Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses

Ionization and recombination times of high-order harmonic generation with single-photon ionization

We theoretically study high-order harmonic generation (HHG) involving an extreme ultraviolet (XUV) pulse and an intense infrared driving field, where the electron is ionized by absorbing a single XUV photon. Using a developed classical-trajectory model that includes Coulomb effects and the improved initial conditions, it is demonstrated that the resulting harmonic emission times match well with those obtained by applying the Gabor transform to data from numerical solutions of time-dependent Schrödinger equations for helium and hydrogen atoms. This confirms a classical HHG scheme under single-photon ionization: The electron, ionized by absorbing one XUV photon, oscillates in the infrared field and may recollide with the parent ion, emitting high-frequency radiation. Therefore, the classical model can determine the ionization and recombination times of the electron in single-photon-ionization HHG. Our work shows great promise for resolving electron dynamics using high-order harmonic spectroscopy under single-photon ionization.

Laser excitation of the 1S-2S transition in singly-ionized helium

Laser spectroscopy of atomic hydrogen and hydrogen-like atoms is a powerful tool for tests of fundamental physics. The 1S-2S transition of hydrogen in particular is a cornerstone for stringent Quantum Electrodynamics (QED) tests and for an accurate determination of the Rydberg constant. We report laser excitation of the 1S-2S transition in singly-ionized helium (3He+), a hydrogen-like ion with much higher sensitivity to QED than hydrogen itself. The transition requires two-photon excitation in the challenging extreme ultraviolet wavelength range, which we achieve with a tabletop coherent laser system suitable for precision spectroscopy. The transition is excited by combining an ultrafast amplified pulse at 790 nm (derived from a frequency comb laser) with its 25th harmonic at 32 nm (produced by high-harmonic generation). The results are well described by our simulations and we achieve a sizable 2S excitation fraction of 10-4 per pulse, paving the way for future precision studies.

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.

On the Analysis of High Harmonic Generation Spectra of Atoms and Molecules Using Molecular Electrostatic Potential

One of the factors that limits the application of the single active electron (SAE) formalism to simulate the high harmonic generation (HHG) spectra of atoms and molecules using the time-dependent Schrödinger equation (TDSE) is the unknown model effective one-dimensional potential energy (V(x)) curve for the SAE. In the present contribution, we show that V(x) can be constructed from the one-dimensional molecular electrostatic potential (MEP) of the respective cation to access theoretical HHG spectra not only for simple atoms but also for multielectron complex molecules.

Parametric attosecond pulse amplification far from the ionization threshold from high order harmonic generation in He. OPTICS EXPRESS 2020;28:24243-24252. [PMID: 32752406 DOI: 10.1364/oe.398595]

Parametric amplification of attosecond coherent pulses around 100 eV at the single-atom level is demonstrated for the first time by using the 3D time-dependent Schrödinger equation in high-harmonic generation processes from excited states of He⁺. We present the attosecond dynamics of the amplification process far from the ionization threshold and resolve the physics behind it. The amplification of a particular central photon energy requires the seed XUV pulses to be perfectly synchronized in time with the driving laser field for stimulated recombination to the He⁺ ground state and is only produced in a few specific laser cycles in agreement with the experimental measurements. Our simulations show that the amplified photon energy region can be controlled by varying the peak intensity of the laser field. Our results pave the way to the realization of compact attosecond pulse intense XUV lasers with broad applications.

Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

Enhanced high-harmonic generation up to the soft X-ray region driven by mid-infrared pulses mixed with their third harmonic

We systematically study the efficiency enhancement of high-harmonic generation (HHG) in an Ar gas cell up to the soft X-ray (SXR) range using a two-color laser field composed of 2.1 μm (ω) and 700 nm (3ω) with parallel linear polarization. Our experiment follows the recent theoretical investigations that determined two-color mid-infrared (IR) pulses, mixed with their third harmonic (ω + 3ω), to be close to optimal driving waveforms for enhancing HHG efficiency in the SXR region [Jin et al., Nature Comm. 5, 4003 (2014)]. We observed sub-optical-cycle-dependent efficiency enhancements of up to 8.2 of photon flux integrated between 20 - 70 eV, and up to 2.2 between 85 - 205 eV. Enhancement of HHG efficiency was most pronounced for the lowest tested backing pressure (≈ 140 mbar), and decreased monotonically as the pressure was increased. The single-color (ω)-driven HHG was optimal at the highest backing pressure tested in the experiment (≈ 375 mbar). Our numerical simulations based on single-atom response and 3D pulse propagation show good qualitative agreement with experimental observations. The lower enhancement at high pressure and higher photon energy indicates that phase matching of two-color-driven HHG is more sensitive to ionization rate and pulse propagation effects than the single-color case. We show that with further improvements to the relative phase jitter and the spatio-temporal overlap of the two beams, the efficiency enhancement could be further improved by at least a factor of ≈ 2.

Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields: the role of Rydberg states

The bi-circular scheme for high harmonic generation, which combines two counter-rotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the weak effects of dynamical symmetry breaking caused by finite pulse duration are amplified by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.

High-Harmonic Generation Enhanced by Dynamical Electron Correlation

We theoretically study multielectron effects in high-harmonic generation (HHG), using all-electron first-principles simulations for a one-dimensional model atom. In addition to the usual plateau and cutoff (from a cation in the present case, since the neutral is immediately ionized), we find a prominent resonance peak far above the plateau and a second plateau extended beyond the first cutoff. These features originate from the dication response enhanced by orders of magnitude due to the action of the Coulomb force from the rescattering electron, and, hence, are a clear manifestation of electron correlation. Although the present simulations are done in 1D, the physical mechanism underlying the dramatic enhancement is expected to hold also for three-dimensional real systems. This will provide new possibilities to explore dynamical electron correlation in intense laser fields using HHG, which is usually considered to be of single-electron nature in most cases.

High-order harmonic generation from Rydberg atoms in inhomogeneous fields

We theoretically investigate the high-order harmonic generation (HHG) from Rydberg atoms considering the spatial inhomogeneity of the driving field. It is found that in the inhomogeneous field, the effect of the cutoff extension in the harmonic spectrum from Rydberg atoms can be extended to multi-cycle regime, while in the homogeneous field case, the extension of the harmonic cutoff is limited to the few-cycle regime (less than two optical cycles). The underlying physics of the cutoff extension from Rydberg atoms in the inhomogeneous field is analyzed based on the classical and quantum-mechanical models. Furthermore, by optimizing the field inhomogeneity, the electron dynamics can be well controlled to generate a smooth supercontinuum in the extended spectral region. This can support the efficient generation of isolated attosecond pulses in Rydberg atoms from multi-cycle laser fields.

Parametric amplification of attosecond pulse trains at 11 nm

We report the first experimental demonstration of the parametric amplification of attosecond pulse trains at around 11 nm. The helium amplifier is driven by intense laser pulses and seeded by high-order harmonics pulses generated in a neon gas jet. Our measurements suggest that amplification takes place only if the seed pulse-trains are perfectly synchronized in time with the driving laser field in the amplifier. Varying the delay, we estimate the durations of the individual extreme ultraviolet pulses within the train to be on the order of 0.2 fs. Our results demonstrate that strong-field parametric amplification can be a suitable tool to amplify weak attosecond pulses from non-destructive pump-probe experiments and it is an important step towards designing amplifiers for realization of energetic XUV pulses with sub-femtosecond duration using compact lasers fitting in university laboratories.

Computational efficiency improvement with Wigner rotation technique in studying atoms in intense few-cycle circularly polarized pulses

We show that by introducing Wigner rotation technique into the solution of time-dependent Schrödinger equation in length gauge, computational efficiency can be greatly improved in describing atoms in intense few-cycle circularly polarized laser pulses. The methodology with Wigner rotation technique underlying our openMP parallel computational code for circularly polarized laser pulses is described. Results of test calculations to investigate the scaling property of the computational code with the number of the electronic angular basis function l as well as the strong field phenomena are presented and discussed for the hydrogen atom.

Coherent extreme ultraviolet light amplification by strong-field-enhanced forward scattering

We theoretically study the response of He atoms exposed simultaneously to an intense IR pulse and a weak extreme ultraviolet (XUV) pulse with photon energies far from the principal atomic He resonances. We find that XUV forward scattering from the nonstationary electronic wave packet promoted by the intense IR driving field is strongly enhanced as compared with the normal weak scattering from bound or free electrons. Based on this effect, we predict that large amplification of XUV radiation can be achieved in the cutoff spectral region of high-harmonic generation in He gas.

Efficient high-order harmonic generation boosted by below-threshold harmonics

High-order harmonic generation (HHG) in gases has been established as an important technique for the generation of coherent extreme ultraviolet (XUV) pulses at ultrashort time scales. Its main drawback, however, is the low conversion efficiency, setting limits for many applications, such as ultrafast coherent imaging, nonlinear processes in the XUV range, or seeded free electron lasers. Here we introduce a novel scheme based on using below-threshold harmonics, generated in a “seeding cell”, to boost the HHG process in a “generation cell”, placed further downstream in the focused laser beam. By modifying the fundamental driving field, these low-order harmonics alter the ionization step of the nonlinear HHG process. Our dual-cell scheme enhances the conversion efficiency of HHG, opening the path for the realization of robust intense attosecond XUV sources.

Optimization of three-color laser field for the generation of single ultrashort attosecond pulse

We present an efficient and realizable scheme for the generation of an ultrashort single attosecond (as) pulse. The feasibility of such a scheme is demonstrated by solving accurately the time-dependent Schrödinger equation using the time-dependent generalized pseudospectral (TDGPS) method. This scheme involves the use of the optimization of the three-color laser fields. The optimized laser pulse is synthesized by three one-color laser pulses with proper relative phases. It can provide a longer acceleration time for the tunneling and oscillating electrons, and allows the electrons to gain more kinetic energy. We show that the plateau of high-order harmonic generation is extended dramatically and a broadband supercontinuum spectra is produced. As a result, an isolated 23 as pulse with a bandwidth of 163 eV can be obtained directly by superposing the supercontinuum harmonics near the cutoff region. We will show that such a metrology can be realized experimentally.

ENHANCEMENT AND EXTENSION OF HIGH-ORDER HARMONIC EMISSION AND AN ISOLATED SUB-100 AS PULSE GENERATION FROM TWO-COLOR LASER FIELDS

We theoretically propose a method to generate a coherent and ultrabroad extreme ultraviolet supercontinuum using Ar + ions. When the medium is exposed to a two-color laser field, which is synthesized by a few-cycle fundamental laser pulse and its second-harmonics pulse, the harmonics spectrum presents a two-plateau structure. For the selection of the short quantum path utilizing the two-color scheme, the supercontinuum in the second plateau is almost synchronously emitted and a single 58 attosecond (as) pulse can be directly obtained. By increasing the intensity of the controlling field or adjusting the delay time of the two laser fields, a more intense isolated as pulse will be generated.

High-order harmonic generation enhanced by XUV light

The combination of high-order harmonic generation (HHG) with resonant XUV excitation of a core electron into the transient valence vacancy that is created in the course of the HHG process is investigated theoretically. In this setup, the first electron performs a HHG three-step process, whereas the second electron Rabi flops between the core and the valence vacancy. The modified HHG spectrum due to recombination with the valence and the core is determined and analyzed for krypton on the 3d→4p resonance in the ion. We assume an 800 nm laser with an intensity of about 10(14) W/cm2 and XUV radiation from the Free Electron Laser in Hamburg (FLASH) with an intensity in the range 10(13)-10(16)W cm2. Our prediction opens perspectives for nonlinear XUV physics, attosecond x rays, and HHG-based spectroscopy involving core orbitals.

Attochirp-free high-order harmonic generation

A method is proposed for arbitrarily engineering the high-order harmonic generation phase achieved by shaping a laser pulse and employing xuv light or x rays for ionization. This renders the production of bandwidth-limited attosecond pulses possible while avoiding the use of filters for chirp compensation. By adding the first 8 Fourier components to a sinusoidal field of 1016 W/cm2, the bandwidth-limited emission of 8 as is shown to be possible from a Li2+ gas. The scheme is extendable to the zs-scale.

Intense isolated attosecond pulse generation in pre-excited medium

We present a theoretical study of isolated attosecond pulse generation in pre-excited medium driven by an intense few-cycle laser pulse. We show that the generation of the macroscopic xuv supercontinuum is governed by the initial population of the excited state. Large initial population of the excited state leads to the high density of the free electrons in the media and strongly changes macroscopic properties of the driving pulse and the supercontinuum, and diminishes the isolated attosecond pulse generation. Instead, small initial population of 5% in the pre-excited media subjected to the few-cycle driving pulse can produce well phase-matched xuv supercontinuum, and a pure intense isolated attosecond pulse with the pulse duration of approximately 150 as and the pulse energy up to 0.5 nJ is directly obtained.

Role of autoionizing state in resonant high-order harmonic generation and attosecond pulse production

We suggest a high-order harmonic generation (HHG) model describing enhancement of the generation efficiency for the harmonic resonant with the transition between the ground and autoionizing state of the generating ion. The results of numerical and analytical calculations based on this model are in good quantitative agreement with the experiments showing HHG enhancement up to 2 orders of magnitude. Moreover, this model reproduces well the essential difference in HHG efficiency for different ions. We show that intense but relatively long attosecond pulses can be generated using the enhanced harmonics.

Carrier-envelope phase measurement from half-cycle high harmonics

We present an efficient method to observe the high harmonics generated in individual half-cycle of the driving laser pulse by mixing a weak ultraviolet pulse, and then the cutoff of each half-cycle harmonic is imaged. The simulation shows that the information of the driving laser pulse, including the laser intensity, pulse duration and carrier-envelope phase, can be in situ retrieved from the harmonic spectrogram. In addition, our results show that this method also distinguishes the half-cycle high harmonics for a pulse longer than 10 fs, suggesting a potential to extend the CEP measurement to the multi-cycle regime.

Dramatic enhancement of high-order harmonic generation

We present a dramatic enhancement [Phys. Rev. Lett. 91, 043002 (2003)] of high-order harmonic generation by simultaneous irradiation of booster harmonics. A key feature of our experiment is the use of mixed gases (Xe and He) with different ionization energies. The harmonics from Xe atoms act as a booster to increase the harmonic yield from He by a factor of 4 x 10(3). The dominance of the dramatic enhancement effect is supported by simulation with the time-dependent Schrödinger equation as well as the observed spatial characteristic of the generated harmonics and dependence on medium conditions.

Destructive interference during high harmonic generation in mixed gases

We report on the first experimental evidence of the destructive and constructive interference of high harmonics generated in a mixed gas of He and Ne, which facilitates the coherent control of high harmonic generation. Theoretically, we develop an analytical model of high harmonic generation in mixed gases and succeed in reproducing the experimental results and deriving the optimization conditions for the process. The observed interference modulation is attributed to the difference between the phases of the intrinsically chirped harmonic pulses from He and Ne, which leads to a novel method for broadband measurement of the harmonic phases and for observing the underlying attosecond electron dynamics.