High Harmonic Generation Process Research Articles

Entanglement and Squeezing of the Optical Field Modes in High Harmonic Generation.

Squeezed optical fields are a powerful resource for a variety of investigations in basic research and technology. However, the generation of intense squeezed light is challenging. Here, we show that intense squeezed light can be produced using strongly laser driven atoms and the so far unrelated process of high harmonic generation. We demonstrate that when the intensity of the driving field significantly depletes the ground state of the atoms, leading to dipole moment correlations, the quantum state of the driving field and the generated high harmonics are entangled and squeezed. Furthermore, we analyze how the resulting quadrature squeezing of the fundamental laser mode after the interaction can be controlled. The findings open the way for the generation of high intensity squeezed light states for a wide range of applications.

Theoretical analysis of perturbative high harmonic wave mixing from plasma surfaces

High harmonic generation modulated by a weakly perturbing laser field enables new wave mixing frequency components, thus allowing in-situ spatiotemporal measurements and wavefront control of attosecond optical pulses. However, perturbative high harmonic wave mixing from plasma surfaces has not been investigated extensively. In this study, we theoretically analyze the plasma high harmonic generation process in the relativistic regime modulated by a perturbing laser field with an arbitrary frequency. New wave mixing frequency components satisfying the conservation laws of photon energy and momentum are observed. The wave mixing component intensities adhere to a power law for the perturbating laser photon number as the perturbing laser intensity increases, thereby revealing perturbative behaviors in the nonperturbative, extremely nonlinear optical process of high harmonic generation. Detailed studies reveal the polarization selection rule and physical mechanism of high harmonic wave mixing. The modulation of the relativistic factor or mass enhancement of electrons on the plasma surface by the perturbing laser field is believed to result in high harmonic wave mixing in the relativistic regime.

Tracking Charge Migration with Frequency-Matched Strobo-Spectroscopy.

We present frequency-matched strobo-spectroscopy (FMSS) of charge migration (CM) in bromobutadiyne, simulated with time-dependent density functional theory. CM + FMSS is a pump-probe scheme that uses a frequency-matched high harmonic generation (HHG)-driving laser as an independent probe step, following the creation of a localized hole on the bromine atom that induces CM dynamics. We show that the delay-dependent harmonic yield tracks the phase of the CM dynamics through its sensitivity to the amount of electron density on the bromine end of the molecule. FMSS takes advantage of the intrinsic attosecond time resolution of the HHG process in which different harmonics are emitted at different times and thus probe different locations of the electron hole. Finally, we show that the CM-induced modulation of the HHG signal is dominated by the recombination step of the HHG process, with a negligible contribution from the ionization step.

Investigation of High Harmonic Generation in Ar-Ne Gas Mixture

"In this study, we experimentally investigate the variation of the phase matching condition of the high harmonic generation (HHG) process with pure argon gas and an argon-neon gas mixture. Phase-matched HHG is generated around the absorption edge of argon gas and then neon gas is added to the original argon gas. The pressure-dependent intensity of the harmonics produced by pure argon gas and the gas mixture is examined. We show that as more neon gas is added to the mixture, the phase matching of the higher order harmonics is less favourable than that of the lower order harmonics. Finally, the total phase mismatch at various gas mixture pressures is discussed. Our experimental results are in agreement with the theoretical calculation."

Disorder-induced effects in high-harmonic generation process in fullerene molecules

The objective of this article is to investigate the profound nonlinear optical response exhibited by inversion symmetric fullerene molecules under the influence of different types of disorders described by the Anderson model. Our aim is to elucidate the localization effects on the spectra of high harmonic generation in such molecules. We show that the disorder-induced effects are imprinted onto molecules’ high-harmonic spectrum. Specifically, we observe a presence of strong even-order harmonic signals already for relatively small disorders. The odd-order harmonics intrinsic for disorder-free systems are generally robust to minor disorders. Both diagonal and off-diagonal disorders lift the degeneracy of states, opening up new channels for interband transitions, leading to the enhancement of the high-harmonic emission. The second harmonic signal has a special behavior depending on the disorder strength. Specifically in the case of diagonal disorder, the second harmonic intensity exhibits a quadratic scaling with the disorder strength, which enables the usage of the harmonic spectrum as a tool in measuring the type and the strength of a disorder.

Wavelength scaling of high harmonic yields and cutoff energies in solids driven by mid-infrared pulses.

The effect of driving wavelengths on high harmonic generation (HHG) have long been a fundamental research topic. However, despite of abundant efforts, the investigation of wavelength scaling of HHG in solids is still confined within the scope of theoretical predictions. In this work, we for the first time to the best of our knowledge, experimentally reveal wavelength scaling of HHG yields and cutoff energy in three typical solid media (namely pristine crystals GaSe, CdTe and polycrystalline ZnSe), driven in a broad mid-infrared (MIR) range from 4.0 to 8.7 µm. It is revealed that when the driving wavelength is shorter than 6.5-7.0 µm, HHG yields decrease monotonously with the MIR driving wavelengths, while they rise abruptly by 1-3 orders of magnitude driven at longer wavelength and exhibit a crest at 7.5 µm. In addition, the cutoff energies are found independent on driving wavelengths across the broad MIR pump spectral range. We propose that the interband mechanism dominates the HHG process when the driving wavelength is shorter than 6.5-7.0 µm, and as the driving wavelength increases, intraband contribution leads to an abrupt rise of the HHG yields, which is verified by the HHG polarization measurement driven at 3.0 and 7.0 µm. This work not only experimentally demonstrate the wavelength scaling of HHG in solids, but more importantly blazes the trail for optimizing the HHG performance by choosing a driving wavelength and provides experimental method to distinguish the interband and intraband dynamics.

Multiphoton excitation and high harmonic generation in rectangular graphene quantum dot

The multiphoton excitation and high harmonic generation (HHG) processes are considered using the microscopic quantum theory of nonlinear interaction of strong coherent electromagnetic (EM) radiation with rectangular graphene quantum dot (RGQD). The dynamic Hartree–Fock approximation is developed for the consideration of the quantum dot-laser field nonlinear interaction at the nonadiabatic multiphoton excitation regime. The many-body Coulomb interaction is described in the extended Hubbard approximation. By numerical results, we show the significance of the RGQD lateral size, shape, and EM wavefield orientation in RGQD of the zigzag edge compear to the armchair edge in the HHG process allowing for increasing the cutoff photon energy and the quantum yield of higher harmonics. The differences via edge on the elongated side of the RGQD have been explained by the investigation of the dipole momentum in both cases. Numerical results have shown that the HHG spectra have a strong anisotropy depending on the orientation of the laser wave, and the cutoff photon energy shifts toward blue with an increase in the transverse size of the RGQD.

Diagnosing the waveform of an ultrashort optical pulse by collinear interferometry

During the high-harmonic generation (HHG) process, information about field interaction with the medium is imprinted in the extreme ultraviolet (XUV) radiation. Here, we present a method for using HHG to diagnose the electric field of an optical pulse under a collinear geometry. When mixing a weak signal pulse with a strong driving pulse collinearly, the far field divergence of the XUV HHG is sensitive to the relative delay between the two pulses, which can be used as an ultrafast subcycle gate to reconstruct the electric field of the signal pulse. This collinear configuration is efficient, easy to operate and avoids artificial high order frequency components in reconstruction as compared to non-collinear schemes.

Realization of a Cost-Effective Deformable Grating for the Extreme-Ultraviolet

The application of a deformable grating to the realization of a time delay compensated monochromator is presented. The grating is realized as a replica on a thin glass substrate and the deformation is realized with a mechanical bender. The monochromator is conceived for the spectral selection of a single harmonic in the spectral range 20-80 nm in beamlines exploiting the high harmonic generation process. A possible optical design requiring only two deformable gratings, a mirror and an intermediate slit is presented.

Generation of isolated intense vortex laser with transverse angular momentum

A scheme is proposed to explore the generation of isolated intense vortex laser pulse with transverse angular momentum (AM), which implies that the total AM is non-collinear with the propagation direction. When two non-collinear vortex beams impinge on a solid thin target symmetrically on the same side, the generated harmonics containing the contributions of the two input pulses are emitted from the target at a predicted angle. The longitudinal AM of the harmonics can be predicted from the AM conservation regarding the photons involved in the high-harmonic generation process. The asymmetry of the energy flux in the vertical direction is confirmed as the transverse AM generation source. As an example, the related phenomenon of the fourth order harmonic has been well confirmed by theoretical analysis and three-dimensional particle-in-cell simulations.

High harmonic generation with many-body Coulomb interaction in rectangular graphene quantum dots of armchair edge

High harmonic generation (HHG) in graphene quantum dots of armchair edge by strong coherent electromagnetic radiation taking into account collective electron-electron scattering as well in such nanosystems is considered. The microscopic quantum theory describing the plane quantum dot-laser field nonlinear interaction within the dynamic Hartree–Fock approximation is developed. The many-body Coulomb interaction is considered in the extended Hubbard approximation. The obtained results indicate the significance of the nanostructure lateral size, shape, and bandgap width in HHG process that allows to increase in the quantum yield of high-order harmonics and the cutoff photon energy.

Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy

We explore pump-probe high harmonic generation (HHG) from monolayer hexagonal-boron-nitride, where a terahertz pump excites coherent optical phonons that are subsequently probed by an intense infrared pulse that drives HHG. We find, through state-of-the-art ab initio calculations, that the structure of the emission spectrum is attenuated by the presence of coherent phonons and no longer comprises discrete harmonic orders, but rather a continuous emission in the plateau region. The HHG yield strongly oscillates as a function of the pump-probe delay, corresponding to ultrafast changes in the lattice such as specific bond compression or stretching dynamics. We further show that in the regime where the excited phonon period and the pulse duration are of the same order of magnitude, the HHG process becomes sensitive to the carrier-envelope phase (CEP) of the driving field, even though the pulse duration is so long that no such sensitivity is observed in the absence of coherent phonons. The degree of CEP sensitivity versus pump-probe delay is shown to be a highly selective measure for instantaneous structural changes in the lattice, providing an approach for ultrafast multidimensional HHG spectroscopy. Remarkably, the obtained temporal resolution for phonon dynamics is ∼1 femtosecond, which is much shorter than the probe pulse duration because of the inherent subcycle contrast mechanism. Our work paves the way toward routes of probing phonons and ultrafast material structural changes with subcycle temporal resolution and provides a mechanism for controlling the HHG spectrum.

Saddle-point exciton signature on high-order harmonic generation in two-dimensional hexagonal nanostructures

The disclosure of basic nonlinear optical properties of graphene-like nanostructures with correlated electron-hole nonlinear dynamics over a wide range of frequencies and pump field intensities is of great importance for both graphene fundamental physics and for the expected novel applications of two-dimensional (2D) hexagonal nanostructures in extreme nonlinear optics. In the current paper, the nonlinear interaction of 2D hexagonal nanostructures with the bichromatic infrared driving field taking into account the many-body Coulomb interaction is investigated. Numerical investigation in the scope of the Bloch equations within the Houston basis that take into account $e\text{--}e$ and $e\text{--}h$ interactions in the Hartree-Fock approximation reveals significant excitonic effects in the high-harmonic generation process in 2D hexagonal nanostructures such as graphene and silicene. It is shown that, due to the correlated electron-hole nonlinear dynamics around the van Hove singularity, spectral caustics in the high-harmonic generation spectrum are induced near the saddle-point excitonic resonances.

Ultrahızlı Optik Darbeler Kullanılarak Azot Molekülünden Yüksek Mertebeli Harmonik Üretimi

Generation of coherent extreme ultraviolet (XUV) pulses is a nonlinear process of high harmonic generation (HHG). HHG produced in molecular nitrogen (N2) medium has been obtained using ultrashort intense laser pulses. The strong laser field was focused onto a gas cell to produce short wavelengths having photon energy up to 54 eV. The highest photon energy is experimentally observed as the 35th order. The absorption of harmonics restricts the harmonic yield efficiency. The harmonic yield is affected by the interaction length and medium pressure. The harmonic yield changes with the medium parameters. The simulation for the absorption length was performed using the Mathematica program. Variation of the harmonic signal has been attributed to the absorption of harmonics, and it is compared with the absorption length.

Probing nonadiabatic dynamics with attosecond pulse trains and soft x-ray Raman spectroscopy.

Linear off-resonant x-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explore different combination schemes for the probe pulse as well as the impact of parameters of the pulse trains on the signals. Furthermore, we show how Raman selection rules and symmetry consideration affect the spectroscopic signal, and we discuss the importance of vibrational contributions to the overall signal. We use two different model systems, representing molecules of different symmetries, and quantum dynamics simulations to study the difference in the spectra. The results suggest that such pulse trains are well suited to capture the key features associated with the electronic coherence.

Role of long-range correlations in high harmonic generation in disordered systems

The mechanism of high harmonic generation (HHG) from condensed matter driven by ultrafast lasers is far from being understood due to the structural diversity and complexity. One of the long-standing open questions is the effect of random disorder in noncrystal HHG. In this work, we identify the critical role of correlations in disordered semiconductor systems and propose them as the criterion to classify the HHG processes. The HHG spectra can be classified into two different categories corresponding to different correlations: short-range correlation and long-range correlation (LRC). Thus correlations build up a solid relationship between the HHG emission and statistical characteristics of a disordered system. In particular, the HHG spectrum from the disordered system with LRC exhibits remarkable consistency with the spectrum from the periodic lattice, revealing that the LRC links HHG processes in disordered and periodic systems. Besides, the mobility edge induced by the long-range correlated disorder enables us to study the behavior of localized- and delocalized-state HHG in one system.

Improved stabilization scheme for extreme ultraviolet quantum interference experiments

Interferometric pump–probe experiments in the extreme ultraviolet (XUV) domain are experimentally very challenging due to the high phase stability required between the XUV pulses. Recently, an efficient phase stabilization scheme was introduced for seeded XUV free electron lasers (FELs) combining shot-to-shot phase modulation with lock-in detection Wituschek et al (2020 Nat. Commun. 11 883). This method stabilized the seed laser beampath on the fundamental ultraviolet wavelength to a high degree. Here, we extend this scheme including the stabilization of the XUV beampath, incorporating phase fluctuations from the FEL high gain harmonic generation process. Our analysis reveals a clear signal improvement with the new method compared to the previous stabilization scheme.

Ultrafast magnetic scattering on ferrimagnets enabled by a bright Yb-based soft x-ray source

Development of ultrafast table-top x-ray sources that can map various spin, orbital, and electronic configurations and reordering processes on their natural time and length scales is an essential topic for modern condensed matter physics as well as ultrafast science. In this work, we demonstrate spatiotemporally resolved resonant magnetic scattering (XRMS) to probe the inner-shell 4d electrons of a rare-earth (RE) composite ferrimagnetic system using a bright > --> 200 e V soft x-ray high harmonic generation (HHG) source, which is relevant for future energy-efficient, high-speed spintronic applications. The XRMS is enabled by direct driving of the HHG process with power-scalable, high-energy Yb laser technology. The optimally phase-matched broadband plateau of the HHG offers a record photon flux ( > --> 2 × 1 0 9 p h o t o n s / s / 1 % bandwidth) with excellent spatial coherence and covers the entire resonant energy range of RE’s N 4 , 5 edges. We verify the underlying physics of our x-ray generation strategy through the analysis of microscopic and macroscopic processes. Using a CoTb alloy as a prototypical ferrimagnetic system, we retrieve the spin dynamics, and resolve a fast demagnetization time of 500 ± 126 f s , concomitant with an expansion of the domain periodicity, corresponding to a domain wall velocity of ∼ 750 m / s . The results confirm that, far from cross-contamination of low-energy absorption edges in multi-element systems, the highly localized states of 4 d electrons associated with the N 4 , 5 edges can provide high-quality core-level magnetic information on par with what can be obtained at the M edges, which is currently accessible only at large-scale x-ray facilities. The analysis also indicates the rich material-, composition-, and probing-energy-dependent driving mechanism of RE-associated multicomponent systems. Considering the rapid emergence of high-power Yb lasers combined with novel nonlinear compression technology, this work indicates potential for next-generation high-performance soft x-ray HHG-based sources in future extremely photon-hungry applications on the table-top scale, such as probing electronic motion in biologically relevant molecules in their physiological environment (liquid phase), and advanced coherent imaging of nano-engineered devices with 5 ∼ 8 n m resolution.

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.

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing.

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs—particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.