Time resolved Fano resonances

Understanding attosecond streaking

This tutorial provides an overview on the theory of attosecond streaking, a pump-probe scheme to extract timing information of ionization processes that has been widely used in the past decade. Emphasis is put on the origin of the Coulomb-laser-coupling (CLC) term, which is crucial in the interpretation of streaking delays. Having gained a proper understanding of how the CLC terms in various publications relate to each other, we will be able to analyze in which regime the streaking delay can be split into a measurement-induced CLC term and a 'pure' ionization delay and under which conditions this splitting may break down. Thus we address the long-standing question of the validity of the widely applied interpretation of the streaking delay as a sum of the CLC term and a 'pure' ionization delay.

Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics

Since the first demonstration of the generation of attosecond pulses (1 as = 10^-18s) in the extreme-ultraviolet spectral region, several measurement techniques have been introduced, at the beginning for the temporal characterization of the pulses, and immediately after for the investigation of electronic and nuclear ultrafast dynamics in atoms, molecules and solids with unprecedented temporal resolution. The attosecond spectroscopic tools established in the last two decades, together with the development of sophisticated theoretical methods for the interpretation of the experimental outcomes, allowed to unravel and investigate physical processes never observed before, such as the delay in photoemission from atoms and solids, the motion of electrons in molecules after prompt ionization which precede any notable nuclear motion, the temporal evolution of the tunneling process in dielectrics, and many others. This review focused on applications of attosecond techniques to the investigation of ultrafast processes in atoms, molecules and solids. Thanks to the introduction and ongoing developments of new spectroscopic techniques, the attosecond science is rapidly moving towards the investigation, understanding and control of coupled electron-nuclear dynamics in increasingly complex systems, with ever more accurate and complete investigation techniques. Here we will review the most common techniques presenting the latest results in atoms, molecules and solids.

Attosecond coherent electron motion in Auger-Meitner decay

In quantum systems, coherent superpositions of electronic states evolve on ultrafast time scales (few femtoseconds to attoseconds; 1 attosecond = 0.001 femtoseconds = 10^-18 seconds), leading to a time-dependent charge density. Here we performed time-resolved measurements using attosecond soft x-ray pulses produced by a free-electron laser, to track the evolution of a coherent core-hole excitation in nitric oxide. Using an additional circularly polarized infrared laser pulse, we created a clock to time-resolve the electron dynamics and demonstrated control of the coherent electron motion by tuning the photon energy of the x-ray pulse. Core-excited states offer a fundamental test bed for studying coherent electron dynamics in highly excited and strongly correlated matter.

Reconstruction of atomic resonances with attosecond streaking

Recent development of spectroscopic techniques based on attosecond radiation has given the community the right tools to study the timing of the photoelectron process. In this work we investigate the effect of Fano resonances in attosecond streaking spectrograms and the application of standard phase-reconstruction algorithms. We show that while the existence of the infrared coupling (ac-Stark shift) hinders the applicability of FROG-like methods, under certain conditions it is still possible to use standard reconstruction algorithms to retrieve the photoemission delay of the bare resonance. Finally, we propose two strategies to study the strength of IR coupling using the attosecond streaking technique.

Revealing Molecular Strong Field Autoionization Dynamics

The novel strong field autoionization (SFAI) dynamics is identified and investigated by channel-resolved angular streaking measurements of two electrons and two ions for the double-ionized CO. Comparing with the laser-assisted autoionization calculations, we demonstrate the electrons from SFAI are generated from the field-induced decay of the autoionizing state with a following acceleration in the laser fields. The energy-dependent photoelectron angular distributions further reveal that the subcycle ac-Stark effect modulates the lifetime of the autoionizing state and controls the emission of SFAI electrons in molecular frame. Our results pave the way to control the emission of resonant high-harmonic generation and trace the electron-electron correlation and electron-nuclear coupling by strong laser fields. The lifetime modulation of quantum systems in the strong laser field has great potential for quantum manipulation of chemical reactions and beyond.

Low-energy photoelectron interference structure in attosecond streaking

By numerically solving the time-dependent Schrödinger equation, we theoretically investigate the dynamics of the low-energy photoelectrons ionized by a single attosecond pulse in the presence of an infrared laser field. The obtained photoelectron momentum distributions exhibit complicated interference structures. With the semiclassical model, the originations for the different types of the interference structures are unambiguously identified. Moreover, by changing the time delay between the attosecond pulse and the infrared laser field, these interferences could be selectively enhanced or suppressed. This enables us to extract information about the ionization dynamics encoded in the interference structures. As an example, we show that the phase of the electron wave-packets ionized by the linearly and circularly polarized attosecond pulses can be extracted from the interference structures of the direct and the near-forward rescattering electrons.

Strong-Field Extreme-Ultraviolet Dressing of Atomic Double Excitation

We report on the experimental observation of a strong-field dressing of an autoionizing two-electron state in helium with intense extreme-ultraviolet laser pulses from a free-electron laser. The asymmetric Fano line shape of this transition is spectrally resolved, and we observe modifications of the resonance asymmetry structure for increasing free-electron-laser pulse energy on the order of few tens of Microjoules. A quantum-mechanical calculation of the time-dependent dipole response of this autoionizing state, driven by classical extreme-ultraviolet (XUV) electric fields, evidences strong-field-induced energy and phase shifts of the doubly excited state, which are extracted from the Fano line-shape asymmetry. The experimental results obtained at the Free-Electron Laser in Hamburg (FLASH) thus correspond to transient energy shifts on the order of a few meV, induced by strong XUV fields. These results open up a new way of performing nonperturbative XUV nonlinear optics for the light-matter interaction of resonant electronic transitions in atoms at short wavelengths.

Analytical Theory of Attosecond Transient Absorption Spectroscopy of Perturbatively Dressed Systems

A theoretical description of attosecond transient absorption spectroscopy for temporally and spatially overlapping XUV and optical pulses is developed, explaining the signals one can obtain in such an experiment. To this end, we employ a two-stage approach based on perturbation theory, which allows us to give an analytical expression for the transient absorption signal. We focus on the situation in which the attosecond XUV pulse is used to create a coherent superposition of electronic states. As we explain, the resulting dynamics can be detected in the spectrum of the transmitted XUV pulse by manipulating the electronic wave packet using a carrier-envelope-phase-stabilized optical dressing pulse. In addition to coherent electron dynamics triggered by the attosecond pulse, the transmitted XUV spectrum encodes information on electronic states made accessible by the optical dressing pulse. We illustrate these concepts through calculations performed for a few-level model.

Coupled nuclear-electronic dynamics in photoionization of H2

In this study we investigate the dissociative photoionization of molecular hydrogen H2, addressing the influence of autoionizing states and nuclear motion on the photoelectron dynamics. Experimental results are compared with ab initio calculations.

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.

Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron

The dynamics of quantum systems are encoded in the amplitude and phase of wave packets. However, the rapidity of electron dynamics on the attosecond scale has precluded the complete characterization of electron wave packets in the time domain. Using spectrally resolved electron interferometry, we were able to measure the amplitude and phase of a photoelectron wave packet created through a Fano autoionizing resonance in helium. In our setup, replicas obtained by two-photon transitions interfere with reference wave packets that are formed through smooth continua, allowing the full temporal reconstruction, purely from experimental data, of the resonant wave packet released in the continuum. In turn, this resolves the buildup of the autoionizing resonance on an attosecond time scale. Our results, in excellent agreement with ab initio time-dependent calculations, raise prospects for detailed investigations of ultrafast photoemission dynamics governed by electron correlation, as well as coherent control over structured electron wave packets.

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.

Dynamical Fano-Like Interference between Rabi Oscillations and Coherent Phonons in a Semiconductor Microcavity System

We report on dynamical interference between short-lived Rabi oscillations and long-lived coherent phonons in CuCl semiconductor microcavities resulting from the coupling between the two oscillations. The Fourier-transformed spectra of the time-domain signals obtained from semiconductor microcavities by using a pump-probe technique show that the intensity of the coherent longitudinal optical phonon of CuCl is enhanced by increasing that of the Rabi oscillation, which indicates that the coherent phonon is driven by the Rabi oscillation through the Fröhlich interaction. Moreover, as the Rabi oscillation frequency decreases upon crossing the phonon frequency, the spectral profile of the coherent phonon changes from a peak to a dip with an asymmetric structure. The continuous wavelet transformation reveals that these peak and dip structures originate from constructive and destructive interference between Rabi oscillations and coherent phonons, respectively. We demonstrate that the asymmetric spectral structures in relation to the frequency detuning are well reproduced by using a classical coupled oscillator model on the basis of dynamical Fano-like interference.

Fano resonance in anodic aluminum oxide based photonic crystals

Anodic aluminum oxide based photonic crystals with periodic porous structure have been prepared using voltage compensation method. The as-prepared sample showed an ultra-narrow photonic bandgap. Asymmetric line-shape profiles of the photonic bandgaps have been observed, which is attributed to Fano resonance between the photonic bandgap state of photonic crystal and continuum scattering state of porous structure. And the exhibited Fano resonance shows more clearly when the sample is saturated ethanol gas than air-filled. Further theoretical analysis by transfer matrix method verified these results. These findings provide a better understanding on the nature of photonic bandgaps of photonic crystals made up of porous materials, in which the porous structures not only exist as layers of effective-refractive-index material providing Bragg scattering, but also provide a continuum light scattering state to interact with Bragg scattering state to show an asymmetric line-shape profile.

Time-dependent resonant scattering: an analytical approach

A time-dependent description is given of a scattering process involving a single resonance embedded in a set of flat continua. An analytical approach is presented which starts from an incident free particle wave packet and yields the Breit-Wigner cross-section formula at infinite times. We show that at intermediate times the so-called Wigner-Weisskopf approximation is equivalent to a scattering process involving a contact potential. Applications in cold-atom scattering and resonance enhanced desorption of molecules are discussed.

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.

Real-time observation of interference between atomic one-electron and two-electron excitations

We present results of real-time tracking of atomic two-electron dynamics in an autoionizing transient wave packet in krypton. A coherent superposition of two Fano resonances is excited with a femtosecond extreme-ultraviolet pulse. The evolution of the corresponding wave packet is subsequently probed with a delayed infrared pulse. In our specific case, we get access to the interference between one- and two-electron excitation channels in the launched wave packet, which is superimposed on its decay through autoionization. A simple model is able to account for the observed dynamical evolution of this wave packet.

Photoelectron angular distributions from autoionizing 4s¹4p⁶6p¹ states in atomic krypton probed with femtosecond time resolution

Photoelectron angular distributions (PADs) are obtained for a pair of 4s(1)4p(6)6p(1) (a singlet and a triplet) autoionizing states in atomic krypton. A high-order harmonic pulse is used to excite the pair of states and a time-delayed 801 nm ionization pulse probes the PADs to the final 4s(1)4p(6) continuum with femtosecond time resolution. The ejected electrons are detected with velocity map imaging to retrieve the time-resolved photoelectron spectrum and PADs. The PAD for the triplet state is inherently separable by virtue of its longer autoionization lifetime. Measuring the total signal over time allows for the PADs to be extracted for both the singlet state and the triplet state. Anisotropy parameters for the triplet state are measured to be β(2)=0.55 ± 0.17 and β(4)=-0.01 ± 0.10, while the singlet state yields β(2)=2.19 ± 0.18 and β(4)=1.84 ± 0.14. For the singlet state, the ratio of radial transition dipole matrix elements, X, of outgoing S to D partial waves and total phase shift difference between these waves, Δ, are determined to be X=0.56 ± 0.08 and Δ=2.19 ± 0.11 rad. The continuum quantum defect difference between the S and D electron partial waves is determined to be -0.15 ± 0.03 for the singlet state. Based on previous analyses, the triplet state is expected to have anisotropy parameters independent of electron kinetic energy and equal to β(2)=5∕7 and β(4)=-12∕7. Deviations from the predicted values are thought to be a result of state mixing by spin-orbit and configuration interactions in the intermediate and final states; theoretical calculations are required to quantify these effects.

Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic pentamers

Arrays of plasmonic pentamers consisting of five metallic nano-disks were designed and fabricated to achieve a pronounced Fano Resonance with polarization-independent far-field spectral response at normal incidence due to the structure symmetry of pentamers. A mass-spring coupled oscillator model was applied to study plasmon interactions among the nano-disks. It was found that the direction of the excitation light polarization can flexibly tune the spatial localization of near-field energy at sub-wavelength scales while the collective optical properties are kept constant. It can lead to a selective storage of excited energy down to sub-20 nm gap at a normal incident with a single light source.

Monitoring and controlling the electron dynamics in helium with isolated attosecond pulses

Helium atoms in the presence of extreme ultraviolet light pulses can lose electrons through direct photoionization or through two-electron excitation followed by autoionization. Here we demonstrate that, by combining attosecond extreme ultraviolet pulses with near infrared femtosecond lasers, electron dynamics in helium autoionization can be not only monitored but also controlled. Furthermore, the interference between the two ionization channels was modified by the intense near infrared laser pulse. To the best of our knowledge, this is the first time that double excitation and autoionization were studied experimentally by using isolated attosecond pulses.

Attosecond time-resolved autoionization of argon

Autoionization of argon atoms was studied experimentally by transient absorption spectroscopy with isolated attosecond pulses. The peak position, intensity, linewidth, and shape of the 3s3p⁶np ¹P Fano resonance series (26.6-29.2 eV) were modified by intense few-cycle near infrared laser pulses, while the delay between the attosecond pulse and the laser pulse was changed by a few femtoseconds. Numerical simulations revealed that the experimentally observed splitting of the 3s3p⁶4p ¹P line is caused by the coupling between two short-lived highly excited states in the strong laser field.

Attosecond streaking enables the measurement of quantum phase

Attosecond streaking, as a measurement technique, was originally conceived as a means to characterize attosecond light pulses, which is a good approximation if the relevant transition matrix elements are approximately constant within the bandwidth of the light pulse. Our analysis of attosecond streaking measurements on systems with a complex response to the photoionizing pulse reveals the relation between the momentum-space wave function of the outgoing electron and the result of conventional retrieval algorithms. This finding enables the measurement of the quantum phase associated with bound-continuum transitions.

The robustness of attosecond streaking measurements

We investigate attosecond streaking measurements, where a spectrogram is described by an ensemble of electron wave packets. Such a description may be required for processes more complex than direct photoemission from an isolated atom; an ensemble of wave packets may also be needed to describe the role of shot-to-shot fluctuations or a non-uniform spatio-temporal profile of attosecond light pulses. Under these conditions, we examine the performance of conventional (FROG) analysis of attosecond streaking measurements.

Optical detection of interfering pathways in subfemtosecond multielectron dynamics

We show how time-resolved coherent anti-Stokes Raman scattering can be used to identify interfering pathways in the relaxation dynamics of autoionizing transients in many-electron systems, on femto- and attosecond time scales. For coherent population of many states, autoionizing wave-packet dynamics is resolved. We identify bound-bound, continuum-bound, and bound-continuum-bound contributions and show that they leave distinct features in the total coherent anti-Stokes Raman scattering signal.

Application of Coulomb wave function discrete variable representation to atomic systems in strong laser fields

We present an efficient and accurate grid method for solving the time-dependent Schrodinger equation for an atomic system interacting with an intense laser pulse. Instead of the usual finite difference (FD) method, the radial coordinate is discretized using the discrete variable representation (DVR) constructed from Coulomb wave functions. For an accurate description of the ionization dynamics of atomic systems, the Coulomb wave function discrete variable representation (CWDVR) method needs three to ten times fewer grid points than the FD method. The resultant grid points of the CWDVR are distributed unevenly so that one has a finer grid near the origin and a coarser one at larger distances. The other important advantage of the CWDVR method is that it treats the Coulomb singularity accurately and gives a good representation of continuum wave functions. The time propagation of the wave function is implemented using the well-known Arnoldi method. As examples, the present method is applied to multiphoton ionization of both the H atom and the H(-) ion in intense laser fields. The short-time excitation and ionization dynamics of H by an abruptly introduced static electric field is also investigated. For a wide range of field parameters, ionization rates calculated using the present method are in excellent agreement with those from other accurate theoretical calculations.

Ultrafast Fano resonance between optical phonons and electron-hole pairs at the onset of quasiparticle generation in a semiconductor

Based on the many-body time-dependent approach applied to the ultrafast time region, we investigate the dynamics of creation of an optical phonon incorporating with the electron-hole continuum in a semiconductor. In the transient Fano resonance, due to an interference between those sharp (optical phonon) and continuum (electron-hole pair) quasiparticles, we find the robust destructive interference at birth of them, i.e., tau approximately 0 if the created phonon is coherent under the irradiation of ultrashort optical pulses. The origin is found to be the potential scattering of the electron-hole pair by the q=0 coherent phonon. This finding agrees well with the recent experiment.