Two-color Field Research Articles

High-order harmonic generation from stretched C2H2 molecules in intense laser fields

We investigate the high harmonic generation from stretched acetylene molecules subjected to intense laser fields employing time-dependent Hartree-Fock methods. It is found that as the C-C and C-H bonds are stretched, the harmonic efficiency increases significantly due to the increased ionization of inner valence $\ensuremath{\sigma}$ orbitals in the monochromatic field, while the harmonic yield will be limited by the strong depletion of the ground-state population under a certain bond length. Moreover, the harmonic emission is affected by the nonadiabatic electron dynamics from the multiorbital coupling effects. In addition, by introducing a two-color field scheme for different C-H bond configurations with the fixed C-C bond, the aforementioned harmonic efficiency will be further enhanced due to laser-induced strong excitation from inner valence orbitals to initially unoccupied orbitals. The above results would be helpful for further understanding multiorbital dynamics in the harmonic generation from polyatomic molecules.

A perspective on integrated atomo-photonic waveguide circuits

Integrated photonic circuits based on suspended photonic rib waveguides, which can be used for coherent trapping, guiding, and splitting of ultra-cold neutral atoms in two-color evanescent light fields near their surfaces, are described. Configurations of quantum inertial sensors based on such integrated atomo-photonic waveguides, which are simultaneously guiding photons and atoms along the same paths, are presented. The difference between free-space and guided atom interferometers in the presence of external forces is explained. The theoretical and technological challenges, to be overcome on the way to the realization of such a platform for quantum technologies, are discussed.

Disentangling enantiosensitivity from dichroism using bichromatic fields.

We discuss how tensorial observables, available in photoelectron angular distributions resulting from interaction between isotropic chiral samples and cross polarized ω-2ω bichromatic fields, allow for chiral discrimination without chiral light and within the electric-dipole approximation. We extend the concept of chiral setup [A. F. Ordonez and O. Smirnova, Phys. Rev. A, 2018, 98, 063428], which explains how chiral discrimination can be achieved in the absence of chiral light, to the case of tensorial observables. We derive selection rules for the enantiosensitivity and dichroism of the bl,m coefficients describing the photoelectron angular distribution valid for both weak and strong fields and for arbitrary ω-2ω relative phase. Explicit expressions for simple perturbative cases are given. We find that, besides the known dichroic non-enantiosensitive [R. E. Goetz, C. P. Koch and L. Greenman, J. Chem. Phys., 2019, 151, 074106], and dichroic-and-enantiosensitive bl,m coefficients found recently [P. V. Demekhin, Phys. Rev. A, 2019, 99, 063406], there are also enantiosensitive non-dichroic bl,m coefficients. These reveal the molecular enantiomer independently of the relative phase between the two colors and are therefore observable even in the absence of stabilization of the ω-2ω relative phase.

Divergence and efficiency optimization in polarization-controlled two-color high-harmonic generation

Improving the brightness of high-harmonic generation (HHG) sources is one of the major goals for next-generation ultrafast, imaging and metrology applications in the extreme-ultraviolet spectrum. Previous research efforts have demonstrated a plethora of techniques to increase the conversion efficiency of HHG. However, few studies so far have addressed how to simultaneously minimize the divergence and improve focusability, which all contribute to an increased brightness of the source. Here, we investigate how to improve both photon yield and divergence, which is directly linked to focusability, when adding the second harmonic to the fundamental driving field. We study the effects of the relative polarization in two-color HHG and compare the results to a one-color configuration. In a perpendicular two-color field, the relative phase between the two colors can be used to suppress or enhance recombination of either the long or the short trajectories. This allows to exert control over the divergence of the harmonics. In a parallel two-color field, the ionization rate is modified through the two-color phase, which selects trajectories during the ionization step. This enhances the total yield. We elaborate on the underlying mechanisms for parallel, perpendicular, and intermediate polarization angles, and confirm our experimental observations with simulations.

Huygens-Fresnel Picture for High Harmonic Generation in Solids.

High harmonic generation (HHG) is usually described by the laser-induced recollision of particlelike electrons, which lies at the heart of attosecond physics and also inspires numerous attosecond spectroscopic methods. Here, we demonstrate that the wavelike behavior of electrons plays an important role in solid HHG. By taking an analogy to the Huygens-Fresnel principle, an electron wave perspective on solid HHG is proposed by using the wavelet stationary-phase method. From this perspective, we have explained the deviation between the cutoff law predicted by the particlelike recollision model and the numerical simulation of semiconductor Bloch equations. Moreover, the emission times of HHG can be well predicted with our method involving the wave property of electrons. However, in contrast, the prediction with the particlelike recollision model shows obvious deviations compared to the semiconductor Bloch equations simulation. The wavelike properties of the electron motion can also be revealed by the HHG in a two-color field.

Probing tunneling dynamics of dissociative H2 molecules using two-color bicircularly polarized fields

Probing and manipulating the electronic motion in the ultrafast laser molecular interaction provides the pathways for quantum imaging and controlling chemical reactions. Recently, the emerging application of attosecond metrology of ultrafast electron dynamics has accessed the time scale of the most fundamental processes in molecular chemical reactions. Here, we probe the tunneling dynamics of internuclear-dependent dissociative reaction of ${\mathrm{H}}_{2}$ with angular streaking using two-color bicircularly polarized femtosecond laser pulses. By measuring high-resolution photoelectron spectroscopy, we disentangle the orientation and internuclear-distance dependent effect of the long-range Coulomb potential and the initial phase on molecular-frame photoelectron momentum distributions, and stereo extract the phase gradient of the tunneling electron wave packets and Wigner time delay during the dissociative ionization using two-color bicircular fields. The work has an insight into the clocking of ultrafast spatiotemporal photoelectron dynamics and the quantum control of molecular chemical processes via sculptured circular fields, which can be applied to polyatomic molecules.

Analyzing the electron trajectories in strong-field tunneling ionization with the phase-of-the-phase spectroscopy.

By numerically solving the time-dependent Schrödinger equation, we theoretically study strong-field tunneling ionization of Ar atom in the parallel two-color field which consists of a strong fundamental pulse and a much weaker second harmonic component. Based on the quantum orbits concept, we analyzed the photoelectron momentum distributions with the phase-of-the-phase spectroscopy, and the relative contributions of the two parts of the photoelectrons produced during the rising and falling edges of the adjacent quarters of the laser cycle are identified successfully. Our results show that the relative contributions of these two parts depend on both of the transverse and longitude momenta. By comparing the results from model atoms with Coulomb potential and short-range potential, the role of the long-range Coulomb interaction on the relative contributions of these two parts of electrons is revealed. Additionally, we show that the effects of Coulomb interaction on ionization time are vital for identifying their relative contributions.

Study on spin angular momentum balance in harmonics generated from counter-rotating two-color laser fields.

High-order harmonics generated from Xe driven by counter-rotating two-color driving fields are studied in the frame of a quantum-field scattering theory, and the spin angular momentum transfer is discussed. The driving field is composed by a circularly polarized (CP) mode and an elliptically polarized (EP) mode. We treat the EP mode as a compostition of counter-rotating CP fields of unequal intensity. We use a pair of phased generalized Bessel functions to describe the harmonic generation amplitude, and the conservation of the spin angular momentum during harmonic generation in the two-color field is derived in a solid base and in a straightforward way. The experimentally observed V-type and Λ-type distributions of the harmonic spectra with ellipticity are recovered theoretically. Balance pattern of the spin angular momentum is disclosed substantially.

Attosecond pulse trains with elliptical polarization from an orthogonally polarized two-color field

Generation of an elliptically polarized attosecond pulse train by an orthogonally polarized two-color (OTC) laser field is investigated theoretically and simulated numerically. The OTC field consists of two linearly polarized fields with orthogonal polarizations and frequencies that are integer multiples of the fundamental frequency ω . For the ω − 3 ω OTC field, the emitted harmonics are elliptically polarized so that they may form an elliptically polarized attosecond pulse train provided that a group of harmonics is phase-locked. This is the case if only one quantum orbit generates the corresponding part of the harmonic spectrum. If so, then two attosecond pulses are emitted per optical cycle due to the dynamical symmetry of the ω − 3 ω OTC field. Atomic targets with an s ground state only generate attosecond pulses with almost linear polarization. Using, however, targets with a p ground state, attosecond pulses with substantial ellipticity can be produced because ground states with opposite magnetic quantum numbers m = + 1 and m = − 1 produce harmonics with opposite helicities at different rates. In this case, the harmonic intensity and harmonic ellipticity are different for the ground states with the magnetic quantum number m = ± 1 . These differences are the source of the attosecond pulse ellipticity and can be controlled using the relative phase as a control parameter. In addition, by choosing a particular group of harmonics, one can select the desired ellipticity of the attosecond pulse train.

Electron trajectory backanalysis for spectral profile in two-color terahertz generation

The gas-phase medium ionized by two-color femtosecond field produces supercontinuum radiation ranging from the terahertz to midinfrared band. Under the strong-field approximation, the electron trajectory backanalysis is exploited to interpret the spectral profile of terahertz radiation. Meanwhile, the electron trajectory method can correlate terahertz spectral profiles and photoelectron momentum distributions (PEMDs). The coherent superposition of electron trajectories released from the consecutive cycles is found to induce the high-frequency cutoff and sharpen the spectral bandwidth of supercontinuum radiation, tightly coinciding with the intercycle interference fringes in PEMDs. The trajectory analysis exhibits that single electron interference plays an important role in the terahertz generation process. Our method provides an intuitive interpretation in terms of electron trajectory perspective and sheds light on the microscopic mechanisms of terahertz generation.

Enhanced chiral-sensitivity of Coulomb-focused electrons in strong field ionization

Strong-field light–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.

Steering of circular dichroism in biharmonic ionization of atoms

Circular dichroism in photoelectron angular distributions of general biharmonic (i.e., $n\ensuremath{\omega}+m\ensuremath{\omega}$) atomic ionization is analyzed theoretically and given along with ``experimental guidelines'' on how it can be steered towards its maximum. It is shown that such a maximum circular dichroism can always be achieved for the ionization of an arbitrary atom and for any incident fundamental photon energy by fine control of only two experimental parameters: the relative flux and phase difference of the two components of the radiation field. In this Letter, we provide a simple analytical description of the circular dichroism as well as a set of rules which enables full control over its magnitude. Our findings are demonstrated explicitly for the ionization of helium with a two-color field composing a fundamental beam and its second harmonic.

Enhanced dynamically assisted pair production in spatial inhomogeneous electric fields with the frequency chirping

Chirped dynamically assisted pair production in spatial inhomogeneous electric fields is studied by the Dirac-Heisenberg-Wigner formalism. The effects of the chirp parameter on the reduced momentum spectrum, the reduced total yield of the created pairs for either low or high frequency one-color field and two-color dynamically assisted combinational fields are investigated in detail. Also, the enhancement factor is obtained in the later two-color field case. It is found that for the low frequency field, no matter whether it is accompanied by the other high frequency field, its chirping has a little effect on the pair production. For the one-color high frequency field or/and two-color fields, the momentum spectrum exhibits incomplete interference and the interference effect becomes more and more remarkable as chirp increases. We also find that in the chirped dynamically assisted field, the reduced total yield is enhanced significantly when the chirps are acting on the two fields, compared with that the chirp is acting only for the low frequency strong field. Specifically, by the chirping, it is found the reduced pair number is increased by more than one order of magnitude in the field with a relative narrow spatial scale, while it is enhanced at least two times in other case of field with larger spatial scales or even in the quasi-homogeneous region. We also obtain some optimal chirp parameters and spatial scales for the total yield and enhancement factor in different scenarios of the studied external field. These results may provide a theoretical basis for possible experiments in the future.

Symmetries and Selection Rules of the Spectra of Photoelectrons and High-Order Harmonics Generated by Field-Driven Atoms and Molecules

Using the strong-field approximation we systematically investigate the selection rules for high-order harmonic generation and the symmetry properties of the angle-resolved photoelectron spectra for various atomic and molecular targets exposed to one-component and two-component laser fields. These include bicircular fields and orthogonally polarized two-color fields. The selection rules are derived directly from the dynamical symmetries of the driving field. Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent molecular orbital. In addition, we briefly discuss some properties of the high-order harmonic spectra generated by a few-cycle laser field. The symmetry properties of the angle-resolved photoelectron momentum distribution are also determined by the dynamical symmetry of the driving field. We consider the first two terms in a Born series expansion of the T matrix, which describe the direct and the rescattered electrons. Dynamical symmetries involving time translation generate rotational symmetries obeyed by both terms. However, those that involve time reversal generate reflection symmetries that are only observed by the direct electrons. Finally, we explain how the symmetry properties, imposed by the dynamical symmetry of the driving field, are altered for molecular targets.

Enhancing high-order harmonic generation by controlling the diffusion of the electron wave packet

We experimentally study the enhancement of high-order harmonic generation (HHG) driven by synthesized ω − 3 ω laser fields, where we control whether the ionization rate or the electron wave packet’s diffusion is the dominant enhancement mechanism. When minimizing the electron wave packet’s diffusion, the excursion times of the corresponding electron trajectories are reduced by a factor of 2 or more. This result is important for imaging techniques that use the returning electron wave packet to probe the remaining ion. Furthermore, we achieve a 10 × to 3800 × enhancement of the harmonic yield driven by the bichromatic fields relative to that of an optimized single-color field, showing that the bichromatic fields improve HHG’s capability as a light source. We also measure that the two-color field’s harmonics have half the divergence angle compared to their single-color counterpart, suggesting that the “short” electron trajectories play a more prominent role compared to their “long” trajectory counterparts, thus improving the wavefront of the emerging harmonic beam.

Effect of ionization asymmetry on high harmonic generation from oriented CO in orthogonal two-color fields

We investigate the high harmonic generation from oriented CO molecules in orthogonal two-color (OTC) fields by solving the three-dimensional time-dependent Hartree–Fock equation. The infrared fundamental laser pulse with frequency ω polarized along the molecular axis drives the harmonic generation process, while a weak second harmonic field with frequency ω 1 = 2ω perturbs the electron dynamics along the direction perpendicular to molecular axis. We observe non-integer order harmonics of ω 1 generated from CO with its polarization perpendicular to the molecular axis, which differs from aligned H2 under the same laser fields. Combining the Lewenstein model with the classical electronic trajectory analysis, we find the ionization asymmetry along molecular axis in polar molecules under the cross modulation of the OTC fields results in the difference of high harmonics between CO and H2.

Study of pair production in inhomogeneous two-color electric fields using the computational quantum field theory

We first demonstrate theoretically that the computational quantum field theory is equivalent to the quantum kinetic theory for pair creation in a spatially homogeneous and time-dependent electric field, then verify numerically their equivalence for pair creation in one-dimensional time-dependent electric fields, and finally investigate detailedly the effects of the field frequency, spatial width, pulse duration, and relative phase on dynamically assisted Schwinger pair production in an inhomogeneous two-color electric field. It is found that the enhancement effect of pair creation is very sensitive to the field frequency and generally very obvious for a shorter field width, a longer pulse duration, and a relative phase of maximizing the field strength. These results can provide a significant reference for the optimal control theory of pair creation which aims to maximize the created pair yield within a given scope of field parameters.

Controlling high harmonic generation using inhomogeneous two-color driving laser pulse

High harmonic generation (HHG) is strongly modified near plasmonic nanostructures due to confinement and inhomogeneity of the electromagnetic field. Previous studies have revealed low-intensity generation of HHG and extension of the plateau; however, the roles of potential shape and a combination of inhomogeneous infrared (IR) and blue fields on HHG have not been studied. In this work, we study HHG driven by inhomogeneous two-color (800–400 nm) IR and blue femtosecond pulses by numerically solving the time-dependent Schrödinger equation. HHG spectra are computed for two different models: for a short-range potential, which supports a single-bound state, and for a long-range potential, which supports a Rydberg series, to show potential dependence on inhomogeneous two-color HHG. A substantial enhancement in the value of the cut-off resulting from inhomogeneity up to the ∼600th order, extending beyond the water window, is found for both the models. The HHG spectra are highly sensitive to the relative phase of the two-color fields and this sensitivity increases with increasing inhomogeneity. Possibilities of efficiently generating and controlling attosecond pulse train and isolated attosecond pulse are discussed.

Generation of necklace-shaped high harmonics in a two-color vortex field.

We numerically studied gas high-harmonic generation in a two-color vortex laser field using the non-adiabatic Lewenstein model. Macroscopic responses were calculated by numerically solving the three-dimensional propagation equation in cylindrical coordinates. It was confirmed that unique high-harmonic signals with necklace-like shapes exhibit orbital angular momentum (OAM). The azimuthally distributed necklace harmonics exhibit periodic modulation as a function of laser frequency and topological charges of the driving field. Phase investigation showed that the OAM of the necklace harmonics is attributable to the tuning of the relative intensity of the two driving pulses. These findings provide a new dimension for high-harmonic manipulation in the vortex field. The two-color vortex field is the first scheme proposed for manipulating the intensity profile of high harmonics.

Enhancement of the photocurrents injected in gapped graphene by the orthogonally polarized two-color laser field.

We theoretically investigate the photocurrents injected in gapped graphene by the orthogonally polarized two-color laser field. Depending on the relative phase, the photocurrents can be coherently controlled by deforming the electron trajectory in the reciprocal space. Under the same field strength, the peak photocurrent in the orthogonally polarized two-color field is about 20 times larger than that for linearly polarized light, and about 3.6 times for elliptically polarized light. The enhancement of the photocurrent can be attributed to an obvious asymmetric distribution of the real population in the reciprocal space, which is sensitive to the waveform of the laser field and related to the quantum interference between the electron trajectories. Our work provides a noncontact method to effectively enhance the injected current in graphene.