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We probe the dynamics of tunnel ionization via high harmonic generation. We characterize the ionization dynamics in helium atoms, and apply our approach to resolve subtle differences in ionization from different orbitals of a CO2 molecule.

A unique type of singularity common in wave phenomena, known as caustics, links processes observed in many different branches of physics [1]. We investigate the role of caustics in attosecond science and in particular the physical process behind high harmonic generation. By exploiting singularities of the three-step model that describes HHG, we can manipulate and enhance specific features in the emitted harmonic spectrum. This new level of control holds promises in both scientific and technological aspects of attosecond science, and provides a deeper insight into the basic mechanism underlying the high harmonic generation process.

Strong-field lightâ€"matter interactions initiate a wide range of phenomena in which the quantum paths of electronic wavepackets can be manipulated by tailoring the laser field. Among the electrons released by a strong laser pulse from atomic and molecular targets, some are subsequently driven back to the vicinity of the ionic core by the oscillating laser field. The trajectories of these returning electrons are bent toward the core by the ionic potential, an effect known as Coulomb focusing. This process, studied over the past two decades, has been associated with the long range influence of the Coulomb potential. Here we explore the structural properties of the Coulomb focusing phenomenon. Specifically, we numerically study the sensitivity of the returning electron dynamics to the anisotropy of the ionic potential. We employ orthogonally polarized two-color strong fields and chiral molecules, whose asymmetric features lead to unambiguous fingerprints of the potential on the freed electrons. The Coulomb-focused electrons show an enhanced sensitivity to chirality, related to an asymmetric attoclock-like angular streaking stemming from field-assisted scattering of the electrons onto the chiral ionic potential. Anisotropic features of the ionic potential thus monitor the motion of Coulomb-focused electrons throughout their returning paths, shedding light on the structural properties of the interaction. [ABSTRACT FROM AUTHOR]

Ultrafast strong-field physics provides insight into quantum phenomena that evolve on an attosecond time scale, the most fundamental of which is quantum tunneling. The tunneling process initiates a range of strong field phenomena such as high harmonic generation (HHG), laser-induced electron diffraction, double ionization and photoelectron holography—all evolving during a fraction of the optical cycle. Here we apply attosecond photoelectron holography as a method to resolve the temporal properties of the tunneling process. Adding a weak second harmonic (SH) field to a strong fundamental laser field enables us to reconstruct the ionization times of photoelectrons that play a role in the formation of a photoelectron hologram with attosecond precision. We decouple the contributions of the two arms of the hologram and resolve the subtle differences in their ionization times, separated by only a few tens of attoseconds. [ABSTRACT FROM AUTHOR]

Attosecond physics offers new insights into ultrafast quantum phenomena involving electron dynamics on the fastest measurable timescales. The rapid progress in this field enables us to re-visit one of the most fundamental strong-field phenomena: field-induced tunnel ionization. In this work, we employ high-harmonic generation to probe the electron wavefunction during field-induced tunnelling through a potential barrier. By using a combination of strong and weak driving laser fields, we modulate the atomic potential barrier on optical subcycle timescales. This induces a temporal interferometer between attosecond bursts originating from consecutive laser half-cycles. Our study provides direct insight into the basic properties of field-induced tunnelling, following the evolution of the electronic wavefunction within a temporal window of approximately 200 attoseconds. [ABSTRACT FROM AUTHOR]

Many intriguing phenomena in nature-from phase transitions to black holes-occur at singularities. A unique type of singularity common in wave phenomena, known as caustics, links processes observed in many different branches of physics. Here, we investigate the role of caustics in attosecond science and in particular the physical process behind high harmonic generation. We experimentally demonstrate spectral focusing in high harmonic generation, showing a robust intensity enhancement of an order of magnitude over a spectral width of several harmonics. This new level of control holds promises in both scientific and technological aspects of attosecond science. Moreover, our study provides a deeper insight into the basic mechanism underlying the high harmonic generation process, revealing its quantum nature and universal properties. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a new approach that was first presented by Shafir et al (2009 Nat. Phys. 5 412-6) to probe the symmetry of atomic wavefunctions via the high harmonic generation process. In this scheme, we control the two-dimensional (2D) motion of a free electron using a two-color field to probe the atoms from different angles. We present a new theoretical analysis that focuses on the spherical symmetry of atomic potentials. We analyze previously presented experimental results (Shafir et al 2009 Nat. Phys. 5 412-6) and demonstrate the ability to distinguish between spherically symmetric (s state) and non-spherically symmetric (p state) orbitals. Finally, we discuss the limitations of our approach and compare it with alternative methods. [ABSTRACT FROM AUTHOR]

Strong-field light–matter interactions can encode the spatial properties of the electronic wavefunctions that contribute to the process. In particular, the broadband harmonic spectra, measured for a series of molecular alignments, can be used to create a tomographic reconstruction of molecular orbitals. Here, we present an extension of the tomography approach to systems that cannot be naturally aligned. We demonstrate this ability by probing the two-dimensional properties of atomic wavefunctions. By manipulating an electron–ion recollision process, we are able to resolve the symmetry of the atomic wavefunction with high contrast. [ABSTRACT FROM AUTHOR]

While high harmonic generation from atoms is relatively well understood, the ability to align gas-phase molecules opens an opportunity to more deeply understand the underlying physics. Many assumptions, such as the single active electron approximation, neglect of the Coulomb potential, the strong field approximation, and the assumption of plane waves, are being challenged by new experimental observations. We study high harmonic emission from aligned molecules such as N2, O2 and CO2. We present experimental measurements of the amplitude of the emission as a function of molecular angle, as well as the polarization state. [ABSTRACT FROM AUTHOR]

Generating attosecond pulses has required a radically different approach from previous ultrafast optical methods. The technology of attosecond measurement, however, is built on established methods of characterizing femtosecond pulses: the pulse is measured after it has left the region where it was produced. We offer a completely different approach: in situ measurement. That is, we integrate attosecond-pulse production and measurement in a manner that can be applied to many high-order nonlinear interactions. To demonstrate this approach, we combine a low-intensity (<10−3) second-harmonic beam with the fundamental beam, to gently perturb the production process without significantly modifying it. The attosecond-pulse duration is read from the modulation of the even-harmonic signal as a function of the two-field delay. Increasing the second-harmonic intensity slightly (<10−2), we extend measurement to control. We demonstrate control by manipulating the high-harmonic spectrum with high efficiency. [ABSTRACT FROM AUTHOR]

In strong-field light-matter interactions, the strong laser field dominates the dynamics. However, recent experiments indicate that the Coulomb force can play an important role as well. In this Letter, we have studied the photoelectron momentum distributions produced from noble gases in elliptically polarized, 800 nm laser light. By performing a complete mapping of the three-dimensional electron momentum, we find that Coulomb focusing significantly narrows the lateral momentum spread. We find a surprisingly sensitive dependence of Coulomb focusing on the initial transverse momentum distribution, i.e., the momentum at the moment of birth of the photoelectron. We also observe a strong signature of the low-energy structure in the above threshold ionization spectrum. [ABSTRACT FROM AUTHOR]

Recollision processes provide direct insight into the structure and dynamics of electronic wave functions. However, the strength of the process sets its basic limitations--the interaction couples numerous degrees of freedom. In this Letter we decouple the basic steps of the process and resolve the role of the ionic potential which is at the heart of a broad range of strong field phenomena. Specifically, we measure high harmonic generation from argon atoms. By manipulating the polarization of the laser field we resolve the vectorial properties of the interaction. Our study shows that the ionic core plays a significant role in all steps of the interaction. In particular, Coulomb focusing induces an angular deflection of the electrons before recombination. A complete spatiospectral analysis reveals the influence of the potential on the spatiotemporal properties of the emitted light. [ABSTRACT FROM AUTHOR]

The waveforms of attosecond pulses produced by high-harmonic generation carry information on the electronic structure and dynamics in atomic and molecular systems. Current methods for the temporal characterization of such pulses have limited sensitivity and impose significant experimental complexity. We propose a new linear and all-optical method inspired by widely used multidimensional phase retrieval algorithms. Our new scheme is based on the spectral measurement of two attosecond sources and their interference. As an example, we focus on the case of spectral polarization measurements of attosecond pulses, relying on their most fundamental property—being well confined in time. We demonstrate this method numerically by reconstructing the temporal profiles of attosecond pulses generated from aligned CO2 molecules. [ABSTRACT FROM AUTHOR]

We investigated the giant resonance in xenon by high-order harmonic generation spectroscopy driven by a two-color field. The addition of a nonperturbative second harmonic component parallel to the driving field breaks the symmetry between neighboring subcycles resulting in the appearance of spectral caustics at two distinct cutoff energies. By controlling the phase delay between the two color components it is possible to tailor the harmonic emission in order to amplify and isolate the spectral feature of interest. In this Letter we demonstrate how this control scheme can be used to investigate the role of electron correlations that give birth to the giant resonance in xenon. The collective excitations of the giant dipole resonance in xenon combined with the spectral manipulation associated with the two-color driving field allow us to see features that are normally not accessible and to obtain a good agreement between the experimental results and the theoretical predictions. [ABSTRACT FROM AUTHOR]

Probing electronic wave functions of polyatomic molecules is one of the major challenges in high-harmonic spectroscopy. The extremely nonlinear nature of the laser-molecule interaction couples the multiple degrees of freedom of the probed system. We combine two-dimensional control of the electron trajectories and vibrational control of the molecules to disentangle the two main steps in high-harmonic generation--ionization and recombination. We introduce a new measurement scheme, frequency-resolved optomolecular gating, which resolves the temporal amplitude and phase of the harmonic emission from excited molecules. Focusing on the study of vibrational motion in N2O4, we show that such advanced schemes provide a unique insight into the structural and dynamical properties of the underlying mechanism. [ABSTRACT FROM AUTHOR]

Ever since its discovery 1 , the notion of the Berry phase has permeated all branches of physics and plays an important part in a variety of quantum phenomena 2 . However, so far all its realizations have been based on a continuous evolution of the quantum state, following a cyclic path. Here we introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals, in which the electronic wavefunction accumulates a geometric phase during a discrete evolution between different bands, while preserving the coherence of the process. We experimentally reveal this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of higher-order harmonics. Our work provides an opportunity for the study of geometric phases, leading to a variety of observations in light-driven topological phenomena and attosecond solid-state physics., (© 2024. The Author(s).)

Symmetries are ubiquitous in condensed matter physics, playing an important role in the appearance of different phases of matter. Nonlinear light matter interactions serve as a coherent probe for resolving symmetries and symmetry breaking via their link to selection rules of the interaction. In the extreme nonlinear regime, high harmonic generation (HHG) spectroscopy offers a unique spectroscopic approach to study this link, probing the crystal spatial properties with high sensitivity while opening new paths for selection rules in the XUV regime. In this Letter we establish an advanced HHG polarimetry scheme, driven by a multicolor strong laser field, to observe the structural symmetries of solids and their interplay with the HHG selection rules. By controlling the crystal symmetries, we resolve nontrivial polarization states associated with new spectral features in the HHG spectrum. Our scheme opens new opportunities in resolving the symmetries of quantum materials, as well as ultrafast light driven symmetries in condensed matter systems.

The Coulomb interaction between a photoelectron and its parent ion plays an important role in a large range of light-matter interactions. In this paper we obtain a direct insight into the Coulomb interaction and resolve, for the first time, the phase accumulated by the laser-driven electron as it interacts with the Coulomb potential. Applying extreme-ultraviolet interferometry enables us to resolve this phase with attosecond precision over a large energy range. Our findings identify a strong laser-Coulomb coupling, going beyond the standard recollision picture within the strong-field framework. Transformation of the results to the time domain reveals Coulomb-induced delays of the electrons along their trajectories, which vary by tens of attoseconds with the laser field intensity.

Low frequency Raman spectroscopy resolves the slow vibrations resulting from collective motions of molecular structures. This frequency region is extremely challenging to access via other multidimensional methods such as 2D-IR. In this paper, we describe a new scheme which measures 2D Raman spectra in the low frequency regime. We separate the pulse into a spectrally shaped pump and a transform-limited probe, which can be distinguished by their polarization states. Low frequency 2D Raman spectra in liquid tetrabromoethane are presented, revealing coupling dynamics at frequencies as low as 115 cm -1 . The experimental results are supported by numerical simulations which replicate the key features of the measurement. This method opens the door for the deeper exploration of vibrational energy surfaces in complex molecular structures.

Solid-state high-harmonic generation (HHG) by an intense infra-red (IR) laser field offers a new route to generate coherent attosecond light pulses in the extreme ultraviolet regime. The propagation of the IR driving field in the dense solid medium is accompanied by non-linear processes which shape the generating waveform. In this work, we introduce a monolithic scheme in which we both exploit the non-linear propagation to manipulate a two color driving field, as well as generate high harmonics within a single crystal. We show that the resulting non-commensurate, bi-chromatic, generating field provides precise control over the periodicity of the HHG process. This control enables us to manipulate the spectral positions of the discrete harmonic peaks. Our method advances solid-state HHG spectroscopy, and offers a simple route towards tunable, robust XUV sources.

High-harmonic generation (HHG) is a powerful tool to generate coherent attosecond light pulses in the extreme ultraviolet. However, the low conversion efficiency of HHG at the single atom level poses a significant practical limitation for many applications. Enhancing the efficiency of the process defines one of the primary challenges in the application of HHG as an advanced XUV source. In this work, we demonstrate a new mechanism, which in contrast to current methods, enhances the HHG conversion efficiency purely on a single particle level. We show that using a bichromatic driving field, sub-optical-cycle control and enhancement of the tunnelling ionization rate can be achieved, leading to enhancements in HHG efficiency by up to two orders of magnitude. Our method advances the perspectives of HHG spectroscopy, where isolating the single particle response is an essential component, and offers a simple route toward scalable, robust XUV sources.

Single-photon ionization is one of the most fundamental light matter interactions in nature, serving as a universal probe of the quantum state of matter. By probing the emitted electron, one can decode the full dynamics of the interaction. When photo-ionization is evolving in the presence of a strong laser field, the fundamental properties of the mechanism can be signicantly altered. Here we demonstrate how the liberated electron can perform a self-probing measurement of such interaction with attosecond precision. Extreme ultraviolet attosecond pulses initiate an electron wavepacket by photo-ionization, a strong infrared field controls its motion, and finally electron-ion collision maps it into re-emission of attosecond radiation bursts. Our measurements resolve the internal clock provided by the self-probing mechanism, obtaining a direct insight into the build-up of photo-ionization in the presence of the strong laser field.

High harmonic generation (HHG) spectroscopy has opened up a new frontier in ultrafast science, where electronic dynamics can be measured on an attosecond time scale. The strong laser field that triggers the high harmonic response also opens multiple quantum pathways for multielectron dynamics in molecules, resulting in a complex process of multielectron rearrangement during ionization. Using combined experimental and theoretical approaches, we show how multi-dimensional HHG spectroscopy can be used to detect and follow electronic dynamics of core rearrangement on sub-laser cycle time scales. We detect the signatures of laser-driven hole dynamics upon ionization and reconstruct the relative phases and amplitudes for relevant ionization channels in a CO 2 molecule on a sub-cycle time scale. Reconstruction of channel-resolved complex ionization amplitudes on attosecond time scales has been a long-standing goal of high harmonic spectroscopy. Our study brings us one step closer to fulfilling this initial promise and developing robust schemes for sub-femtosecond imaging of multielectron rearrangement in complex molecular systems.

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called 'diffraction before destruction' experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing the phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.

High-order harmonic generation in polyatomic molecules generally involves multiple channels of ionization. Their relative contribution can be strongly influenced by the presence of resonances, whose assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach for the investigation of unaligned polyatomic molecules, using SF6 as an example. We combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Fragment-resolved above-threshold ionization measurements reveal that strong-field ionization opens at least three channels. A shape resonance in one of them is found to dominate the signal in the 20-26 eV range. This resonance induces a phase jump in the harmonic emission, a switch in the polarization state and different dynamical responses to molecular vibrations. This study demonstrates a method for extending high-harmonic spectroscopy to polyatomic molecules, where complex attosecond dynamics are expected.

Phase measurement is a long-standing challenge in a wide range of applications, from X-ray imaging to astrophysics and spectroscopy. While in some scenarios the phase is resolved by an interferometric measurement, in others it is reconstructed via numerical optimization, based on some a-priori knowledge about the signal. The latter commonly use iterative algorithms, and thus have to deal with their convergence, stagnation, and robustness to noise. Here we combine these two approaches and present a new scheme, termed double blind Fourier holography, providing an efficient solution to the phase problem in two dimensions, by solving a system of linear equations. We present and experimentally demonstrate our approach for the case of lens-less imaging.

The tunnelling of a particle through a barrier is one of the most fundamental and ubiquitous quantum processes. When induced by an intense laser field, electron tunnelling from atoms and molecules initiates a broad range of phenomena such as the generation of attosecond pulses, laser-induced electron diffraction and holography. These processes evolve on the attosecond timescale (1 attosecond ≡ 1 as = 10(-18) seconds) and are well suited to the investigation of a general issue much debated since the early days of quantum mechanics--the link between the tunnelling of an electron through a barrier and its dynamics outside the barrier. Previous experiments have measured tunnelling rates with attosecond time resolution and tunnelling delay times. Here we study laser-induced tunnelling by using a weak probe field to steer the tunnelled electron in the lateral direction and then monitor the effect on the attosecond light bursts emitted when the liberated electron re-encounters the parent ion. We show that this approach allows us to measure the time at which the electron exits from the tunnelling barrier. We demonstrate the high sensitivity of the measurement by detecting subtle delays in ionization times from two orbitals of a carbon dioxide molecule. Measurement of the tunnelling process is essential for all attosecond experiments where strong-field ionization initiates ultrafast dynamics. Our approach provides a general tool for time-resolving multi-electron rearrangements in atoms and molecules--one of the key challenges in ultrafast science.

Ultrafast science is inherently, due to the lack of fast enough detectors and electronics, based on nonlinear interactions. Typically, however, nonlinear measurements require significant powers and often operate in a limited spectral range. Here we overcome the difficulties of ultraweak ultrafast measurements by precision time-domain localization of spectral components. We utilize this for linear self-referenced characterization of pulse trains having ∼ 1 photon per pulse, a regime in which nonlinear techniques are impractical, at a temporal resolution of ∼ 10 fs. This technique does not only set a new scale of sensitivity in ultrashort pulse characterization, but is also applicable in any spectral range from the near-infrared to the deep UV.

We study high-order harmonic generation in aligned molecules close to the ionization threshold. Two distinct contributions to the harmonic signal are observed, which show very different responses to molecular alignment and ellipticity of the driving field. We perform a classical electron trajectory analysis, taking into account the significant influence of the Coulomb potential on the strong-field-driven electron dynamics. The two contributions are related to primary ionization and excitation processes, offering a deeper understanding of the origin of high harmonics near the ionization threshold. This Letter shows that high-harmonic spectroscopy can be extended to the near-threshold spectral range, which is in general spectroscopically rich.

We have measured high-order harmonic generation spectra of D2, N2, and CO2 by mixing orthogonally polarized 800 and 400 nm laser fields. The intensity of the high-harmonic spectrum is modulated as we change the relative phase of the two pulses. For randomly orientated molecules, the phase of the intensity modulation depends on the symmetry of the molecular orbitals from which the high harmonics are emitted. This allows us to identify the symmetry of any orbital that contributes to high-harmonic generation, even without aligning the molecule. Our approach can be a route to imaging dynamical changes in three-dimensional molecular orbitals on a time scale as short as a few hundred attoseconds.

We perform high harmonic generation spectroscopy of aligned nitrogen molecules to characterize the attosecond dynamics of multielectron rearrangement during strong-field ionization. We use the spectrum and ellipticity of the harmonic light to reconstruct the relative phase between different ionization continua participating in the ionization, and thus determine the shape and location of the hole left in the molecule by strong-field ionization. Our interferometric technique uses transitions between the ionic states, induced by the laser field on the subcycle time scale.

Molecular structures, dynamics and chemical properties are determined by shared electrons in valence shells. We show how one can selectively remove a valence electron from either Pi vs. Sigma or bonding vs. nonbonding orbital by applying an intense infrared laser field to an ensemble of aligned molecules. In molecules, such ionization often induces multielectron dynamics on the attosecond time scale. Ionizing laser field also allows one to record and reconstruct these dynamics with attosecond temporal and sub-Angstrom spatial resolution. Reconstruction relies on monitoring and controlling high-frequency emission produced when the liberated electron recombines with the valence shell hole created by ionization.

High harmonic emission occurs when an electron, liberated from a molecule by an incident intense laser field, gains energy from the field and recombines with the parent molecular ion. The emission provides a snapshot of the structure and dynamics of the recombining system, encoded in the amplitudes, phases and polarization of the harmonic light. Here we show with CO(2) molecules that high harmonic interferometry can retrieve this structural and dynamic information: by measuring the phases and amplitudes of the harmonic emission, we reveal 'fingerprints' of multiple molecular orbitals participating in the process and decode the underlying attosecond multi-electron dynamics, including the dynamics of electron rearrangement upon ionization. These findings establish high harmonic interferometry as an effective approach to resolving multi-electron dynamics with sub-Angström spatial resolution arising from the de Broglie wavelength of the recombining electron, and attosecond temporal resolution arising from the timescale of the recombination event.

We describe the roles of multiple electronic continua in high-harmonic generation from aligned molecules. First, we show how the circularity of emitted harmonics tracks the interplay of different electronic continua participating in the nonlinear response. Second, we show that the interplay of different continua can lead to large variations of harmonic phases. Finally, we show how multiple electronic continua allow one to shape the polarization of high harmonics and attosecond pulses.

We study high-order harmonic generation in excited media using a four-wave-mixing-like configuration. We analyze the spatial profile of high harmonics emitted by a grating of rotationally excited molecules as a function of the pump-probe delay. We demonstrate a dramatic improvement in the contrast of the diffracted signal relative to the total high harmonic signal. This allows us to observe subtle effects in the rotational wave packet excitation such as the pump-intensity dependence of the wave packet dynamics. High harmonic transient grating spectroscopy can be extended to all forms of molecular excitation and to weak resonant excitation.

High harmonic emission in isotropic gases is polarized in the same direction as the incident laser polarization. Laser-induced molecular alignment allows us to break the symmetry of the gas medium. By using aligned molecules in high harmonic generation experiments, we show that the polarization of the extreme ultraviolet emission depends strongly on the molecular alignment and the orbital structure. Polarization measurements give insight into the molecular orbital symmetry. Furthermore, molecular alignment will allow us to produce attosecond pulses with time-dependent polarization.