Atomic High-harmonic Generation Research Articles

Analog Simulation of High-Harmonic Generation in Atoms

The demanding experimental access to the ultrafast dynamics of materials challenges our understanding of their electronic response to applied strong laser fields. For this purpose, trapped ultracold atoms with highly controllable potentials have become an enabling tool to describe phenomena in a scenario in which some effects are more easily accessible and 12 orders of magnitude slower. In this work, we introduce a mapping between the parameters of attoscience platforms and atomic cloud simulators and propose an experimental protocol to access the emission spectrum of high-harmonic generation, a regime that has so far been elusive to cold-atom simulation. As we illustrate, the benchmark offered by these simulators can provide new insights into the conversion efficiency of extended and short nuclear potentials, as well as the response to applied elliptical polarized fields or ultrashort few-cycle pulses. Published by the American Physical Society 2024

High Photon Number Entangled States and Coherent State Superposition from the Extreme Ultraviolet to the Far Infrared.

We present a theoretical demonstration on the generation of entangled coherent states and of coherent state superpositions, with photon numbers and frequencies orders of magnitude higher than those provided by the current technology. This is achieved by utilizing a quantum mechanical multimode description of the single- and two-color intense laser field driven process of high harmonic generation in atoms. It is found that all field modes involved in the high harmonic generation process are entangled, and upon performing a quantum operation, lead to the generation of high photon number optical cat states spanning from the far infrared to the extreme ultraviolet spectral region. This provides direct insights into the quantum mechanical properties of the optical field in the intense laser matter interaction. Finally, these states can be considered as a new resource for fundamental tests of quantum theory, quantum information processing, or sensing with nonclassical states of light.

Generation of optical Schrödinger cat states in intense laser–matter interactions

The physics of intense laser-matter interactions is described by treating the light pulses classically, anticipating no need to access optical measurements beyond the classical limit. However, the quantum nature of the electromagnetic fields is always present. Here, we demonstrate that intense laser-atom interactions may lead to the generation of highly non-classical light states. This was achieved by using the process of high-harmonic generation in atoms, in which the photons of a driving laser pulse of infrared frequency are up-converted into photons of higher frequencies in the extreme ultraviolet spectral range. The quantum state of the fundamental mode after the interaction, when conditioned on the high-harmonic generation, is a so-called Schr\"odinger cat state, which corresponds to a superposition of two distinct coherent states: the initial state of the laser and the coherent state reduced in amplitude that results from the interaction with atoms. The results open the path for investigations towards the control of the non-classical states, exploiting conditioning approaches on physical processes relevant to high-harmonic generation.

Wigner function analysis of high harmonic generation in atoms

The Wigner function provides the expression of phase space dynamics in quantum mechanics. In an application to non-linear optics, we describe its construction from time-dependent wavefunctions generated by numerical simulations, performed in both one and three dimensions, of the interaction of atoms with strong laser fields. From this analysis, the elements of the semi-classical three-step model of high-harmonic generation are extracted directly from the solution of the time-dependent Schrödinger equation. It is demonstrated that information contained in the Wigner function that is not relevant to this analysis may be removed by spatial filtering and state-projection operations.

How electronic dephasing affects the high-harmonic generation in atoms

In this work, we investigate how the high-harmonic generation (HHG) spectrum is affected by electronic dephasing applied to the quantum state of the emitter. By means of a theoretical and computational protocol based on quantum chemistry and the theory of open quantum systems, i.e. the stochastic Schrödinger equation [J. Chem. Phys. 148, 204112 (2018)], a study of dephasing on the harmonics of hydrogen and argon atoms is reported here. This approach provides a wave function-based insight on the coherence time of harmonics, from a purely point of view of the quantum state of the system irradiated by a laser. Interplay between dephasing time and the pulse parameters, as intensity and frequency, is also investigated for hydrogen. A reasonable agreement with literature data on argon atom is found. Future work will focus on the application of this computational approach to study the possible effect of dephasing on the HHG spectrum of molecules, and to investigate the interplay between plasmons and dephasing in the plasmon-enhanced HHG spectrum of Ar atoms in presence of metallic nanotips [Nature 453, 757 (2008)].

Subatomic scale study of atom-generated higher-order harmonic

<sec>The higher-order harmonics generated from an atom irradiated by ultarashort laser pulses is one of the important ways to obtain ultrashort attosecond pulses and coherent XUV sources. In order to produce a high-inntensity XUV source, one needs to study the mechanism of harmonic generation. The mechanism of the atomic high harmonic generation can be well understood by the semi-classical three-step model. First, the electron tunnels the barrier formed by the atomic potential and laser electric field, and then it propagates freely in the laser field and can be driven back to the mother ion where it recombines with the ground state of ion. Although the cutoff energy of the high harmonic can be predicted by this model, it cannot provide more information about the harmonic efficiency and the spectral structure. Recently, the generation mechanism of high harmonic has been studied by using the Bohmian trajectory scheme based on the time dependent wave packet. It is found that the harmonic structure can be reconstructed qualitatively by using a single Bohmian trajectory. The more accurate structure of harmonic spectrum needs more Bohmian trajectories. The calculation of these trajectories requires a lot of computation resources because the trajectory calculation is from the numerical solution for the time-dependent Schrödinger equation. In this work, we numerically solve the time-dependent Schrödinger equation of a model atom irradiated by ultrashort laser pulses. The time-dependent dipole moments at different spatial locations are calculated from the time-dependent wave function. The harmonic spectra are calculated from the Fourier transform of the time dipole moments. The harmonic spectra of different spatial locations show that the main emission positions of harmonic emission are near the nuclear region. One can observe the odd- and even-order harmonics at the different spatial positions. There has a larger radiation intensity for the integer-order harmonic. For the odd-order harmonics, their harmonic phases are the same on both sides of <i>x</i> = 0. For the even-order harmonics, their harmonic phases each have a pi difference on both side of <i>x</i> = 0. By using the filtering scheme, we analyze the phases of an harmonic at different spatial locations. It is found that the phase difference leads the odd-order harmonics to increase and the even-order harmonics to disappear. These findings contribute to the understanding of the physical mechanism of higher harmonic generated from an atom irradiated by strong laser pulses.</sec>

Finite-system effects on high-order harmonic generation: From atoms to solids

Using time-dependent density functional theory, high-harmonic generation (HHG) is studied in one-dimensional structures of sizes from a single nucleus up to hundreds of nuclei. The HHG cutoff is observed to extent linearly with the system size from the well known atomic HHG cutoff and is found to converge into the previously observed cutoffs for bulk solids only for large systems. A change in the response from that of single atoms or small molecules is observed from system sizes of $N$ $\approx$ 6 nuclei and becomes independent of system size at $N \gtrsim 60$. The system-size dependence of the observed HHG cutoffs is found to follow the limitations, set by the finite size solid, on the classical motion of electron-hole pairs. Because of the relation between recombination energy and electron-hole propagation length in the system, high-energy recombination events are not possible in small systems but become accessible for larger systems resulting in the change of the cutoff energies with system size. When varying the field intensity we observe that the cutoffs move linearly with the intensity even for small systems of $N\gtrsim 6$ that are far from the limit of a bulk solid.

Atomic-like high-harmonic generation from two-dimensional materials.

The generation of high-order harmonics from atomic and molecular gases enables the production of high-energy photons and ultrashort isolated pulses. Obtaining efficiently similar photon energy from solid-state systems could lead, for instance, to more compact extreme ultraviolet and soft x-ray sources. We demonstrate from ab initio simulations that it is possible to generate high-order harmonics from free-standing monolayer materials, with an energy cutoff similar to that of atomic and molecular gases. In the limit in which electrons are driven by the pump laser perpendicularly to the monolayer, they behave qualitatively the same as the electrons responsible for high-harmonic generation (HHG) in atoms, where their trajectories are described by the widely used semiclassical model, and exhibit real-space trajectories similar to those of the atomic case. Despite the similarities, the first and last steps of the well-established three-step model for atomic HHG are remarkably different in the two-dimensional materials from gases. Moreover, we show that the electron-electron interaction plays an important role in harmonic generation from monolayer materials because of strong local-field effects, which modify how the material is ionized. The recombination of the accelerated electron wave packet is also found to be modified because of the infinite extension of the material in the monolayer plane, thus leading to a more favorable wavelength scaling of the harmonic yield than in atomic HHG. Our results establish a novel and efficient way of generating high-order harmonics based on a solid-state device, with an energy cutoff and a more favorable wavelength scaling of the harmonic yield similar to those of atomic and molecular gases. Two-dimensional materials offer a unique platform where both bulk and atomic HHG can be investigated, depending on the angle of incidence. Devices based on two-dimensional materials can extend the limit of existing sources.

Similarities and differences between high-harmonic generation in atoms and solids

The basic features of high-harmonic generation in dilute atomic gases and solid-state systems are analyzed using a microscopic many-body theory. Whereas it is sufficient for atomic gases to include the ground state and the ionization continuum, the semiconductor approach has to deal with the relevant interband polarizations and intraband currents. For both systems, a closed set of Bloch-type equations is derived, which has to be solved numerically. As common features, the emission of odd-order harmonics, the development of a plateau, and a high-frequency cutoff are observed if the solid system is modeled as a two-band system. However, already the addition of a third coupled band effectively breaks the inversion symmetry and leads to the appearance of even harmonic orders with comparable strength. In all cases, frequency- and time-resolved studies reveal a fundamentally different timing in the emission dynamics of the individual frequency components in atomic and solid-state systems, which can be attributed to the presence of energy bands in solids.

High-Harmonic Generation in Solids: Bridging the Gap Between Attosecond Science and Condensed Matter Physics

We review recent progress in understanding the dominant mechanism driving high-harmonic generation in solids. Three-dimensional two-band single active electron calculations predict that the major emission arises from the recombination of electron-hole pairs upon their creation and acceleration in the laser field, in analogy to atomic high-harmonic generation. The main goal of this study is to review a simple quasi-classical trajectory formalism and use it to better understand the fundamental properties of high-harmonic generation in solids and how they compare to high-harmonic generation in atomic and molecular gases. The simple formalism presents a valuable tool for extending attosecond science from the gas to the condensed matter phase. This is demonstrated by discussing the potential synthesis of attosecond pulses from solids.

Theory of high-harmonic generation in solids

High-harmonic generation (HHG) in bulk crystals exposed to intense mid-infrared lasers with photon energies below the bandgap is investigated theoretically. A three dimensional, two-band model that considers both interband and intraband currents is used. It is shown that the interband current is the dominant mechanism for HHG in solids. A physical interpretation of interband HHG – similar to atomic HHG – is provided by saddle point analysis. The effects of dephasing time and driving field wavelength on the harmonic specrum are investigated.

Semiclassical analysis of high harmonic generation in bulk crystals

High harmonic generation (HHG) in solids is investigated. We find that interband emission is dominant for the midinfrared laser driver frequencies, whereas intraband emission dominates the far-infrared range. Interband HHG is similar to atomic HHG and therewith opens the possibility to apply atomic attosecond technology to the condensed matter phase. Interband emission is investigated with a quasiclassical method, by which HHG can be modeled based on the classical trajectory analysis of electron-hole pairs. This analysis yields a simple approximate cutoff law for HHG in solids. Differences between HHG in atoms and solids are identified that are important for adapting atomic attosecond technology to make it applicable to condensed matter.

Theoretical analysis of high-harmonic generation in solids.

We investigate theoretically high-harmonic generation (HHG) in bulk crystals exposed to intense midinfrared lasers with photon energies smaller than the band gap. The two main mechanisms, interband and intraband HHG, are explored. Our analysis indicates that the interband current neglected so far is the dominant mechanism for HHG. Saddle point analysis in the Keldysh limit yields an intuitive picture of interband HHG in solids similar to atomic HHG. Interband and intraband HHG exhibit a fundamentally different wavelength dependence. This signature can be used to experimentally distinguish between the two mechanisms in order to verify their importance.

Spin–orbit effects in atomic high-harmonic generation

Spin–orbit interactions lead to small energy gaps between the outermost p1/2 and p3/2 shells of noble gas atoms. Strong-field pulses tunnel-ionize an electron out of either shell resulting in spin–orbit-driven hole motion. These hole dynamics affect the high-harmonic generation (HHG) yield. However, the spectral shape as well as the angular distribution of the HHG emission is not influenced by spin–orbit coupling. We demonstrate the spin–orbit effect on atomic krypton by solving the multi-electron Schrödinger equation with the time-dependent configuration-interaction singles approach. We also provide pulse parameters where this effect can be identified in experiments through an enhancement in the HHG yield as the wavelength of the strong-field pulse increases.

HIGH HARMONIC GENERATION IN ATOMS, MOLECULES AND NANOSTRUCTURES

High harmonic generation (HHG) has attracted tremendous attention over two decades. This paper presents a brief review of high harmonic generation in atoms, molecules and nanostructures. Through a simple classical model, we first review a few important concepts in HHG. We then discuss how the electric field initial phase affects the harmonic yield, and explain the reason behind the cutoff law. We focus on HHG in nanostructures. As an example, a detailed calculation in C 60 is presented.

Ultrahigh Harmonics from Laser-Assisted Ion-Atom Collisions

We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.

X-ray amplification by laser controlled coherent bremsstrahlung.

A coherent x-ray generation scheme is proposed which involves characteristics of free electron lasers and atomic high harmonic generation schemes. A thin solid layer or any other periodic atomic structure with limited dimensions is exposed to a short, superintense laser pulse. The electrons are extracted from the layer due to the extreme force and penetrate periodically through the ionic structure. Consequently, thousands of harmonics of the laser radiation field are shown to coherently amplify along the interaction length. The small signal gain of the generated x-ray radiation exceeds that arising from the multiphoton Compton process in plasmas and is competitive with that in the leading x-ray free electron lasers.