Oriented rotational wave-packet dynamics studies via high harmonic generation

In situ characterization of laser-induced strong field ionization phenomena

Accurately characterizing the intensity and duration of strong-field femtosecond pulses within the interaction volume is crucial for attosecond science. However, this remains a major bottleneck, limiting accuracy of the strong-field, and in particular, high harmonic generation experiments. We present a novel scheme for the in situ measurement and control of spatially resolved strong-field femtosecond pulse intensity and duration within the interaction focal region. Our approach combines conjugate focal imaging with in situ ion measurements using gas densities pertinent to attosecond science experiments. Independent measurements in helium and argon, accompanied by a fitting to a strong-field ionization dynamic model, yield accurate and consistent results across a wide range of gas densities and underscores the significance of double ionization, as well as barrier suppression ionization. Direct spatially resolved characterization of the driving laser is a critical step towards resolving the averaging problem in the interaction volume, paving the way for more accurate and reliable attosecond experiments.

Toward Complete All-Optical Intensity Modulation of High-Harmonic Generation from Solids

Optical modulation of high-harmonics generation in solids enables the detection of material properties, such as the band structure, and promising new applications, such as super-resolution imaging in semiconductors. Various recent studies have shown optical modulation of high-harmonics generation in solids, in particular, suppression of high-harmonics generation has been observed by synchronized or delayed multipulse sequences. Here we provide an overview of the underlying mechanisms attributed to this suppression and provide a perspective on the challenges and opportunities regarding these mechanisms. All-optical control of high-harmonic generation allows for femtosecond, and in the future possibly subfemtosecond, switching, which has numerous possible applications: These range from super-resolution microscopy to nanoscale controlled chemistry and highly tunable nonlinear light sources.

Enhanced molecular orientation via NIR-delay-THz scheme: Experimental results at room temperature

Light-induced orientation of gas phase molecules is a long-pursued goal in physics and chemistry. Here, we experimentally demonstrate a six-fold increase in the terahertz-induced orientation of iodomethane (CH₃I) molecules at room temperature, provided by rotational pre-excitation with a moderately intense near-IR pulse. The paper highlights the underlying interference of multiple coherent transition pathways within the rotational coherence manifold and is analyzed accordingly. Our experimental and theoretical results provide desirable and practical means for all-optical experiments on oriented molecular ensembles.

Molecular Orientation-Induced Second-Harmonic Generation: Deciphering Different Contributions Apart

We demonstrate and explore an all-optical technique for direct monitoring of the orientation dynamics in gas-phase molecular ensembles. The technique termed "MOISH" utilizes the transiently lifted inversion symmetry of polar gas media and provides a sensitive and spatially localized probing of the second-harmonic generation signal that is directly correlated with the orientation of the gas. Our experimental results reveal selective electronic and nuclear dynamical contributions to the overall nonlinear optical signal and decipher them apart using the "reporter gas" approach. "MOISH" provides new crucial means for implementing advanced coherent rotational control via concerted excitation by both terahertz and optical fields.

Rotational dynamics and transitions between Λ-type doubling of NO induced by an intense two-color laser field

We numerically investigate the rotational dynamics of NO in the electronic ground X²Π state induced by an intense two-color laser field (10 TW/cm²) as a function of pulse duration (0.3-25 ps). In the short pulse duration of less than 12 ps, rotational Raman excitation is effectively induced and results in molecular orientation. On the contrary, when the pulse duration is longer than 15 ps, the rotational excitation is suppressed. In addition to the rotational excitation, we find that transitions between Λ-type doubling are induced. Significantly, the maximum coherent wave packet between Λ-type doubling in J = 0.5 is generated using the pulse duration of 19.8 ps. The wave packet changes to the eigenstates of Λ = +1 or -1 alternatively, where Λ is the projection of the electronic orbital angular momentum on the N-O axis, which is regarded as the unidirectional rotation of an unpaired 2π electron around the N-O axis in a space-fixed frame as well as in a molecule-fixed frame. The experimental method to observe the alternation of the rotational direction of the electron around the N-O axis is proposed.

Long-Lasting Molecular Orientation Induced by a Single Terahertz Pulse

We present a novel, previously unreported phenomenon appearing in a thermal gas of nonlinear polar molecules excited by a single THz pulse. We find that the induced orientation lasts long after the excitation pulse is over. In the case of symmetric-top molecules, the time-averaged orientation remains indefinitely constant, whereas in the case of asymmetric-top molecules the orientation persists for a long time after the end of the pulse. We discuss the underlying mechanism, study its nonmonotonous temperature and amplitude dependencies, and show that there exist optimal parameters for maximal residual orientation. The persistent orientation implies a long-lasting macroscopic dipole moment, which may be probed by even harmonic generation and may enable deflection by inhomogeneous electrostatic fields.

Odd-even harmonic generation from oriented CO molecules in linearly polarized laser fields and the influence of the dynamic core-electron polarization

We present a detailed theoretical study of the odd-even harmonics generated from the polar molecule CO by the method based on numerically solving the time-dependent Schrödinger equation within the single-active-electron approximation. First, we reproduce the pure even harmonic generation of CO predicted theoretically by Hu et al. using the time-dependent density functional theory [H. Hu et al., Phys. Rev. Lett., 2017, 119, 173201]. Then, based on the Floquet approach, we are able to attribute this behavior to the half-cycle mirror symmetry of the molecule-field system when the polar molecule is perpendicular to the laser polarization. By numerical simulations, we show that this symmetry is broken at orientation angles other than 90° resulting in the odd-even harmonic generation and a non-trivial even-to-odd harmonics ratio strongly dependent on the molecular orientation. Furthermore, we investigate the influence of the dynamic core-electron polarization (DCeP) on the odd-even behavior near the cutoff of the high-order harmonic spectra. We emphasize that the DCeP effect is noticeable for the odd harmonics only.

All-optical field-free three-dimensional orientation of asymmetric-top molecules

Orientation and alignment of molecules by ultrashort laser pulses is crucial for a variety of applications and has long been of interest in physics and chemistry, with the special emphasis on stereodynamics in chemical reactions and molecular orbitals imaging. As compared to the laser-induced molecular alignment, which has been extensively studied and demonstrated, achieving molecular orientation is a much more challenging task, especially in the case of asymmetric-top molecules. Here, we report the experimental demonstration of all-optical field-free three-dimensional orientation of asymmetric-top molecules by means of phase-locked cross-polarized two-color laser pulse. This approach is based on nonlinear optical mixing process caused by the off-diagonal elements of the molecular hyperpolarizability tensor. It is demonstrated on SO2 molecules and is applicable to a variety of complex nonlinear molecules.

Routes of odd-even harmonic emission from oriented polar molecules

We study odd-even high-harmonic generation (HHG) from oriented asymmetric molecules with different symmetries in strong laser fields. A model based on strong-field approximations is used which allows us to resolve the contributions of different emission routes to odd-even HHG. The comparison between the HHG yields of all routes versus one certain route demonstrates that the routes in which the electron ionizes from the gerade component of the asymmetric orbital contribute mainly to odd-even HHG. We show that the potential mechanism is associated with effects of intramolecular interference in tunneling ionization as the bound electron passes through the barrier formed by the laser field and the asymmetric Coulomb potential. The influences of different emission routes on asymmetric orbital imagining with odd-even HHG are also addressed.

Charge migration and charge transfer in molecular systems

The transfer of charge at the molecular level plays a fundamental role in many areas of chemistry, physics, biology and materials science. Today, more than 60 years after the seminal work of R. A. Marcus, charge transfer is still a very active field of research. An important recent impetus comes from the ability to resolve ever faster temporal events, down to the attosecond time scale. Such a high temporal resolution now offers the possibility to unravel the most elementary quantum dynamics of both electrons and nuclei that participate in the complex process of charge transfer. This review covers recent research that addresses the following questions. Can we reconstruct the migration of charge across a molecule on the atomic length and electronic time scales? Can we use strong laser fields to control charge migration? Can we temporally resolve and understand intramolecular charge transfer in dissociative ionization of small molecules, in transition-metal complexes and in conjugated polymers? Can we tailor molecular systems towards specific charge-transfer processes? What are the time scales of the elementary steps of charge transfer in liquids and nanoparticles? Important new insights into each of these topics, obtained from state-of-the-art ultrafast spectroscopy and/or theoretical methods, are summarized in this review.

Pure Even Harmonic Generation from Oriented CO in Linearly Polarized Laser Fields

The first high harmonic spectrum containing only the odd orders was observed in experiments 30 years ago. However, a spectrum containing pure even harmonics has never been observed. We investigate the generation of pure even harmonics from oriented CO molecules in linearly polarized laser fields employing the time-dependent density-functional theory. We find that the even harmonics, with no odd orders, are generated with the polarization perpendicular to the laser polarization when the molecular axis of CO is perpendicular to the laser polarization. The generation of pure even harmonics reveals a type of dipole acceleration originating from the permanent dipole moment. This phenomenon exists in all systems with permanent dipole moments, including bulk crystal and polyatomic molecules.

Helicity-Selective Enhancement and Polarization Control of Attosecond High Harmonic Waveforms Driven by Bichromatic Circularly Polarized Laser Fields

High harmonics driven by two-color counterrotating circularly polarized laser fields are a unique source of bright, circularly polarized, extreme ultraviolet, and soft x-ray beams, where the individual harmonics themselves are completely circularly polarized. Here, we demonstrate the ability to preferentially select either the right or left circularly polarized harmonics simply by adjusting the relative intensity ratio of the bichromatic circularly polarized driving laser field. In the frequency domain, this significantly enhances the harmonic orders that rotate in the same direction as the higher-intensity driving laser. In the time domain, this helicity-dependent enhancement corresponds to control over the polarization of the resulting attosecond waveforms. This helicity control enables the generation of circularly polarized high harmonics with a user-defined polarization of the underlying attosecond bursts. In the future, this technique should allow for the production of bright highly elliptical harmonic supercontinua as well as the generation of isolated elliptically polarized attosecond pulses.

Coherent Radiative Decay of Molecular Rotations: A Comparative Study of Terahertz-Oriented versus Optically Aligned Molecular Ensembles

The decay of field-free rotational dynamics is experimentally studied by two complementary methods: laser-induced molecular alignment and terahertz-field-induced molecular orientation. A comparison between the decay rates of different molecular species at various gas pressures reveals that oriented molecular ensembles decay faster than aligned ensembles. The discrepancy in decay rates is attributed to the coherent radiation emitted by the transiently oriented ensembles and is absent from aligned molecules. The experimental results reveal the dramatic contribution of coherent radiative emission to the observed decay of rotational dynamics and underline a general phenomenon expected whenever field-free coherent dipole oscillations are induced.

Simulating electric field interactions with polar molecules using spectroscopic databases

Ro-vibrational Stark-associated phenomena of small polyatomic molecules are modelled using extensive spectroscopic data generated as part of the ExoMol project. The external field Hamiltonian is built from the computed ro-vibrational line list of the molecule in question. The Hamiltonian we propose is general and suitable for any polar molecule in the presence of an electric field. By exploiting precomputed data, the often prohibitively expensive computations associated with high accuracy simulations of molecule-field interactions are avoided. Applications to strong terahertz field-induced ro-vibrational dynamics of PH₃ and NH₃, and spontaneous emission data for optoelectrical Sisyphus cooling of H₂CO and CH₃Cl are discussed.

Rotational Control of Asymmetric Molecules: Dipole- versus Polarizability-Driven Rotational Dynamics

We experimentally study the optical- and terahertz-induced rotational dynamics of asymmetric molecules in the gas phase. Terahertz and optical fields are identified as two distinct control handles over asymmetric molecules, as they couple to the rotational degrees of freedom via the molecular dipole and polarizability selectively. The distinction between those two rotational handles is highlighted by different types of quantum revivals observed in long-duration (>100  ps) field-free rotational evolution. The experimental results are in excellent agreement with random phase wave function (RPWF) simulations [Phys. Rev. A 91, 063420 (2015)] and provide verification of the RPWF as an efficient method for calculating asymmetric molecular dynamics at ambient temperatures, where exact calculation methods are practically not feasible. Our observations and analysis pave the way for orchestrated excitations by both optical and terahertz fields as complementary rotational handles that enable a plethora of new possibilities in three-dimensional rotational control of asymmetric molecules.

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.

Role of tunnel ionization in high harmonic generation from substituted benzenes

We theoretically study high-harmonic generation in toluene, ortho-xylene and fluorobenzene driven by a 1.8 μm ultrashort pulse. We find that the chemical substitutions have a strong influence on the amplitude and phase of the emission from the highest occupied molecular orbital, despite having a small influence on the orbital itself. We show that this influence is due to the tunnel ionization step, which depends critically on the sign and amplitude of the asymptotic part of the wave function. We discuss how these effects would manifest in phase-sensitive high-harmonic generation spectroscopy experiments.

Controlling attosecond angular streaking with second harmonic radiation

High harmonic generation, which produces a coherent burst of radiation every half cycle of the driving field, has been combined with ultrafast wavefront rotation to create a series of spatially separated attosecond pulses, called the attosecond lighthouse. By adding a coherent second harmonic beam with polarization parallel to the fundamental, we decrease the generating frequency from twice per optical cycle to once. The increased temporal separation increases the pulse contrast. By scanning the carrier envelope phase, we see that the signal is 2π periodic.

Two-pulse field-free orientation reveals anisotropy of molecular shape resonance

We report the observation of macroscopic field-free orientation, i.e., more than 73% of CO molecules pointing in the same direction. This is achieved through an all-optical scheme operating at high particle densities (>10(17)  cm(-3)) that combines one-color (ω) and two-color (ω+2ω) nonresonant femtosecond laser pulses. We show that the achieved orientation solely relies on the hyperpolarizability interaction as opposed to an ionization-depletion mechanism, thus, opening a wide range of applications. The achieved strong orientation enables us to reveal the molecular-frame anisotropies of the photorecombination amplitudes and phases caused by a shape resonance. The resonance appears as a local maximum in the even-harmonic emission around 28 eV. In contrast, the odd-harmonic emission is suppressed in this spectral region through the combined effects of an asymmetric photorecombination phase and a subcycle Stark effect, generic for polar molecules, that we experimentally identify.

Quasi-phase-matching of only even-order high harmonics

High harmonic spectrum of a quasi-monochromatic pump that interacts with isotropic media consists of only odd-order harmonics. Addition of a secondary pump, e.g. a static field or the second harmonic of the primary pump, can results with generation of both odd and even harmonics of the primary pump. We propose a method for quasi-phase matching of only the even-order harmonics of the primary pump. We formulate a theory for this process and demonstrate it numerically. We also show that it leads to attosecond pulse trains with constant carrier envelop phase and high repetition rate.

Transition between mechanisms of laser-induced field-free molecular orientation

The transition between two distinct mechanisms for the laser-induced field-free orientation of CO molecules is observed via measurements of orientation revival times and subsequent comparison to theoretical calculations. In the first mechanism, which we find responsible for the orientation of CO up to peak intensities of 8 × 10(13) W/cm(2), the molecules are impulsively oriented through the hyperpolarizability interaction. At higher intensities, asymmetric depletion through orientation-selective ionization is the dominant orienting mechanism. In addition to the clear identification of the two regimes of orientation, we propose that careful measurements of the onset of the orientation depletion mechanism as a function of the laser intensity will provide a relatively simple route to calibrating absolute rates of nonperturbative strong-field molecular ionization.

Terahertz-induced field-free orientation of rotationally excited molecules

We have used picosecond THz pulses to induce transient field-free orientation of OCS molecules. Coherent optical Raman excitation prepares the molecules in rotational superposition states prior to THz irradiation, substantially enhancing the degree of orientation. The time-dependent alignment and orientation are characterized via Coulomb explosion in an intense probe laser. The degree of OCS orientation is an order of magnitude larger than previously observed following THz irradiation and is achieved with a significantly smaller THz field.The field-free orientation level is comparable to that generated using pulsed, two-color laser fields but is obtained with negligible target ionization.

High-order harmonic spectroscopy for molecular imaging of polyatomic molecules

High-order harmonic generation is a powerful and sensitive tool for probing atomic and molecular structures, combining in the same measurement an unprecedented attosecond temporal resolution with a high spatial resolution of the order of an angstrom. Imaging of the outermost molecular orbital by high-order harmonic generation has been limited for a long time to very simple molecules, like nitrogen. Recently we demonstrated a technique that overcame several of the issues that have prevented the extension of molecular orbital tomography to more complex species, showing that molecular imaging can be applied to a triatomic molecule like carbon dioxide. Here we report on the application of such a technique to nitrous oxide (N₂O) and acetylene (C₂H₂). This result represents a first step towards the imaging of fragile compounds, a category which includes most of the fundamental biological molecules.

Reactive scattering dynamics of rotational wavepackets: a case study using the model H+H2 and F+H2 reactions with aligned and anti-aligned H2

We propose a method to steer the outcome of reactive atom-diatom scattering, using rotational wavepackets excited by strong non-resonant laser pulses. Full close-coupled quantum mechanical scattering calculations of the D+H2 and F+H2 reactions are presented, where the H2 molecule exists as a coherent superposition of rotational states. The nuclear spin selective control over the molecular bond axis alignment afforded by the creation of rotational wavepackets is applied to reactive scattering systems, enabling a nuclear spin selective influence to be exerted over the reactive dynamics. The extension of the conventional eigenstate-to-eigenstate scattering problem to the case in which the initial state is composed of a coherent superposition of rotational states is detailed, and a selection of example calculations are discussed, along with their mechanistic implications. The feasibility of the corresponding experiments is considered, and a suitable simple two pulse laser scheme is shown to strongly differentiate the reactivities of o-H2 and p-H2.

Asymmetric molecular imaging through decoding odd-even high-order harmonics

The exquisite procedure for imaging a molecular orbital with high-order harmonics proposed by Itatani et al. [Nature (London) 432, 867 (2004)] encounters difficulty when extended to an asymmetric molecule because the wave function there usually does not have a definite parity. With the observation that the wave function can be decomposed into a sum of odd and even functions and that the ionization process in harmonic generation is usually not sensitive to the asymmetry of the molecular potential, we predict that asymmetric molecular orbital imaging can be implemented through decoding odd-even high-order harmonics. A generalized tomography procedure is proposed, which has been certified by analytic deduction and numerical simulation. The above finding greatly extends the molecular tomography procedure and will further stimulate related experiments.

Tomographic imaging of asymmetric molecular orbitals with a two-color multicycle laser field

We theoretically demonstrate a scheme for tomographic reconstruction of asymmetric molecular orbitals based on high-order harmonic generation with a two-color multicycle laser field. It is shown that by adjusting the relative phase of the two fields, the returning electrons can be forced to recollide from one direction for all the orientations of molecules. Thus, the reconstruction of the asymmetric orbitals can be carried out with multicycle laser field. This releases the stringent requirement of a single-cycle pulse with a stabilized and controllable carrier-envelope phase for the tomographic imaging of asymmetric molecular orbitals.

Probing polar molecules with high harmonic spectroscopy

We bring the methodology of orienting polar molecules together with the phase sensitivity of high harmonic spectroscopy to experimentally compare the phase difference of attosecond bursts of radiation emitted upon electron recollision from different ends of a polar molecule. This phase difference has an impact on harmonics from aligned polar molecules, suppressing emission from the molecules parallel to the driving laser field while favoring the perpendicular ones. For oriented molecules, we measure the amplitude ratio of even to odd harmonics produced when intense light irradiates CO molecules and determine the degree of orientation and the phase difference of attosecond bursts using molecular frame ionization and recombination amplitudes. The sensitivity of the high harmonic spectrum to subtle phase differences in the emitted radiation makes it a detailed probe of polar molecules and will drive major advances in the theory of high harmonic generation.