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）
Anatoli S. Kheifets, Rickson Wielian, Igor A. Ivanov, Anna Li Wang, Agostino Marinelli, James P. Cryan
We demonstrate an accurate phase retrieval of XUV atomic ionization by streaking the photoelectron in a circularly polarized IR laser field. The streaking phase can then be converted to the atomic time delay containing the Wigner and continuum-continuum components. Our demonstration is based on a numerical solution of the time-dependent Schrödinger equation. We test this technique using the hydrogen atom ionized by an isolated attosecond XUV pulse across a wide range of photon energies. In parallel, we run a series of RABBITT simulations and demonstrate equivalence of the phase and timing information provided by the two methods. This validates the proposed technique and makes it a useful tool that can be applied to a broad range of atomic and molecular targets exposed to XUV radiation from novel free-electron laser sources.
We apply a recently proposed theoretical concept and numerical approach to obtain time delays in extreme ultraviolet (XUV) photoionization of an electron in a short- or long-range potential. The results of our numerical simulations on a space-time grid are compared to those for the well-known Wigner-Smith time delay and different methods to obtain the latter time delay are reviewed. We further use our numerical method to analyze the effect of a near-infrared streaking field on the time delay obtained in the numerical simulations.
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…
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.
Double ionization in intense laser fields can comprise electron correlations, which manifest in the non-independent emission of two electrons from an atom or molecule. However, experimental methods that directly access the electron emission times have been scarce. Here, we explore the application of an all-optical streaking technique to strong-field double ionization both theoretically and experimentally. We show that both sequential and non-sequential double ionization processes lead to streaking delays that are distinct from each other and single ionization. Moreover, coincidence detection o…
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…
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 study strong-field atomic ionization driven by an XUV pulse with a non\-zero displacement, the quantity defined as the integral of the pulse vector potential taken over the pulse duration. We demonstrate that the use of such pulses may lead to an extreme sensitivity of the ionization process to subtle changes of the parameters of a driving XUV pulse, in particular, the ramp-on/off profile and the carrier envelope phase. We illustrate this sensitivity for atomic hydrogen and lithium driven by few-femto\-second XUV pulses with intensity in the $\rm 10^{14}~W/cm^2$ range. We argue that the obs…
We investigate the laser-assisted single XUV photon double ionization of ground state helium. By solving full six-dimensional time-dependent schr{ö}dinger equation, we study the correlation and angular distribution. The discussion in joint energy and angular distributions reveals the competition in odd and even parity double ionization processes in the presence of weak laser field. The emission angle between two photoelectrons can be adjusted by the laser parameters. We depicts how the laser field enhance and/or enable the back-to-back and side-by-side emission of double ionization.
Ionization with ultrashort pulses in the extreme ultraviolet (XUV) regime can be used to prepare an ion in a superposition of spin--orbit substates. In this work, we study the coherence properties of such a superposition, created by ionizing xenon atoms using two phase-locked XUV pulses at different frequencies. In general, if the duration of the driving pulse exceeds the quantum beat period, dephasing will occur. If however, the frequency difference of the two pulses matches the spin--orbit splitting, the coherence can be efficiently increased and dephasing does not occur.
We explore the influence of elliptical polarization on the (non)sequential two-photon double ionization of atomic helium with ultrashort extreme ultraviolet (XUV) light fields using time-dependent full ab-initio simulations. The energy and angular distributions of photoelectrons are found to be strongly dependent on the ellipticity. The correlation minimum in the joint angular distribution becomes more prominently visible with increasing ellipticity. In a pump-probe sequence of two subsequent XUV pulses with varying ellipticities, polarization tagging allows to discriminate between sequential …
Based on the frequency-domain theory, we investigate the above-threshold ionization (ATI) process of an atom in a two-color laser field with infrared (IR) and extreme ultraviolet (XUV) frequencies, where the photon energy of the XUV laser is close to or larger than the atomic ionization threshold. By using the channel analysis, we find that the two laser fields play different roles in an ionization process, where the XUV laser determines the ionization probability by the photon number that the atom absorbs from it, while the IR laser accelerates the ionized electron and hence widens the electr…
The collision-ionization mechanism of nonsequential double ionization (NSDI) process in IR+XUV two-color laser fields [\PRA \textbf{93}, 043417 (2016)] has been investigated by us recently. Here we extend this work to study the collision-excitation-ionization (CEI) mechanism of NSDI processes in the two-color laser fields with different laser conditions. It is found that the CEI mechanism makes a dominant contribution to the NSDI as the XUV photon energy is smaller than the ionization threshold of the He$^+$ ion, and the momentum spectrum shows complex interference patterns and symmetrical str…
Two XUV-photon double ionization of Ne, induced by an intense few-pulse attosecond train with a ~ 4 fs envelope duration is investigated experimentally and theoretically. The experiment is performed at ELI-ALPS utilizing the recently constructed 10 Hz gas phase high-order harmonic generation SYLOS GHHG-COMPACT beamline. A total pulse energy up to ~1 μJ generated in Argon in conjunction with high reflectivity optics in the XUV region, allowed the observation of the doubly charged state of Ne induced by 40 eV central XUV photon energies. The interaction of the intense attosecond pulse train with…
The direct above-threshold ionization (ATI) of diatomic molecules in linearly-polarized infrared and extreme ultraviolet (IR+XUV) laser fields is investigated by the frequency-domain theory based on the nonperturbative quantum electrodynamics. The destructive interference fringes on the angle-resolved ATI spectra, which are closely related to the molecular structure, can be well fitted by a simple predictive formula for any alignment of the molecular axis. By comparing the direct ATI spectra for monochromatic and two-color laser fields, we found that the XUV laser field can both raise the ioni…
We report the observation of multiple ionization of Argon through multi-XUV-photon absorption induced by an unprecedentedly powerful laser driven high-harmonic-generation source. Comparing the measured intensity dependence of the yield of the different Argon charge states with numerical calculations we can infer the different channels -direct and sequential- underlying the interaction. While such studies were feasible so far only with FEL sources, this work connects highly-non-linear-XUV-processes with the ultra-short time scales, inherent to the harmonic pulses, and highlights the advanced pe…
We present an {\it ab initio} and non-perturbative time-dependent approach to the problem of double ionization of a general atom driven by intense XUV laser pulses. After using a highly flexible $B$-Spline $R$-matrix method to generate field-free Hamiltonian and electric dipole matrices, the initial state is propagated in time using an efficient Arnoldi-Lanczos scheme. Test calculations for double ionization of He by a single laser pulse yield good agreement with benchmark results obtained with other methods. The method is then applied to two-color pump-probe processes, for which momentum and …
In anticipation of upcoming two-photon double ionization of atoms and particularly Helium, under strong short wavelength radiation sources (45 eV), we present quantitative signatures of direct two-photon double ejection, in the photoelectron spectrum (PES) and the peak power dependence, that can be employed in the interpretation of related data. We show that the PES provides the cleanest signature of the process. An inflection (knee) in the laser power dependence of double ionization is also discernible, within a window of intensities which depends on the pulse duration and cross sections
We consider the ionization of neon induced by a femtosecond laser pulse composed of overlapping, linearly polarized bichromatic extreme ultraviolet and infrared fields. In particular, we study the effects of the infrared light on a two-pathway ionization scheme for which Ne 2s22p53s1P is used as intermediate state. Using time-dependent calculations, supported by a theoretical approach based on the strong-field approximation, we analyze the ionization probability and the photoelectron angular distributions associated with the different sidebands of the ionization spectrum. Complex oscillations …
We present a theoretical study of atomic laser-assisted photoionization emission (LAPE). We consider an atom driven by a linearly polarized XUV laser in two different scenarios: i) a single attosecond pulse (in both the streaking and sideband regimes) and ii) an attosecond pulse train. The process takes place assisted by a linearly polarized infrared (IR) laser field. In all these cases the energy and angle-resolved photoelectron spectrum (PES) is determined by a leading contribution, related to the intracycle factor [Gramajo et al., J. Phys. B 51, 055603 (2018)], complemented by other ones, d…
We analyze the photoelectron angular distribution in two-pathway interference between non\-resonant one-photon and resonant two-photon ionization of neon. We consider a bichromatic femtosecond XUV pulse whose fundamental frequency is tuned near the $2p^5 3s$ atomic states of neon. The time-dependent Schrödinger equation is solved and the results are employed to compute the angular distribution and the associated anisotropy parameters at the main photoelectron line. We also employ a time-dependent perturbative approach, which allows obtaining information on the process for a large range of puls…
We present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultra violet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time dependent Dirac equation and compare its predictions with those of the corresponding non-relativistic Schr{ö}dinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduces a finite yet small decrease i…
High-order above-threshold ionization (HATI) spectrum in IR+XUV two-color laser fields has been investigated. We found that the quantum features corresponding to the absorption of the XUV photon is well illustrated by a peculiar dip structure in the second plateau of the HATI spectrum. By the channel analysis, we show that the angular distribution of the spectrum is attributed to the coherent summation over contributions of different channels, and the dip structure in the spectrum is directly related to the absorption of one XUV photon of the ionized electron during the laser-assisted collisio…
We provide a detailed quantitative study of the possible role of a small admixture of harmonics on resonant two-photon ionization. The motivation comes from the occasional presence of 2nd and 3rd harmonics in FEL radiation. We obtain the dependence of ionic yields on the intensity of the fundamental, the percentage of 2nd harmonic and the detuning of the fundamental from resonance. Having examined the cases of one and two intermediate resonances, we arrive at results of general validity and global behavior, showing that even a small amount of harmonic may seem deceptively innocuous.
We study the ionization of atomic hydrogen in the direction of polarization due to a linearly polarized XUV pulse in the presence a strong field IR. We describe the photoelectron spectra as an interference problem in the time domain. Electron trajectories steming from different optical laser cycles give rise to intercycle interference energy peaks known as sidebands. These sidebands are modulated by a grosser structure coming from the intracycle interference of the two electron trajectories born during the same optical cycle. We make use of a simple semiclassical model which offers the possibi…
We analyze the time delay between emission of photoelectrons from the outer valence $ns$ and $np$ sub-shells in noble gas atoms following absorption of an attosecond XUV pulse. By solving the time dependent Schrödinger equation and carefully examining the time evolution of the photoelectron wave packet, we establish the apparent "time zero" when the photoelectron leaves the atom. Various processes such as elastic scattering of the photoelectron on the parent ion and many-electron correlation affect the quantum phase of the dipole transition matrix element, the energy dependence of which define…
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 use a Wigner distribution-like function based on the strong field approximation theory to obtain the time-energy distributions and the ionization time distributions of electrons ionized by an XUV pulse alone and in the presence of an infrared (IR) pulse. In the case of a single XUV pulse, although the overall shape of the ionization time distribution resembles the XUV-envelope, its detail shows dependence on the emission direction of the electron and the carrier-envelope phase of the pulse, which mainly results from the low-energy interference structure. It is further found that the electro…
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…
A unitary model describing the electronic transitions in an atom subject to a strong high frequency laser pulse is proposed. The model fully accounts for the initial state coupling with the continuum spectrum. Continuum-continuum as well as discrete-discrete transitions are neglected. The model leads to a single integro-differential equation for the initial state amplitude. Exact numerical and approximate closed semi-analytical solutions of this equation are obtained. A comparison of present results with full time dependent Schrödinger equation solution for Hydrogen atoms subject to a laser pu…
We study the breakup of $\text{H}_2^+$ exposed to super-intense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict contro…
We present a theoretical study of ionization of the hydrogen atom due to an XUV pulse in the presence of an IR laser with both fields linearly polarized in the same direction. In particular, we study the energy distribution of photoelectrons emitted perpendicularly to the polarization direction. By means of a very simple semiclassical model which considers electron trajectories born at different ionization times, the electron energy spectrum can be interpreted as the interplay of Intra and Intercycle interferences. The intracycle interference pattern stems from the coherent superposition of fo…
The development of ultra-short intense laser sources in the visible and extreme ultraviolet (XUV) spectral range led to fascinating studies in laser-matter interactions and attosecond science. In the majority of these studies the system under investigation interacts with a focused laser beam, which ionizes the system. The ionization products are usually measured by devices, which spatiotemporally integrate the ionization signal originating from the entire focal area, discarding in this way valuable information about the ionization dynamics that take place in the interaction volume. Here, we re…
It is shown that it is feasible to use ultrashort time delay between two XUV femtosecond pulses in order to control two photon resonant ionization. The proposal is demonstrated on the spectrum of Helium, in terms of nonperturbative solutions of the time dependent Schroedinger equation. Comparison with results from second order time dependent perturbation theory provides additional insight.
We investigate electron momentum distributions from single ionization of Ar by two orthogonally polarized laser pulses of different color. The two-color scheme is used to experimentally control the interference between electron wave packets released at different times within one laser cycle. This intracycle interference pattern is typically hard to resolve in an experiment. With the two-color control scheme these features become the dominant contribution to the electron momentum distribution. Furthermore the second color can be used for streaking of the otherwise interfering wave packets estab…
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.
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…
We report on electron momentum distributions from single ionization of Ar in strong orthogonally polarized two-color (OTC) laser fields measured with the COLTRIMS technique. We study the effect of Coulomb focusing whose signature is a cusp like feature in the center of the electron momentum spectrum. While the direct electrons show the expected strong dependence on the phase between the two colors, surprisingly the Coulomb focused structure is almost not influenced by the weak second harmonic streaking field. This effect is explained by the use of a CTMC simulation which describes the tunneled…
Recent experimental developments of high-intensity, short-pulse XUV light sources are enhancing our ability to study electron-electron correlations. We perform time-dependent calculations to investigate the so-called "sequential" regime (photon energy above 54.4 eV) in the two-photon double ionization of helium. We show that attosecond pulses allow to induce and probe angular and energy correlations of the emitted electrons. The final momentum distribution reveals regions dominated by the Wannier ridge break-up scenario and by post-collision interaction.
The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target (atoms) with regard to the beam …
We present the first demonstration of two-photon double ionization of neon using an intense extreme ultraviolet (XUV) attosecond pulse train (APT) in a photon energy regime where both direct and sequential mechanisms are allowed. For an APT generated through high-order harmonic generation (HHG) in argon we achieve a total pulse energy close to 1 $μ$J, a central energy of 35 eV and a total bandwidth of $\sim30$ eV. The APT is focused by broadband optics in a neon gas target to an intensity of $3\cdot10^{12} $W$\cdot$cm$^{-2}$. By tuning the photon energy across the threshold for the sequential …
A theoretical study of ionization of the hydrogen atom due to an XUV pulse in the presence of an IR laser is presented. Well-established theories are usually used to describe the problem of laser assisted photoelectron effect. However, the well-known soft-photon approximation firstly posed by Maquet et al in Journal of Modern Optics 54, 1847 (2007) and Kazansky's theory in Phys. Rev. A 82, 033420 (2010) completely fails to predict the electron emission prependicularly to the polarization direction. Making use of a simple semiclassical model, we study the angle-resolved energy distribution of p…
Strong field ionization provides a unique mean to address complex dynamics of an electron in competing Coulomb and laser fields. Recent streak camera experiment (Kübel, et al., Phys. Rev. Lett. 119, 183201) analyzed asymmetries in the low-energy region of ejected electron momenta distribution and associated them with multiple rescattering of the electron on the parent ion. In this work we directly confirm the multiple rescattering nature of the asymmetry in the low-energy region. Such electron-ion collisions cannot be described within one-dimensional simulations even taking into account focal-…
We review the main aspects of multiple photoionization processes in atoms exposed to intense, short wavelength radiation. The main focus is the theoretical framework for the description of such processes as well as the conditions under which direct multiphoton multiple ionization processes can dominate over the sequential ones. We discuss in detail the mechanisms available in different wavelength ranges from the infrared to the hard X-rays. The effect of field fluctuations, present at this stage in all SASE free-electron-laser (FEL) facilities, as well as the effect of the interaction volume i…
The dissociative ionization of H2+ interacting with intense, femtosecond extreme-ultraviolet laser pulses is investigated theoretically. This is done by numerical propagation of the time-dependent Schrödinger equation for a colinear one-dimensional model of H2+, with electronic and nuclear motion treated exactly within the limitations of the model. The joint-energy spectra (JES) are extracted for the fragmented electron and nuclei by means of the t-SURFF method. The dynamic interference effect, which was first observed in one-electron atomic systems, is in the present work observed for H2+, em…
We propose a new scenario to apply IR-pump-XUV-probe schemes to resolving strong field ionization induced and attosecond pulse driven electron-hole dynamics and coherence in real time. The coherent driving of both the infrared laser and the attoscond pulse correlates the dynamics of the core-hole and the valence-hole which leads to the otherwise forbidden absorption and emission of XUV photon. An analytical model is developed based on the strong-field approximation by taking into account of the essential multielectron configurations. The emission spectra from the core-valence transition and th…
The double-slit interference in single-photon ionization of the diatomic molecular ion $\mathrm{H}_2^+$ is theoretically studied beyond the dipole approximation. Via simulating and comparing the interactions of the prealigned $\mathrm{H}_2^+$ and the hydrogen atom with the xuv pulses propagating in different directions, we illustrate two kinds of effects that are encoded in the interference patterns of the photoelectrons from $\mathrm{H}_2^+$: (i) the photon-momentum transfer and (ii) the finite speed of light. While both effects could modify the maxima of the interference fringes, we show tha…
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.
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.
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…
Semi-classical molecular dynamics simulations of small rare gas clusters in short laser pulses of 100 nm wavelength were performed. For comparison, the cluster response to 800 nm laser pulses was investigated as well. The inner ionization dynamics of the multi-electron atoms inside the cluster was treated explicitly. The simulation results underpin that at XUV wavelengths collisions play an important role in the energy absorption. The generation of the surprisingly high charge states of Xe atoms inside clusters, as they were observed in the free-electron laser experiment at DESY, Hamburg, Germ…
Intense extreme-ultraviolet (XUV) pulses enable the investigation of XUV-induced nonlinear processes and are a prerequisite for the development of attosecond pump - attosecond probe experiments. While highly nonlinear processes in the XUV range have been studied at free-electron lasers (FELs), high-harmonic generation (HHG) has allowed the investigation of low-order nonlinear processes. Here we suggest a concept to optimize the HHG intensity, which surprisingly requires a scaling of the experimental parameters that differs substantially from optimizing the HHG pulse energy. As a result, we are…
