Attosecond Extreme Ultraviolet Pulses Research Articles

Attosecond-pump attosecond-probe x-ray spectroscopy of liquid water.

Attosecond-pump/attosecond-probe experiments have long been sought as the most straightforward method for observing electron dynamics in real time. Although there has been much success with overlapped near-infrared femtosecond and extreme ultraviolet attosecond pulses combined with theory, true attosecond-pump/attosecond-probe experiments have been limited. We used a synchronized attosecond x-ray pulse pair from an x-ray free-electron laser to study the electronic response to valence ionization in liquid water through all x-ray attosecond transient absorption spectroscopy (AX-ATAS). Our analysis showed that the AX-ATAS response is confined to the subfemtosecond timescale, eliminating any hydrogen atom motion and demonstrating experimentally that the 1b1 splitting in the x-ray emission spectrum is related to dynamics and is not evidence of two structural motifs in ambient liquid water.

Shaping extreme-ultraviolet attosecond pulses by tuning the minimum in high-order harmonic generation with two gas jets

Shaping extreme-ultraviolet attosecond pulses by tuning the minimum in high-order harmonic generation with two gas jets

Time‐Resolved Photoemission Electron Microscopy on a ZnO Surface Using an Extreme Ultraviolet Attosecond Pulse Pair

AbstractElectrons photoemitted by extreme ultraviolet attosecond pulses derive spatially from the first few atomic surface layers and energetically from the valence band and highest atomic orbitals. As a result, it is possible to probe the emission dynamics from a narrow 2D region in the presence of optical fields, as well as obtain elemental specific information. However, combining this with spatially‐resolved imaging is a long‐standing challenge because of the large inherent spectral width of attosecond pulses, as well as the difficulty of making them at high repetition rates. Here, this work demonstrates an attosecond interferometry experiment on a zinc oxide (ZnO) surface using spatially and energetically resolved photoelectrons. Photoemission electron microscopy is combined with near‐infrared pump ‐ extreme ultraviolet probe laser spectroscopy and the instantaneous phase of an infrared field is resolved with high spatial resolution. Results show how the core level states with low binding energy of ZnO are well suited to perform spatially resolved attosecond interferometry experiments. A distinct phase shift of the attosecond beat signal is observed across the laser focus which is attributed to wavefront differences between the pump and the probe fields at the surface. This work demonstrates a clear pathway for attosecond interferometry with high spatial resolution at atomic scale surface regions opening up for a detailed understanding of nanometric light‐matter interaction.

Electron vortices generation of photoelectron of H2+ by counter-rotating circularly polarized attosecond pulses

Molecular-frame photoelectron momentum distributions (MF-PMDs) of an H2+ molecule ion in the presence of a pair of counter-rotating circularly polarized attosecond extreme ultraviolet laser pulses is studied by numerically solving the two-dimensional time-dependent Schrödinger equation within the frozen-nuclei approximation. At small time delay, our simulations show that the electron vortex structure is sensitive to the time delay and relative phase between the counter-rotating pulses when they are partially overlapped. By adjusting time delay and relative phase, we have the ability to manipulate the MF-PMDs and the appearance of spiral arms. We further show that the internuclear distance can affect the spiral vortices due to its different transition cross sections in the parallel and perpendicular geometries. The lowest-order perturbation theory is employed to interpret these phenomena qualitatively. It is concluded that the internuclear distance-dependent transition cross sections and the confinement effect in diatomic molecules are responsible for the variation of vortex structures in the MF-PMDs.

Attosecond ionization dynamics of modulated, few-cycle XUV pulses

Few-cycle, attosecond extreme ultraviolet (XUV) pulses in the strong field regime are becoming experimentally feasible, prompting theoretical investigating of the ionization dynamics induced by such pulses. Here, we provide a systematic study of the atomic ionization dynamics beyond the regime of the slowly varying envelope approximation. We discuss the properties of such XUV pulses and report on temporal and spectral modulations unique to the attosecond nature of the pulse. By employing different levels of theory, namely the numerical solution to the time-dependent Schrödinger equation, perturbation theory and a semi-analytical approach, we investigate the ionization of atoms by modulated, few-cycle XUV pulses and distinguish first and higher order effects. In particular, we study attosecond ionization in different intensity regimes aided by a general wave function splitting algorithm. Our results show that polarization and interference effects in the continuum prominently drive ionization in the few-cycle regime and report on carrier-envelope phase (CEP)- and intensity-dependent asymmetries in the photoelectron spectra. The use of spectrally modulated attosecond pulses allows us to distinguish between temporal effects causing asymmetries and dynamic interference, and spectral effects inducing a redshift of the photoelectron spectrum.

Attosecond photoionization delays in the vicinity of molecular Feshbach resonances

Temporal delays extracted from photoionization phases are currently determined with attosecond resolution by using interferometric methods. Such methods require special care when photoionization occurs near Feshbach resonances due to the interference between direct ionization and autoionization. Although theory can accurately handle these interferences in atoms, in molecules, it has to face an additional, so far insurmountable problem: Autoionization is slow, and nuclei move substantially while it happens, i.e., electronic and nuclear motions are coupled. Here, we present a theoretical framework to account for this effect and apply it to evaluate time-resolved and vibrationally resolved photoelectron spectra and photoionization phases of N2 irradiated by a combination of an extreme ultraviolet (XUV) attosecond pulse train and an infrared pulse. We show that Feshbach resonances lead to unusual non-Franck-Condon vibrational progressions and to ionization phases that strongly vary with photoelectron energy irrespective of the vibrational state of the remaining molecular cation.

Measuring autoionization decay lifetimes of optically forbidden inner valence excited states in neon atoms with attosecond noncollinear four-wave-mixing spectroscopy

Attosecond noncollinear four wave mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48 eV XUV photon excites a 2s electron into the 2s2p6[np] Rydberg series, broadband NIR pulses couple the 2s2p6[3p] XUV-bright state to neighboring 2s2p6[3s] and 2s2p6[3d] XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or bright states, respectively. Experimental lifetimes for the 3s, 3p, and 3d states are measured to be 7 +/- 2 fs, 48 +/- 8 fs, and 427 +/- 40 fs, respectively, with 95% confidence. Accompanying calculations with two independent ab initio theoretical methods, NewStock and ASTRA, verify the findings. The results support the expected trend that the autoionization lifetime should be longer for states that have a smaller penetration in the radial region of the 2s core hole, which in this case is for the higher angular momentum Rydberg orbitals. The underlying theory thus links the lifetime results to electron correlation and provides an assessment of the direct and exchange terms in the autoionization process.

Attosecond imaging of photoinduced dynamics in molecules using time-resolved photoelectron momentum microscopy

We explore the novel capabilities offered by attosecond extreme ultraviolet and x-ray pulses that can be now generated by free-electron lasers and high-harmonics generation sources for probing photon-induced electron dynamics in molecules. We theoretically analyze how spatial and temporal dependence of charge migration in a pentacene molecule can be followed by means of time-resolved photoelectron microscopy on the attosecond time scale. Performing the analysis, we accurately take into account that an attosecond probe pulse leads to considerable spectral broadening. We demonstrate that the excited-state dynamics of a neutral pentacene molecule in the real space map onto unique features of photoelectron momentum maps.

High-resolution attosecond imaging of an atomic electron wave function in momentum space

An electron wave function is characterized by the phase and amplitude distributions over position or momentum space. Recent attosecond technologies allow us to obtain the phase information of photoelectrons using interference between several optical transition pathways. We demonstrate that by employing a two-path photoionization interference process, the complex wave function of the photoelectron is fully mapped in two-dimensional momentum space. We ionize neon gas by an extreme ultraviolet (XUV) attosecond pulse train consisting of both odd and even harmonics in the presence of an infrared (IR) laser field. By controlling the generation process of the attosecond pulse train, we isolate two ionization pathways for interfering with the photoelectrons: one is the two-photon ionization process due to the odd harmonic excitation with one IR photon absorption, and the other is the one-photon ionization by an even harmonic. We record the photoelectron momentum distributions via velocity map imaging as a function of the XUV and IR delay. Using three different experimental conditions, we show that the detailed structure of the amplitude and phase distributions of photoelectrons can be resolved in the two-dimensional momentum space within the bandwidth determined by the attosecond XUV pulse. We separate the measured photoelectron wave function into those produced by each ionization pathway. Our method will be applicable to more complex molecules.

Roles of the transition amplitude phases in photoelectron asymmetry of single strong attosecond pulse

The angular distributions of the photoelectrons in ionization of hydrogen atom by both circularly and linearly polarized intense extreme ultraviolet (XUV) attosecond pulse are investigated by numerically solving the time-dependent Schrödinger equation. We clearly identify nonperturbative features in studying the asymmetrical photoelectron angular distributions in the polarization plane for the XUV photon energy (16.3 eV) close to the ionization threshold, while such nonperturbative features are absent for higher photon energy (36 eV) in the same pulse intensity region. In addition to the carrier-envelope phase (CEP) dependence, the ejection asymmetry of the photoelectron is also sensitive to the relative phases of transition amplitudes in absorbing one photon and two photons. As a consequence, the CEPs corresponding to the maximal (or zero) asymmetry obviously vary as the pulse intensity increases in a moderately large region from 1 × 1015 W cm−2 to 30 × 1015 W cm−2. We attribute the intensity dependence of the transition amplitude phases to a consequence of the depletion of population as well as the Stark energy shift of the initial state. We show that the relative phases of transition amplitudes can be precisely decoded from the pulse intensity dependence of the ejection asymmetry and those phases are insensitive to the ellipticity of the laser pulse.

Few-Femtosecond Isotope Effect in Polyatomic Molecules Ionized by Extreme Ultraviolet Attosecond Pulse Trains.

Following ionization by an extreme ultraviolet (XUV) attosecond pulse train, a polyatomic molecule can be promoted to more-than-one excited states of the residual ion. The ensuing relaxation dynamics is often facilitated by several reaction coordinates, making them difficult to disentangle by the usual spectroscopic means. Here, we show that in atto-chemistry isotope labeling can be an efficient tool for unraveling the relaxation pathways in highly excited photoionized molecules. Employing an XUV pump pulse and a near-infrared probe pulse, we found the nuclear as well as coupled electron-nuclear dynamics in ethylene to be almost 40% faster compared to that of its deuterated counterpart. The findings, which are supported by advanced nonadiabatic dynamics calculations, led to the identification of the relevant nuclear coordinates controlling the relaxation. Our experiment highlights the relevance of ultrashort XUV pulses to capture the isotopic effect in few-femtosecond molecular photodynamics.

Retrieval of photoionization group delay in chirped-attosecond pulses photoelectron streaking experiments

Photoionization time delays have been investigated in many streaking experiments in which an extreme ultraviolet (XUV) attosecond pulse is used to ionize the target in the presence of a dressing infrared laser field. The discrepancies between the photoionization time delays thus experiment measured and those from many sophisticated theoretical simulations have generated a great deal of controversy in recent years. The difficulty of achieving an accuracy of the retrieved time delays comes from two facts: a so-called wavepacket approximation is introduced to construct the photoionization electron wavepacket, this approximation is invalid if atto-chirp of XUV is non-zero; the other one is that the lower sensitivity of the streaking spectra to the phase of the photoionization transition dipole. Here we present a time delay retrieval method born from our recently proposed ‘phase retrieval of broadband pulses auto correlation’ (PROBP-AC) technology to overcome above limitations. We carefully exam the validity of our method and make a few compare with some other common used retrieval codes, and the simulations demonstrate that more accurate results can be retrieved using PROBP AC. Based on the present method, the angular dependent photoionization time delays can also be retrieved. Our investigation casts doubts on the measured group time delays in previous streaking experiments. We also mention here that a single photoionization group time delay at the XUV peak energy is not enough to represent a complete photoemission process; instead, a fully characterization of the photoionization group time delay over the whole bandwidth of the wave packet is required.

Phase-locking of time-delayed attosecond XUV pulse pairs.

We present a setup for the generation of phase-locked attosecond extreme ultraviolet (XUV) pulse pairs. The attosecond pulse pairs are generated by high harmonic generation (HHG) driven by two phase-locked near-infrared (NIR) pulses that are produced using an actively stabilized Mach-Zehnder interferometer compatible with near-single cycle pulses. The attosecond XUV pulses can be delayed over a range of 400 fs with a sub-10-as delay jitter. We validate the precision and the accuracy of the setup by XUV optical interferometry and by retrieving the energies of Rydberg states of helium in an XUV pump-NIR probe photoelectron spectroscopy experiment.

Experimental Control of Quantum-Mechanical Entanglement in an Attosecond Pump-Probe Experiment.

Entanglement is one of the most intriguing aspects of quantum mechanics and lies at the heart of the ongoing second quantum revolution, where it is a resource that is used in quantum key distribution, quantum computing, and quantum teleportation. We report experiments demonstrating the crucial role that entanglement plays in pump-probe experiments involving ionization, which are a hallmark of the novel research field of attosecond science. We demonstrate that the degree of entanglement in a bipartite ion + photoelectron system, and, as a consequence, the degree of vibrational coherence in the ion, can be controlled by tailoring the spectral properties of the attosecond extreme ultraviolet laser pulses that are used to create them.

Bright High-Harmonic Generation through Coherent Synchrotron Emission Based on the Polarization Gating Scheme

Relativistic surface high harmonics, combined with the use of polarization gating, present a promising route towards intense single attosecond pulses. However, they impose stringent requirements on ultra-high laser contrast and are restricted by large intensity losses in real experiments. Here, we numerically demonstrate that by setting an optimal time delay in the polarization gating scheme, the intensity of the generated single attosecond pulses can become approximately 100 times stronger than that with nonoptimal time delay in the coherent synchrotron emission process. When a petawatt-class driving laser irradiates a solid target, an ultra-dense electron nanobunch and a strong space-charge sheath develop, and the accumulated electrostatic energy is only released in half of the laser cycle when this electron nanobunch moves backward. This process results in the emission of intense high harmonics. Our study provides a reliable method for developing bright attosecond extreme ultraviolet pulses.

Precise measurement of attosecond dynamics of NO molecular shape resonance

Shape resonance is an important and ubiquitous phenomenon in the process of molecular scattering and photoionization. The study of the attosecond photoemission time delay in the vicinity of the shape resonance is of great significance for understanding its intrinsic origin on a nature time scale of electron motion. In this paper, an advanced attosecond coincidence interferometer consisting of a near-infrared femtosecond light source and an extreme ultraviolet attosecond pulse train is used to study the shape resonance process of the 4σ electron of nitric oxide molecules via reconstructing attosecond harmonic beating by measuring the interference of two-photon transitions (RABBIT). The energy dependent effective ionization time delay in the vicinity of the resonance energy region is reported. By comparing the relationship between the two-photon transition delay and the one-photon transition delay, it is found that the Wigner delay of the single-photon process is the main reason for the two-photon transition delay changing with energy. The effect of continuum-continuum delay is further explored. Theoretical calculations of the initial state (bound state) and final state (resonance state) electron wave function orbits of the resonance show that the shape resonance assisted time delay is dominated by the electrons trapped in the centrifugal potential barrier.

Emissions of brilliant attosecond pulse in circular polarization by using inclined lasers

We propose a practical approach to produce intense circularly polarized (CP) attosecond pulses using inclined linearly polarized (LP) lasers from relativistic plasma mirrors. Due to the dynamics of the plasma surface currents at the radiation point, the phase difference of high-order harmonics in the two orthogonal transverse directions approaches π/2 by proper inclination angle and incident angle of the driving laser. One- and three-dimensional particle-in-cell simulations show that CP attosecond extreme-ultraviolet pulses with an intensity about 3.1×1020 W/cm2 are obtained by using a LP laser with an intensity of 1.3×1021 W/cm2, both the inclination and incident angles of which are 45°. This approach is more feasible than previous approaches using CP/two-color driving lasers, and such a CP attosecond source provides a unique tool for a variety of chirality-sensitive applications.

Control of Attosecond Entanglement and Coherence.

Calculations are presented of vibrational wave packet dynamics in H_{2}^{+} ions formed by ionization of neutral H_{2} by a pair of attosecond extreme ultraviolet laser pulses, using time-delayed dissociation of the cation by an ultraviolet probe pulse. The strength of experimentally observable two-level quantum beats as a function of the attosecond two-pulse delay can be related to ion+photoelectron entanglement resulting from the ionization process. This conclusion is supported by an evaluation of the purity of the reduced ion and photoelectron density matrices.

Method for high precision measurement of decaying dynamics using attosecond wave-mixing spectroscopy.

Ultrafast wave-mixing spectroscopies involving extreme ultraviolet (EUV) attosecond pulses provide unprecedented insight into electronic dynamics. Here, we proposed a versatile lifetime-detection method for doubly excited states with odd or even parities by mixing an attosecond EUV pulse with two few-cycle near infrared (NIR) pulses in atomic helium under a noncollinear geometry. By properly choosing the time order of the pulse sequence, the spatially resolved nonlinear signals carry significant information of the decaying dynamics of excited states, which can be utilized to retrieve the lifetimes of states with different parities in a single measurement. The validity and robustness of the method has been verified by numerical simulations based on a few-level model of helium including the spatial distribution of atoms. The accuracy of the lifetime measurement method is better than a few hundred attoseconds. It provides a powerful tool for probing decaying dynamics of the electronic wave packet with superb resolution.

The Coulomb effects in laser-assisted single photoionization

Attosecond photoionization time delays reveal information about an outgoing electron getting away from the Coulomb potential. In this study, we improve the eikonal approximation model that overestimates the laser-Coulomb coupling effect in the laser-assisted photoionization of atoms. The improved eikonal approximation model can be accurate on about the 2 asec level relative to the time-dependent Schrödinger equation results. The improvement of photoionization time delays demonstrates that the electrons ionized by extreme ultraviolet attosecond pulse possesses momentum larger than the asymptotical momentum due to the attractive Coulomb potential of the parent ion. These results will give a deeper insight into understanding the laser-assisted single photoionization.