We employ the R-matrix with time-dependence method to study attosecond angular streaking of F$^-$. Using this negative ion, free of long-range Coulomb interactions, we elucidate the role of short-range electron correlation effects in an attoclock scheme. Through solution of the multielectron time-dependent Schrodinger equation, we aim to bridge the gap between experiments using multielectron targets, and one-electron theoretical approaches. We observe significant negative offset angles in the photoelectron momentum distributions, despite the short-range nature of the binding potential. We show that the offset angle is sensitive to the atomic structure description of the residual F atom. We also investigate the response of co- and counter-rotating electrons, and observe an angular separation in their emission.
We present fully ab initio simulations of attosecond streaking for ionization of helium accompanied by shake-up of the second electron. This process represents a prototypical case for strongly correlated electron dynamics on the attosecond timescale. 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 qua…
In attosecond streaking, an electron is released by a short xuv pulse into a strong near infrared laser field. When the laser coupling between two states in the target is weak relative to the detuning, the streaking technique, which allows for a complete determination of the driving field, also gives an accurate measurement of the relative phase of the atomic or molecular ionization matrix elements from the two states through the interference from the two channels. The interference may change the phase of the photoelectron streaking signal within the envelope of the ir field, an effect to be a…
A new theoretical approach to the description of the attosecond streaking measurements of atomic photoionization is presented. It is a fully quantum mechanical description based on numerical solving of the time-dependent Schroedinger equation which includes the atomic field as well as the fields of the XUV and IR pulses. Also a simple semiempirical description based on sudden approximation is suggested which agrees very well with the exact solution.
We report on the first streaking measurement of water-window attosecond pulses generated via high harmonic generation, driven by sub-2-cycle, CEP-stable, 1850 nm laser pulses. Both the central photon energy and the energy bandwidth far exceed what has been demonstrated thus far, warranting the investigation of the attosecond streaking technique for the soft X-ray regime and the limits of the FROGCRAB retrieval algorithm under such conditions. We also discuss the problem of attochirp compensation and issues regarding much lower photo-ionization cross sections compared with the XUV in addition t…
We revisit the time-resolved 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 B-spline R-matrix method is employed to calculate accurate Eisenbud-Wigner-Smith time delays from multi- electron dipole transition matrix elements for photoionization. The additional laser field-induced time shifts in the exit channel are obtained from separate, time-dependent simulations of a full streaking proce…
Attosecond streaking is one of the most fundamental processes in attosecond science allowing for a mapping of temporal (i.e. phase) information on the energy domain. We show that on the single-particle level attosecond streaking time shifts contain spectral phase information associated with the Eisenbud-Wigner-Smith (EWS) time delay, provided the influence of the streaking infrared field is properly accounted for. While the streaking phase shifts for short-ranged potentials agree with the associated EWS delays, Coulomb potentials require special care. We show that the interaction between the o…
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 complex response to the photoionizing pulse establishes a 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-…
We numerically investigate attosecond streaking time delays in the photoemission of valence and 2p core electrons of aluminum surface. We find that electron emission from the core level band is delayed by $Δτ=100$ attoseconds relative to the release of electrons from the valence band. We show that this relative time offset in electron emission is caused by the screening of the streaking laser field by conduction electrons.
We theoretically study time-resolved 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 field-free photoionization process itself and from probe-field induced corrections. We perform accurate quantum-mechanical as well as classical simulations of attosecond streaking for effective one-electron systems and determine all relevant contributions to the time delay with attosecond precisio…
The present work focuses on the characterisation of the amount of orbital angular momentum (OAM) encoded in the twisted attosecond pulses via energy- and angle-resolved attosecond streaking in pump-probe setup. It is found that the photoelectron spectra generated by the linearly polarised twisted pulse with different OAM values exhibit angular modulations, whereas circularly polarised twisted pulse yields angular isotropic spectra. It is demonstrated that the energy- and angle-resolved streaking spectra are sensitive to the OAM values of the twisted pulse. Moreover, the different combinations …
Attosecond streaking of atomic photoemission holds the promise to provide unprecedented information on the release time of the photoelectron. We show that attosecond streaking phase shifts indeed contain timing (or spectral phase) information associated with the Eisenbud-Wigner-Smith time delay matrix of quantum scattering. However, this is only accessible if the influence of the streaking infrared (IR) field on the emission process is properly accounted for. The IR probe field can strongly modify the observed streaking phase shift. We show that the part of the phase shift ("time shift") due t…
We study the influence of polarization effects in streaking by combined atto- and femtosecond pulses. The polarization-induced terms alter the streaking spectrum. The normal streaking spectrum, which maps to the vector potential of the femtosecond pulse, is modified by a contribution following the field instead. We show that polarization effects may lead to an apparent temporal shift, that needs to be properly accounted for in the analysis. The effect may be isolated and studied by angle-resolved photoelectron spectroscopy from oriented polar molecules. We also show that polarization effects w…
Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry an additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences and demonstrate how it offers a novel tool to monitor non-adiabatic dynamics as it occurs in the vicinity of conical intersections and …
We present the first numerical 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 Eisenbud-Wigner-Smith time delay as a function of energy and emission angle becomes observable in the streaking time shift provided laser field-induced components are accounted for. The strongly enhanced photoemission time shifts are traced to destructive Cohen-Fano (or two-center) interferences. Signatures of these interferences in the streaking trace are shown to be enhanced when the ionic fr…
We show that time ordering underlying time-dependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of time-resolved two-photon double ionization (TPDI) of helium by an attosecond XUV pulse. The Eisenbud-Wigner-Smith time delay for the emission of a two-electron 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 dis…
Laser-assisted photoemission from a solid is considered within a numerically exactly solvable one-dimensional model of a crystal. The effect of the inelastic scattering and of the finite duration of the pump pulse on the photoelectron dynamics is elucidated. The phenomenological result that the photoexcited wave packet moves with the group velocity dE/dk and traverses on average the distance equal to the mean free path is found to hold for energies far from the spectral gaps of the final state band structure. On the contrary, close to a spectral gap the photoelectron is found to move during th…
The use of semiclassical models based on the Strong Field Approximation (SFA) is ubiquitous in strong field multi-photon ionization and underlies many key developments in attosecond science, including the description of High Harmonic Generation (HHG). However, such models are notably lacking in streaking experiments, which use an attosecond pulse to initiate single-photon ionization and a lower frequency infrared pulse to provide timing information. Here, we introduce a classical Wigner propagation (CWP) method, which analogously to semiclassical models in strong field ionization, treats the i…
Tunnelling, one of the key features of quantum mechanics, ignited an ongoing debate about the value, meaning and interpretation of 'tunnelling time'. Until recently the debate was purely theoretical, with the process considered to be instantaneous for all practical purposes. This changed with the development of ultrafast lasers and in particular, the 'attoclock' technique that is used to probe the attosecond dynamics of electrons. Although the initial attoclock measurements hinted at instantaneous tunnelling, later experiments contradicted those findings, claiming to have measured finite tunne…
We develop the two-electron attosecond streak camera under realistic conditions using a quasi-classical model. We assume extreme ultra-violet (XUV) attosecond pulses with a full width at half maximum (FWHM) of 24 attoseconds, centered at 120 eV and a streaking infrared laser field of 1600 nm, and intensity of $1.8 \times 10^{12}$ W/cm$^2$. The proposed method is shown to be capable to time resolve intra-atomic collisions in double ionization.
Through solution of the multielectron, semi-relativistic, time-dependent Schrödinger equation, we show that angular streaking produces strongly spin-polarized electrons in a noble gas. The degree of spin polarization increases with the Keldysh parameter, so that angular streaking -- ordinarily applied to investigate tunneling -- may be repurposed to generate strongly spin-polarized electron bunches. Additionally, we explore modifications of the angular streaking scheme that also enhance spin polarization.
Time-resolved electronic processes on the attosecond scale have recently become experimentally accessible through the development of laser-based pump-probe interrogation techniques such as the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. In this work, we demonstrate that by combining the concepts of the attosecond streak camera and the attoclock, time resolved processes down to the time scale of tens of zeptoseconds come into reach. Key to advancing to this remarkable level of time precision by this method term…
The magnetic-field effect of the laser pulse is investigated in laser-assisted XUV ionization. By numerically solving the three-dimensional time-dependent Schrödinger equation, we find that the photoelectron momentum distribution is distorted by the magnetic-field effect of the IR streaking field. It results in a transverse-momentum- and time-delay-dependent longitudinal photoelectron momentum shift, which is further analytically confirmed by employing the nondipole corrected strong field approximation. We also demonstrate that the magnetic field does not affect the time shift retrieved from t…
Phase retrieval from angular streaking of XUV atomic ionization
Research School of Physics, The Australian National University（澳大利亚国立大学物理研究生院）；General, Theoretical and Computer Physics, Saratov State University（萨马拉国立大学一般、理论与计算物理）；Center for Relativistic Laser Science, Institute for Basic Science (IBS)（基础科学研究院相对论激光科学中心）；Stanford PULSE Institute, SLAC National Accelerator Laboratory（斯坦福PULSE研究所，SLAC国家加速器实验室）
We generalize the one electron attosecond streaking camera to time-resolve the correlated two-electron escape dynamics during a collision process involving a deep core electron. The collision process is triggered by an XUV attosecond pulse and probed by a weak infrared field. The principle of our two-electron streak camera is that by placing the maximum of the vector potential of the probing field at the time of collision we get the maximum splitting of the inter-electronic angle of escape. We thus identify the time of collision.
Attosecond angular streaking measurements have revealed deep insights into the timing of tunnel ionization processes of atoms in intense laser fields. So far experiments of this type have been performed only with a cold-target recoil-ion momentum spectrometer (COLTRIMS). Here, we present a way to apply attosecond angular streaking experiments to a velocity map imaging spectrometer (VMIS) with few-cycle pulses at a repetition rate of 10 kHz and a high ionization yield per pulse. Three-dimensional photoelectron momentum distributions from strong-field ionization of helium with an elliptically po…
Temporally shaping the density of electron beams using light forms the basis for a wide range of established and emerging technologies, including free-electron lasers and attosecond electron microscopy. The modulation depth of compressed electron pulses is a key figure of merit limiting applications. In this work, we present an approach for generating background-free attosecond electron pulse trains by sequential inelastic electron-light scattering. Harnessing quantum interference in the fractional Talbot effect, we suppress unwanted background density in electron compression by several orders…
Measured photoionization time delays may exhibit large variations as a function of the emission angles, even for spherically symmetric targets, as shown in recent RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) experiments. The contributions from different pathways to the two-photon quantum channels can already explain the observed phase jumps that shape those angular distributions. Here, we propose a simple analytical model to describe angularly-resolved RABBITT spectra as a function of the relative polarization angle between the ionizing attosecond pu…
We investigate two-photon double ionization of helium by intense ($10^{15} W/cm^2$) ultrashort ($\approx 300$ as) soft X-ray pulses (E = 91.6 eV). The time-dependent two-electron Schrödinger equation is solved using a coupled channel method. We show that for ultrashort pulses the angular distribution of ejected electrons depends on the pulse duration and provides novel insights into the role of electron correlations in the two-electron photoemission process. The angular distribution at energies near the ``independent electron'' peaks is close to dipolar while it acquires in the ``valley'' of c…
We develop a novel technique for modeling of atomic and molecular ionization in superposition of XUV and IR fields with characteristics typical for attosecond streaking and RABBITT experiments. The method is based on solving the time-dependent Schrödinger equation in the coordinate frame expanding along with the photoelectron wave packet. The efficiency of the method is demonstrated by calculating angular anisotropy of photoemission time delay of the H$_2^+$ ion in a field configuration of recent RABBITT experiments.
We present a theory of time-resolved photoionisation in the presence of a vortex beam. In a pump-probe setup, an extreme ultraviolet or an x-ray pump pulse triggers ionization, which is probed by a synchronized infrared pulse with non-zero orbital angular momentum. We show, how this property of the probe pulse affects the electron dynamics upon ionization, in a way that is independent of the initial and final angular momentum states of the ionizing system.
For a circularly polarized single-color field at a central frequency of $2ω$ the final electron momentum distribution upon strong field ionization does not carry any information about the phase of the initial momentum distribution. Adding a weak, co-rotating, circularly polarized field at a central frequency of $ω$ gives rise to a sub-cycle interference pattern (holographic angular streaking of electrons (HASE)). This interference pattern allows for the retrieval of the derivative of the phase of the initial momentum distribution after tunneling $ϕ^{\prime}_{\mathrm{off}}(p_i)$. A trajectory-b…
Attosecond angular streaking, also known as the "attoclock", employs a short elliptically polarized laser pulse to tunnel ionize an electron from an atom or a molecule and to put a time stamp on this process by deflecting the photoelectron in the angular spatial direction. This deflection can be used to evaluate the time the tunneling electron spends under the classically inaccessible barrier and to determine whether this time is finite. In this review, we examine the latest experimental and theoretical findings and present a comprehensive set of evidence supporting the zero tunneling time sce…
Ultrashort electron pulses are crucial for time-resolved electron diffraction and microscopy of fundamental light-matter interaction. In this work, we study experimentally and theoretically the generation and characterization of attosecond electron pulses by optical-field-driven compression and streaking at dielectric or absorbing interaction elements. The achievable acceleration and deflection gradient depends on the laser-electron angle, the laser's electric and magnetic field directions and the foil orientation. Electric and magnetic fields have similar contributions to the final effect and…
We study the temporal aspects of laser-assisted extreme ultraviolet (XUV) photoionization using attosecond pulses of harmonic radiation. The aim of this paper is to establish the general form of the phase of the relevant transition amplitudes and to make the connection with the time-delays that have been recently measured in experiments. We find that the overall phase contains two distinct types of contributions: one is expressed in terms of the phase-shifts of the photoelectron continuum wavefunction while the other is linked to continuum--continuum transitions induced by the infrared (IR) la…
Coherent, broadband pulses of extreme ultraviolet (XUV) light provide a new and exciting tool for exploring attosecond electron dynamics. Using photoelectron streaking, interferometric spectrograms can be generated that contain a wealth of information about the phase properties of the photoionization process. If properly retrieved, this phase information reveals attosecond dynamics during photoelectron emission such as multielectron dynamics and resonance processes. However, until now, the full retrieval of the continuous electron wavepacket phase from isolated attosecond pulses has remained c…
In a seminal article, Fano predicts that absorption of light occurs preferably with increase of angular momentum. Here we generalize Fano's propensity rule to laser-assisted photoionization, consisting of absorption of an extreme-ultraviolet photon followed by absorption or emission of an infrared photon. The predicted asymmetry between absorption and emission leads to incomplete quantum interference in attosecond photoelectron interferometry. It explains both the angular-dependence of the photoionization time delays and the delay-dependence of the photoelectron angular distributions. Our theo…
Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach due to the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we achieve full decoding of the intricate angle-dependent dynamics of a photoemission process in helium, spectrally and anisotropically structured by twophoton transitions through intermediate bound states. Using spectrally- and angularly-resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude towards the photo…
Extracting single photoionization time delays associated with atomic (or molecular) species from attosecond time scale two-photon experiments usually relies on the theoretical description of continuum-continuum transitions. The available models for those processes predict a universal phase contribution, independent of the angular quantum numbers of final states. However, a recent experimental-theoretical study [Fuchs, \emph{et al.} Optica 7, 154 (2020)] determined a sizable time delay dependence on the angular momentum of near-threshold photoelectrons. In this study, we present an analytical m…
Tunnelling lies at the heart of quantum mechanics and is a fundamental process in attosecond science, molecular biology, and quantum devices. Whether tunnelling takes time and how a microscopic particle transits through a barrier have been debated since the early days of quantum mechanics. The time required for an electron to tunnel through an atomic potential barrier has been measured with attosecond angular streaking (attoclock), and a recent work on the hydrogen atom claimed that electron tunnelling is instantaneous. However, the time required for Rb atoms to tunnel through an optical poten…
Numerical attoclock is a theoretical model of attosecond angular streaking driven by a very short, nearly a single oscillation, circularly polarized laser pulse. The reading of such an attoclock is readily obtained from a numerical solution of the time-dependent Schrödinger equation as well as a semi-classical trajectory simulation. By making comparison of the two approaches, we highlight the essential physics behind the attoclock measurements. In addition, we analyze the predictions of the Keldysh-Rutherford model of the attoclock [Phys. Rev. Lett. 121, 123201 (2018)]. In molecular hydrogen, …
Quantum coherence plays a fundamental role in the study and control of ultrafast dynamics in matter. In the case of photoionization, entanglement of the photoelectron with the ion is a well known source of decoherence when only one of the particles is measured. Here we investigate decoherence due to entanglement of the radial and angular degrees of freedom of the photoelectron. We study two-photon ionization via the 2s2p autoionizing state in He using high spectral resolution photoelectron interferometry. Combining experiment and theory, we show that the strong dipole coupling of the 2s2p and …
We investigate the possibility to monitor the dynamics of autoionizing states in real time and control the yields of different ionization channels in helium by simulating XUV-pump IR-probe experiments focused on the N=2 threshold. The XUV pulse creates a coherent superposition of doubly excited states which is found to decay by ejecting electrons in bursts. Prominent interference fringes in the photoelectron angular distribution of the $2s$ and $2p$ ionization channels are observed, along with sizable out-of-phase quantum beats in the yields of the corresponding parent ions.
Attosecond pulses in the soft-X-ray (SXR) to water-window energy region offer the tools for creating and studying target specific localized inner-shell electrons or holes in materials, enable monitoring or controlling charge and energy flows in a dynamic system on attosecond timescales. Recently, a number of laboratories have reported generation of continuum harmonics in the hundred-electron-volt to kilovolt region with few-cycle long-wavelength mid-infrared lasers. These harmonics have the bandwidth to support pulses with duration of few- to few-ten attoseconds. But harmonics generated in a g…
Photoionization from energetically distinct electronic states may have a relative time delay of tens of attoseconds. Here we demonstrate that pulses of optical vortices allow measuring such attoseconds delays from magnetic sublevels, even from a spherically symmetric target. The difference in the time delay is substantial and exhibits a strong angular dependence. Furthermore, we find an atomic scale variation in the time delays depending on the target orbital position in the laser spot. The findings offer thus a qualitatively new way for a spatio-temporal sensing of the magnetic states from wh…
Ionization by relativistically intense short laser pulses is studied in the framework of strong-field quantum electrodynamics. Distinctive patterns are found in the energy probability distributions of photoelectrons. Except of the already observed patterns, which were studied in Phys. Rev. A {\bf 94}, 013402 (2016), we discover an additional interference-free smooth supercontinuum in the high-energy portion of the spectrum, reaching tens of kiloelectronovolts. As we show, the latter is sensitive to the driving field intensity and it can be detected in a narrow polar-angular window. Once these …
