Analytic description of the high-energy plateau in harmonic generation by atoms: can the harmonic power increase with increasing laser wavelengths?

High-order harmonics enhancement in laser-induced plasma

The methods of enhancement of the strong high-order harmonics of femtosecond pulses in laser-induced plasma are demonstrated. It comprises the application of the four techniques allowing the enhancement of harmonics in different spectral ranges. Among them are the selection of targets for ablation to create the conditions for resonance enhancement of single harmonic, formation of the quasi-phase-matching of a spectrally tunable group of harmonics, application of the two-color pump of plasma, and the formation of nanoparticles-contained plasmas. The number of generated coherent XUV photons increased in the region of single resonantly enhanced harmonic (62 nm) and the shorter-wavelength region (30-50 nm). The above techniques of harmonics enhancement allowed a significant (up to 50 times) growth in a whole harmonic yield in the case of indium plasma. We discuss the reasons preventing the joint implementation of the four methods of harmonics enhancement in the same spectral region.

Contribution of the collective electron dynamics to the polarization response of an atom subjected to intense IR and weak XUV pulses

We analyze the polarization response of a single Ne atom in an intense infrared (IR) laser field and weak extreme ultraviolet (XUV) isolated attosecond pulse (IAP). The analysis is based on the numerical solution of the time-dependent Kohn-Sham equations and the recently developed perturbation theory in the XUV field for an atom subjected to an intense IR field. In our numerical results, we observe a significant increase in the magnitude of the atomic polarization response at the frequencies near the carrier frequency of the IAP and associate it with XUV-induced collective dynamics contributing to the polarizability of Ne. The specific interference between IR- and XUV-induced channels is discussed, and its utilization for retrieving the phase of the generated harmonics in the IR field is suggested.

Resonance absorption of the inner shell during high-order harmonic generation

In this work, we report the observation of resonance absorption of the inner shell during the high-order harmonic generation (HHG) from xenon (Xe) and krypton (Kr). The absorption peaks show a periodic variation with the change of carrier-envelope phase of driving laser pulses and the delay of two-color laser field, which indicates the absorption peaks come from the collective multielectron effects during the HHG. With the increase of gas pressure, the depth of absorption peak will continue to increase, while due to the phase matching effect, there will be an optimal pressure for the intensity of harmonic signal. Our experimental results pave the way to uncover the physical mechanism of the collective multielectron effects involving inner-shell electrons in the HHG process.

Electron Dynamics and Correlations During High-Order Harmonic Generation in Be

We investigate theoretically the high-order harmonic generation in beryllium atom irradiated by a short 1850 nm linearly polarized laser pulse in the intermediate strong-field ionization regime with the Keldysh parameter of 0.85. To this end, the respective time-dependent Schrödinger equation is solved by the time-dependent restricted-active-space configuration-interaction (TD-RASCI) method. By systematically increasing the active space of included configurations, we demonstrate an individual effect of different physical processes evoked by the pulse, which, all together, significantly enrich and extend the computed high-order harmonic generation spectrum.

Dialogue on analytical and ab initio methods in attoscience

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

It is all about phases: ultrafast holographic photoelectron imaging

Photoelectron holography constitutes a powerful tool for the ultrafast imaging of matter, as it combines high electron currents with subfemtosecond resolution, and gives information about transition amplitudes and phase shifts. Similarly to light holography, it uses the phase difference between the probe and the reference waves associated with qualitatively different ionization events for the reconstruction of the target and for ascertaining any changes that may occur. These are major advantages over other attosecond imaging techniques, which require elaborate interferometric schemes in order to extract phase differences. For that reason, ultrafast photoelectron holography has experienced a huge growth in activity, which has led to a vast, but fragmented landscape. The present review is an organizational effort towards unifying this landscape. This includes a historic account in which a connection with laser-induced electron diffraction is established, a summary of the main holographic structures encountered and their underlying physical mechanisms, a broad discussion of the theoretical methods employed, and of the key challenges and future possibilities. We delve deeper in our own work, and place a strong emphasis on quantum interference, and on the residual Coulomb potential.

Harmonic Generation from Neutral Manganese Atoms in the Vicinity of the Giant Autoionization Resonance

High harmonics from laser-ablated plumes are mostly generated from ionic species. We demonstrate that with ultrashort infrared (∼1.82  μm) driving lasers, high harmonics from laser-ablated manganese are predominantly generated from neutral atoms, a transition metal atom with an ionization potential of 7.4 eV. Our results open the possibility to advance laser-ablation technique to study the dynamics of neutral atoms of low ionization potential. Moreover, as manganese contains giant autoionizing resonance, intense and broadband high harmonics have been demonstrated from this resonance at energies from 49 to 53 eV. This opens the possibility to generate intense attosecond pulses directly from the giant resonances, as well as to study these resonances using high-harmonic spectroscopy.

Multiple rescattering processes in high-order harmonic generation from molecular system

The molecular multiple rescattering processes have been theoretically investigated via solving the time-dependent Schrödinger equation. Not only has the physical model been established, but also the related rescatterings originating from recombination with parent nucleus and with neighboring nucleus have been distinguished. Moreover, it has shown that the rescatterings originating from recombination with parent nucleus are similar with those atomic rescatterings, while those rescatterings from recombination with neighboring nucleus both before and after reversing the direction of the laser field are more sensitive to the internuclear distance. With time-frequency distribution and classical electron dynamics, the underlying mechanisms are revealed.

Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation

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.

Bicircular High-Harmonic Spectroscopy Reveals Dynamical Symmetries of Atoms and Molecules

We introduce bicircular high-harmonic spectroscopy as a new method to probe dynamical symmetries of atoms and molecules and their evolution in time. Our approach is based on combining a circularly polarized femtosecond fundamental field of frequency ω with its counterrotating second harmonic 2ω. We demonstrate the ability of bicircular high-harmonic spectroscopy to characterize the orbital angular momentum symmetry of atomic orbitals. We further show that breaking the threefold rotational symmetry of the generating medium-at the level of either the ensemble or that of a single molecule-results in the emission of the otherwise parity-forbidden frequencies 3qω  (q∈N), which provide a background-free probe of dynamical molecular symmetries.

Effect of Initial Vibrational-State Excitation on Subfemtosecond Photodynamics of Water

We discuss the effect of initial vibrational-state excitation on the subfemtosecond photodynamics of water. Photoelectron spectra of Franck-Condon ionization to the (2)B1 state of the H2O(+) (D2O(+)) from the ground and several vibrationally excited states of the neutral are reported. Also calculated are ratios of the high-order harmonic generation (HHG) signals as a function of time for each initial vibrational state of the neutral molecule as predicted from the ratios of the square of the autocorrelation functions for D2O(+) and H2O(+). They reveal maxima as a function of time for each vibrational state of the neutral molecule. In turn, the HHG signals are found to be enhanced with vibrational excitation, with the calculated expectation values of the bond lengths and bond angle revealing quasiperiodic oscillations in time for all initial vibrational states of the neutral species. Although the bond lengths show only a marginal increase, the bond angle is found to be enhanced markedly by vibrational excitation, this being therefore responsible for the observed rise in the HHG signal.

Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.

Electrons in atoms exhibit many-body collective behaviours that can be studied by highbrightness X-rays from FELs. Here, the authors examine two-photon above threshold ionization of xenon and find that nonlinearities in the response uncover that more than one state underpins the 4d giant resonance.

Spatiotemporal isolation of attosecond soft X-ray pulses in the water window

Attosecond pulses at photon energies that cover the principal absorption edges of the building blocks of materials are a prerequisite for time-resolved probing of the triggering events leading to electronic dynamics such as exciton formation and annihilation. We demonstrate experimentally the isolation of individual attosecond pulses at the carbon K-shell edge (284 eV) in the soft X-ray water window with pulse duration below 400 as and with a bandwidth supporting a 30-as pulse duration. Our approach is based on spatiotemporal isolation of long-wavelength-driven harmonics and validates a straightforward and scalable approach for robust and reproducible attosecond pulse isolation.

Probing nuclear motion by frequency modulation of molecular high-order harmonic generation

Molecular high-order harmonic generation (MHOHG) in a non-Born-Oppenheimer treatment of H(2)(+), D(2)(+), is investigated by numerical simulations of the corresponding time-dependent Schrödinger equations in full dimensions. As opposed to previous studies on amplitude modulation of intracycle dynamics in MHOHG, we demonstrate redshifts as frequency modulation (FM) of intercycle dynamics in MHOHG. The FM is induced by nuclear motion using intense laser pulses. Compared to fixed-nuclei approximations, the intensity of MHOHG is much higher due to the dependence of enhanced ionization on the internuclear distance. The width and symmetry of the spectrum of each harmonic in MHOHG encode rich information on the dissociation process of molecules at the rising and falling parts of the laser pulses, which can be used to retrieve the nuclear dynamics. Isotope effects are studied to confirm the FM mechanism.

Universality of returning electron wave packet in high-order harmonic generation with midinfrared laser pulses

We show that a returning electron wave packet in high-order harmonic generation (HHG) with midinfrared laser pulses converges to a universal limit for a laser wavelength above about 3 μm. The results are consistent among the different methods: a numerical solution of the time-dependent Schrödinger equation, the strong-field approximation, and the quantum orbits theory. We further analyze how the contribution from different electron "trajectories" survives the macroscopic propagation in the medium. Our result thus provides a new framework for investigating the wavelength scaling law for the HHG yields.

Wavelength scaling of high harmonic generation close to the multiphoton ionization regime

We study the wavelength scaling of high harmonic generation efficiency with visible driver wavelengths in the transition between the tunneling and the multiphoton ionization regimes where the Keldysh parameter is around unity. Our experiment shows a less dramatic wavelength scaling of efficiency than the conventional case for near- and mid-IR driver wavelengths, and it is well explained by a generalized three-step model for increased Keldysh parameters that employs complex ionization times in addition to the nonadiabatic ionization. The complex ionization time is critical to avoid the divergence when replacing the quasistatic ionization model by the more general nonadiabatic ionization model. Together, the two modifications present a consistent description of the influence of the atomic potential on the rescattering process in the intermediate Keldysh regime.

Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media

We present a method for producing a single circularly polarized attosecond pulse by an intense few cycle elliptically polarized laser pulse combined with a terahertz field from numerical solutions of the time-dependent Schrödinger equation for the molecular ion H2(+). It is found that in the presence of a 62.5 THz (λ=4800  nm) field at an intensity of ∼10(14)  W/cm2, a single circularly polarized 114 as pulse can be generated by an elliptical polarized laser pulse at a wavelength of 400 nm with an ellipticity of ϵ=0.59. The efficiency of circular polarization attosecond pulse generation is interpreted based on a classical model of single electron recollision with the parent ion.

Multichannel molecular high-order harmonic generation from asymmetric diatomic molecules

Multichannel molecular high-order harmonic generation (MHOHG) from a single electron asymmetric molecular ion HeH2+ is investigated numerically. It is found that considerable resonant excitation occurs by laser induced electron transfer (LIET) to neighboring ions and multiple frequency (fractional-order) harmonics are observed from the excited states shifted by some energy Δ from the main Nω energy harmonics. A time series analysis is used to confirm this MHOHG channel which is created by initial ionization from the excited state prepared by LIET and recombination to the neighboring ion at specific field phases, resulting in interference between recombination pathways from ground and excited states.

Controlling the interference of multiple molecular orbitals in high-harmonic generation

We demonstrate a new method to investigate the origin of spectral structures in high-harmonic generation. We report detailed measurements of high-harmonic spectra in aligned nitrogen and carbon dioxide molecules. Varying the wavelength and intensity of the generating laser field, we show that the minimum in aligned N2 molecules is nearly unaffected, whereas the minimum in aligned CO2 molecules shifts over more than 15 eV. Our quantitative analysis shows that both the interference of multiple orbitals and their structural characteristics affect the position of the minimum. Our method provides a simple approach to the investigation of the high-harmonic generation process in more complex molecules.

Wavelength effect on atomic and molecular high harmonic generation driven by a tunable infrared parametric source

We experimentally investigate the wavelength effect on high-order harmonic generation (HHG) in CH(4) molecules and Xe atoms driven by a tunable infrared parametric source, and observe that the molecular HHG around the vibrational resonance is more sensitive to the driver wavelength than HHG from an atomic gas with comparable ionization potential. The results can be attributed to the light nuclear motion induced by the driving laser field, and it becomes possible to control the proton vibration in the molecular HHG by tuning the infrared wavelength of the driving laser.