Separation of photoionization and measurement-induced delays

Photoionization of matter is one of the fastest electronic processes in nature. Experimental measurements of photoionization dynamics have become possible through attosecond metrology. However, all experiments reported to date contain a so-far unavoidable measurement-induced contribution, known as continuum-continuum (CC) or Coulomb-laser-coupling delay. In traditional attosecond metrology, this contribution is nonadditive for most systems and nontrivial to calculate. Here, we introduce the concept of mirror symmetry-broken attosecond interferometry, which enables the direct and separate measurement of both the native one-photon ionization delays and the CC delays. Our technique solves the longstanding challenge of experimentally isolating these two contributions. This advance opens the door to the next generation of accurate measurements and precision tests that will set standards for benchmarking the accuracy of electronic structure and electron-dynamics methods.

Identifying photoelectron releasing order in strong-field dissociative ionization of H2

Driven by intense laser fields, the outgoing photoelectrons in molecules possess a quiver motion, resulting in the rise of the effective ionization potential. The coupling of the field-dressed ionization potential with abundant molecular dynamics complicates the laser-molecule interactions. Here, we demonstrate an approach to resolve photoelectron releasing order in the dissociative and non-dissociative channels of multiphoton ionization driven by an orthogonally polarized two-color femtosecond laser pulse. The photoelectron kinetic energy releases and the regular nodes in the photoelectron angular distributions due to the participation of different continuum partial waves allow us to deduce the field-dressed ionization potential of various channels. It returns the ponderomotive energy experienced by the outgoing electron and reveals the corresponding photoionization instants within the laser pulse. Our results provide a route to explore the complex strong-field ionization dynamics of molecules using two-dimensional photoelectron momentum spectroscopy.

Isolated attosecond X-ray pulses from superradiant thomson scattering by a relativistic chirped electron mirror

Time-resolved investigation of electron dynamics relies on the generation of isolated attosecond pulses in the (soft) X-ray regime. Thomson scattering is a source of high energy radiation of increasing prevalence in modern labs, complementing large scale facilities like undulators and X-ray free electron lasers. We propose a scheme to generate isolated attosecond X-ray pulses based on Thomson scattering by colliding microbunched electrons on a chirped laser pulse. The electrons collectively act as a relativistic chirped mirror, which superradiantly reflects the laser pulse into a single localized beat. As such, this technique extends chirped pulse compression, developed for radar and applied in optics, to the X-ray regime. In this paper we theoretically show that, by using this approach, attosecond soft X-ray pulses with GW peak power can be generated from pC electron bunches at tens of MeV electron beam energy. While we propose the generation of few cycle X-ray pulses on a table-top system, the theory is universally scalable over the electromagnetic spectrum.

Attosecond dynamics of multi-channel single photon ionization

Photoionization of atoms and molecules is one of the fastest processes in nature. The understanding of the ultrafast temporal dynamics of this process often requires the characterization of the different angular momentum channels over a broad energy range. Using a two-photon interferometry technique based on extreme ultraviolet and infrared ultrashort pulses, we measure the phase and amplitude of the individual angular momentum channels as a function of kinetic energy in the outer-shell photoionization of neon. This allows us to unravel the influence of channel interference as well as the effect of the short-range, Coulomb and centrifugal potentials, on the dynamics of the photoionization process.

Understanding of photoionization dynamics, one of the fastest processes in nature, requires the characterization of all underlying ionization channels. Here the authors use an interferometry technique based on attosecond pulses to measure the phase and amplitude of the individual angular momentum channels in the photoionization of neon.

Ultrafast double motion-picture recording technique for propagating light pulses with an ultrashort time difference

Ultrafast imaging techniques involving light propagation, which can record light-pulse propagation as a motion picture, are commonly applied in various fields. However, conventional ultrafast imaging techniques cannot obtain multiple motion- pictures with an ultrashort time difference. In this Letter, we propose an imaging technique to obtain double motion-pictures of propagating light pulses with an ultrashort time difference. To record double motion-pictures of propagating light pulses without superposition of the motion pictures, we employ a space-division multiplexing technique for recording holograms. Also, we construct and introduce an optical delay setup for generating light pulses with an ultrashort time difference. In the experimental demonstration of the proposed technique, we observe the first and second light propagations for a duration of 6.9 ps with a 1.78-ps time difference.

Anisotropic dynamics of two-photon ionization: An attosecond movie of photoemission

Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach because of 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 two-photon transitions through intermediate bound states. Using spectrally and angularly resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude toward the photoelectron quantum state. This allows reconstructing in space, time, and energy the complete formation of the photoionized wave packet.

Raman Interferometry between Autoionizing States to Probe Ultrafast Wave-Packet Dynamics with High Spectral Resolution

Photoelectron interferometry with femtosecond and attosecond light pulses is a powerful probe of the fast electron wave-packet dynamics, albeit it has practical limitations on the energy resolution. We show that one can simultaneously obtain both high temporal and spectral resolution by stimulating Raman interferences with one light pulse and monitoring the modification of the electron yield in a separate step. Applying this spectroscopic approach to the autoionizing states of argon, we experimentally resolved its electronic composition and time evolution in exquisite detail. Theoretical calculations show remarkable agreement with the observations and shed light on the light-matter interaction parameters. Using appropriate Raman probing and delayed detection steps, this technique enables highly sensitive probing and control of electron dynamics in complex systems.

RhoDyn: A ρ-TD-RASCI Framework to Study Ultrafast Electron Dynamics in Molecules

This article presents the program module RhoDyn as part of the OpenMOLCAS project intended to study ultrafast electron dynamics within the density-matrix-based time-dependent restricted active space configuration interaction framework (ρ-TD-RASCI). The formalism allows for the treatment of spin-orbit coupling effects, accounts for nuclear vibrations in the form of a vibrational heat bath, and naturally incorporates (auto)ionization effects. Apart from describing the theory behind and the program workflow, the paper also contains examples of its application to the simulations of the linear L_2,3 absorption spectra of a titanium complex, high harmonic generation in the hydrogen molecule, ultrafast charge migration in benzene and iodoacetylene, and spin-flip dynamics in the core excited states of iron complexes.

Revealing the Target Electronic Structure with Under-Threshold RABBITT

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) reveals the target atom electronic structure when one of the transitions proceeds from below the ionization threshold. Such an under-threshold RABBITT resonates with the target bound states and thus maps faithfully the discrete energy levels and the corresponding oscillator strengths. We demonstrate this sensitivity by considering the Ne atom driven by the combination of the XUV and IR pulses at the fundmanetal laser frequency in the 800 and 1000 nm ranges.

Keldysh time bounds of laser-driven ionization dynamics

We revisit the energy-time uncertainty underpinning of the pointwise bounds of laser-driven ionization dynamics. When resolved within the driver pulse and its field cycle, these bounds are shown to manifest the key signature tendencies of photoionization current dynamics-a smooth growth within the pulse in the regime of multiphoton ionization and an abrupt, almost stepwise photocurrent buildup within a fraction of the field cycle in the limit of tunneling ionization. In both regimes, the Keldysh time, defined as the ratio of the Keldysh parameter to the driver frequency, serves as a benchmark for the minimum time of photoionization, setting an upper bound for the photoelectron current buildup rate.

Coherent electron displacement for quantum information processing using attosecond single cycle pulses

Coherent electron displacement is a conventional strategy for processing quantum information, as it enables to interconnect distinct sites in a network of atoms. The efficiency of the processing relies on the precise control of the mechanism, which has yet to be established. Here, we theoretically demonstrate a new route to drive the electron displacement on a timescale faster than that of the dynamical distortion of the electron wavepacket by utilizing attosecond single-cycle pulses. The characteristic feature of these pulses relies on a vast momentum transfer to an electron, leading to its displacement following a unidirectional path. The scenario is illustrated by revealing the spatiotemporal nature of the displaced wavepacket encoding a quantum superposition state. We map out the associated phase information and retrieve it over long distances from the origin. Moreover, we show that a sequence of such pulses applied to a chain of ions enables attosecond control of the directionality of the coherent motion of the electron wavepacket back and forth between the neighbouring sites. An extension to a two-electron spin state demonstrates the versatility of the use of these pulses. Our findings establish a promising route for advanced control of quantum states using attosecond single-cycle pulses, which pave the way towards ultrafast processing of quantum information as well as imaging.

Laser picoscopy of valence electrons in solids

Valence electrons contribute a small fraction of the total electron density of materials, but they determine their essential chemical, electronic and optical properties. Strong laser fields can probe electrons in valence orbitals^1-3 and their dynamics^4-6 in the gas phase. Previous laser studies of solids have associated high-harmonic emission^7-12 with the spatial arrangement of atoms in the crystal lattice^13,14 and have used terahertz fields to probe interatomic potential forces¹⁵. Yet the direct, picometre-scale imaging of valence electrons in solids has remained challenging. Here we show that intense optical fields interacting with crystalline solids could enable the imaging of valence electrons at the picometre scale. An intense laser field with a strength that is comparable to the fields keeping the valence electrons bound in crystals can induce quasi-free electron motion. The harmonics of the laser field emerging from the nonlinear scattering of the valence electrons by the crystal potential contain the critical information that enables picometre-scale, real-space mapping of the valence electron structure. We used high harmonics to reconstruct images of the valence potential and electron density in crystalline magnesium fluoride and calcium fluoride with a spatial resolution of about 26 picometres. Picometre-scale imaging of valence electrons could enable direct probing of the chemical, electronic, optical and topological properties of materials.

High conversion efficiency of an optical parametric amplifier pumped by 1 kHz Ti:Sapphire laser pulses for tunable high-harmonic generation

We report that high-conversion efficiency of nearly 50% has been realized by combining a commercially available Ti:Sapphire femtosecond, 1 kHz laser system and an optical parametric amplifier (OPA). For an input energy of 2.2 mJ/pulse at 1 kHz and 35 fs duration, the total OPA output energy of the signal plus idler pulses is 1.09 mJ/pulse at a signal wavelength of 1310 nm. We found that the output beam profile is almost flat-top due to high gain saturation in the OPA. Using the signal pulse, we generate high-harmonics in gases and measure the velocity map images of photoelectrons ionized from argon gas as a function of the signal wavelength. We observe that in a particular range of the high-harmonic photon energy, a four-fold photoelectron angular structure is observed in the low kinetic energy region. Our results indicate that the output pulses with the high-conversion efficiency OPA and super Gaussian beam profile can be used for experiments requiring generation of tunable high-harmonics in the extreme ultra-violet region.

Quantum control and characterization of ultrafast ionization with orthogonal two-color laser pulses

We study ultrafast ionization dynamics using orthogonally polarized two-color (OTC) laser pulses involving the resonant "first plus second" (ω + 2ω) scheme. The scheme is illustrated by numerical simulations of the time-dependent Schrödinger equation and recording the photoelectron momentum distribution. On the basis of the simulations of this resonant ionization, we identify signatures of the dynamic Autler-Townes effect and dynamic interference, in which their characterization is not possible in the spectral domain. Taking advantage of the OTC scheme we show that these dynamical effects, which occur at the same time scale, can be characterized in momentum space by controlling the spatial quantum interference. In particular, we show that with the use of this control scheme, one can tailor the properties of the control pulse to lead to enhancement of the ionization rate through the Autler-Townes effect without affecting the dynamic interference. This enhancement is shown to result from constructive interferences between partial photoelectron waves having opposite-parity, and found to manifest by symmetry-breaking of the momentum distribution. The scenario is investigated for a prototype of a hydrogen atom and is broadly applicable to other systems. Our findings may have applications for photoelectron interferometers to control the electron dynamics in time and space, and for accurate temporal characterization of attosecond pulses.

Fano's Propensity Rule in Angle-Resolved Attosecond Pump-Probe Photoionization

In a seminal article, Fano predicts that absorption of light occurs preferably with increase of angular momentum. 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 theory is verified by experimental results in Ar in the 20-40 eV range.

Spatiotemporal observations of light propagation in multiple polarization states

Real-time imaging techniques involving light propagation are commonly applied in the fields of physics, chemistry, and biomedicine. However, conventional techniques provide only the intensity change associated with light propagation. Here, we propose an imaging technique to visualize the ultrafast behavior of the polarization state of a propagating light pulse with four different linear polarization components. This approach provides ultrahigh temporal resolution to observe the light in motion. We recorded a motion picture of a three-dimensional image of a light pulse propagating through a diffuser and a calcite crystal at 56.8 and 75.4 ps, respectively. This technique can contribute to revealing the polarization state of propagating light pulses in a medium and ultrafast phenomenon.

Attosecond single-cycle undulator light: a review

Research at modern light sources continues to improve our knowledge of the natural world, from the subtle workings of life to matter under extreme conditions. Free-electron lasers, for instance, have enabled the characterization of biomolecular structures with sub-ångström spatial resolution, and paved the way to controlling the molecular functions. On the other hand, attosecond temporal resolution is necessary to broaden our scope of the ultrafast world. Here we discuss attosecond pulse generation beyond present capabilities. Furthermore, we review three recently proposed methods of generating attosecond x-ray pulses. These novel methods exploit the coherent radiation of microbunched electrons in undulators and the tailoring of the emitted wavefronts. The computed pulse energy outperforms pre-existing technologies by three orders of magnitude. Specifically, our simulations of the proposed Soft X-ray Laser at MAX IV (Lund, Sweden) show that a pulse duration of 50-100 as and a pulse energy up to 5 [Formula: see text]J is feasible with the novel methods. In addition, the methods feature pulse shape control, enable the incorporation of orbital angular momentum, and can be used in combination with modern compact free-electron laser setups.

Electron correlation driven non-adiabatic relaxation in molecules excited by an ultrashort extreme ultraviolet pulse

The many-body quantum nature of molecules determines their static and dynamic properties, but remains the main obstacle in their accurate description. Ultrashort extreme ultraviolet pulses offer a means to reveal molecular dynamics at ultrashort timescales. Here, we report the use of time-resolved electron-momentum imaging combined with extreme ultraviolet attosecond pulses to study highly excited organic molecules. We measure relaxation timescales that increase with the state energy. High-level quantum calculations show these dynamics are intrinsic to the time-dependent many-body molecular wavefunction, in which multi-electronic and non-Born−Oppenheimer effects are fully entangled. Hints of coherent vibronic dynamics, which persist despite the molecular complexity and high-energy excitation, are also observed. These results offer opportunities to understand the molecular dynamics of highly excited species involved in radiation damage and astrochemistry, and the role of quantum mechanical effects in these contexts.

The many-body quantum nature of molecules determines their static and dynamic properties, but remains the main obstacle in their accurate description. Here, the authors employ ultrafast spectroscopic methods to explore the dynamics of highly excited organic molecules, revealing many-body effects and hints of coherent vibronic dynamics which persist despite their molecular complexity.

Frequency-resolved photon-electronic spectroscopy for excited state population detection

Atomic excitation to excited states in a strong laser field is the key to high-order harmonic generation below the ionization threshold, yet it remains unclear mainly due to the lack of proper detection methods. We propose a frequency-resolved photon-electron spectroscopy technique to reconstruct a population of excited states with the second delayed laser pulse. The technique utilizes Fourier transformation to separate ionization from different excited states to different positions on the spectrum. With the advantage of separation, we provide a scheme to reconstruct populations on different excited states after the first pulse. The scheme is validated by a high-precision population reconstruction of helium and hydrogen atoms.

X-Ray Sum Frequency Diffraction for Direct Imaging of Ultrafast Electron Dynamics

X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved x-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear x-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation carried out with a visible pump and a broadband x-ray diffraction pulse, yields snapshots of the transition charge densities, which represent the electron density variations upon optical excitation. The technique is illustrated by ab initio simulations of transition charge density imaging for the optically induced electronic dynamics in a donor or acceptor substituted stilbene.

Selectivity of Electronic Coherence and Attosecond Ionization Delays in Strong-Field Double Ionization

Experiments are presented on real-time probing of coherent electron dynamics in xenon initiated by strong-field double ionization. Attosecond transient absorption measurements allow for characterization of electronic coherences as well as relative ionization timings in multiple electronic states of Xe^{+} and Xe^{2+}. A high degree of coherence g=0.4 is observed between ^{3}P_{2}^{0}-^{3}P_{0}^{0} of Xe^{2+}, whereas for other possible pairs of states the coherences are below the detection limits of the experiments. A comparison of the experimental results with numerical simulations based on an uncorrelated electron-emission model shows that the coherences produced by strong-field double ionization are more selective than predicted. Surprisingly short ionization time delays, 0.85 fs, 0.64 fs, and 0.75 fs relative to Xe^{+} formation, are also measured for the ^{3}P_{2}, ^{3}P_{0}, and ^{3}P_{1} states of Xe^{2+}, respectively. Both the unpredicted selectivity in the formation of coherence and the subfemtosecond time delays of specific states provide new insight into correlated electron dynamics in strong-field double ionization.

Anisotropic photoemission time delays close to a Fano resonance

Electron correlation and multielectron effects are fundamental interactions that govern many physical and chemical processes in atomic, molecular and solid state systems. The process of autoionization, induced by resonant excitation of electrons into discrete states present in the spectral continuum of atomic and molecular targets, is mediated by electron correlation. Here we investigate the attosecond photoemission dynamics in argon in the 20–40 eV spectral range, in the vicinity of the 3s⁻¹np autoionizing resonances. We present measurements of the differential photoionization cross section and extract energy and angle-dependent atomic time delays with an attosecond interferometric method. With the support of a theoretical model, we are able to attribute a large part of the measured time delay anisotropy to the presence of autoionizing resonances, which not only distort the phase of the emitted photoelectron wave packet but also introduce an angular dependence.

Ionization time delays are of interest in understanding the photoionization mechanism in atoms and molecules in ultra-short time scales. Here the authors investigate the angular dependence of photoionization time delays in the presence of an autoionizing resonance in argon atom using RABBITT technique.

Analytical model of waveform-controlled single-cycle light pulses from an undulator

This Letter builds upon a recent concept [Phys. Rev. Lett.113, 104801 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.104801] for producing ultrashort optical pulses through the coherent radiation of electrons in an undulator. Each pulse contains only a single oscillation cycle, and has a controlled waveform (and hence a stable carrier-envelope phase). While the concept had been demonstrated numerically, this Letter provides an analytical model for the radiation mechanism, thereby revealing three key observations: (i) the correlation between the waveforms of the optical and undulator fields; (ii) the free-space dispersion of transversely confined light; and (iii) the dependence of the optical pulse shape on the undulator field strength.

Tracking the dynamics of electron expulsion

Electron holography is used to map out the wave function of a photo-emitted electron