ twocolor sculpted laser fields to experimentally tune and probe the influence of the Coulomb field on the strongfielddriven wavepacket as observed by twodimensional electron and ion momentum spectra. By comparison of measured spectra with predictions of the threedimensional timedependent Schrödinger equation as well as the quasiclassical limit of the SFA, the strongfield classical trajectory model, we are able to trace back the influence of the Coulomb field to the timing of the wavepacket release with subcycle precision.  
Published: 20130430 

Production of veryhighn strontium Rydberg atomsS. Ye, X. Zhang, T.C. Killian, F.B. Dunning, M. Hiller, S. Yoshida, S. Nagele, J. Burgdörfer 

The production of veryhighn (n∼300–500) strontium Rydberg atoms is explored using a crossedlaseratombeam geometry. n^{1}S_{0} and n^{1}D_{2} states are created by twophoton excitation via the 5s5p ^{1}P_{1} intermediate state using radiation with wavelengths of ∼461 and ∼413 nm. Rydberg atom densities as high as ∼3 × 10^{5} cm^{−3} have been achieved, sufficient that RydbergRydberg interactions can become important. The isotope shifts in the Rydberg series limits are determined by tuning the 461nm light to preferentially excite the different strontium isotopes. Photoexcitation in the presence of an applied electric field is examined. The initially quadratic Stark shift of the n^{1}P_{1} and n^{1}D_{2} states becomes nearlinear at higher fields and the possible use of n^{1}D_{2} states to create strongly polarized, quasionedimensional electronic states in strontium is discussed. The data are analyzed with the aid of a twoactiveelectron (TAE) approximation. The twoelectron Hamiltonian, within which the Sr^{2+} core is represented by a semiempirical potential, is numerically diagonalized allowing the calculation of the energies of highn Rydberg states and their photoexcitation probabilities.  
Published: 20131028 

Photoionization of helium by attosecond pulses: Extraction of spectra from correlated wave functionsL. Argenti, R. Pazourek, J. Feist, S. Nagele, M. Liertzer, E. Persson, J. Burgdörfer, E. Lindroth 

We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wave packet resulting from the integration of the timedependent Schr¨odinger equation in a finiteelement discrete variable representation basis. These techniques are projection on products of hydrogenic bound and continuum states, projection onto multichannel scattering states computed in a Bspline closecoupling basis, and a technique based on exterior complex scaling implemented in the same basis used for the time propagation. These methods allow one to monitor the population of continuum states in wave packets created with ultrashort pulses in different regimes. Applications include photo cross sections and anisotropy parameters in the spectral region of doubly excited resonances, timeresolved photoexcitation of autoionizing resonances in an attosecond pumpprobe setting, and the energy and angular distribution of correlated wave packets for twophoton double ionization.  
Published: 20130513 

Timeresolved photoemission on the attosecond scale: opportunities and challengesR. Pazourek, S. Nagele, J. Burgdörfer 

The interaction of laser pulses of subfemtosecond 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 twoelectron 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 measurementinduced time delays in a pumpprobe setting when the photoionized electronic wavepacket is probed by a modestly strong infrared streaking field. We identify distinct contributions due to initialstate polarization, Coulomblaser coupling in the final continuum state as well as finalstate interaction with the entangled residual ionic state. Extensions to multielectron systems and to the extraction of time information in the presence of decohering processes are discussed. 

Published: 20130404 

Classicalquantum correspondence in atomic ionization by midinfrared pulses: Multiple peak and interference structuresC. Lemell, J. Burgdörfer, S. Gräfe, K.I. Dimitriou, D.G. Arbo, X.M. Tong 

Atomic ionization by strong and ultrashort laser pulses with frequencies in the midinfrared spectral region have revealed novel features such as the lowenergy structures. We have performed fully threedimensional quantum dynamical as well as classical trajectory Monte Carlo simulations for pulses with wavelengths from λ = 2000 to 6000 nm. Furthermore, we apply distortedwave quantum approximations. This allows to explore the quantumclassical correspondence as well as the (non) perturbative character of the ionization dynamics driven by longwavelength pulses. We observe surprisingly rich structures in the differential energy and angular momentum distribution which sensitively depend on λ, the pulse duration τ_{p}, and the carrierenvelope phase Φ_{CEP}.  
Published: 20130122 
