Molecular Wave Packet Research Articles

Long-lived electronic coherences in molecular wave packets probed with pulse-shape spectroscopy

Long-lived electronic coherences in molecular wave packets probed with pulse-shape spectroscopy

Laser-induced modification of an excited-state vibrational wave packet in neutral H2 observed in a pump-control scheme

We observe and modify a molecular vibrational wave packet in an electronically excited state of the neutral hydrogen molecule. In an extreme-ultraviolet (XUV) time-domain absorption spectroscopy experiment, we launch a vibrational wave packet in the DΠu13pπ state of H2 and track its time evolution via the coherent dipole response. The reconstructed time-dependent dipole from experimentally measured XUV absorption spectra provides access to the revival of the vibrational wave packet, which we control via an intense near-infrared (NIR) pulse. Tuning the intensity of the NIR pulse, we observe the revival of the wave packet to be significantly modified, which is supported by the results of a multilevel simulation as well as an analytical model based on state-specific phase shifts. The NIR field is applied only 7 fs after the creation of the wave packet but influences its evolution up to at least its first revival at 270 fs. This experimental approach for nonlocal-in-time laser modification of quantum dynamics in a pump-control scheme enabled by molecular self-probing is generally applicable to a large range of molecules and materials as it only requires the observation of absorption spectra. Published by the American Physical Society 2024

Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics.

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events.

Manipulating molecular rotational wave packets with resonant terahertz pulses

We found the phase differences of the expansion coefficients in rotational wave packet are in linear relationships with the phases of corresponding pulses when gas-phase linear molecules are irradiated by pulses in resonant with their rotational transitions. Using these relationships, we can accurately control the wave packet by first determine the phases of the controlling pulses, and then optimize the durations (or amplitudes) of the pulses to demanded population. We also compared the phase relationships obtained from ground and other initial rotational eigenstates and analyzed the reason for lowered orientation degree in non-zero temperature conditions.

Exploring the vibrational series of pure trilobite Rydberg molecules

In trilobite Rydberg molecules, an atom in the ground state is bound by electron-atom scattering to a Rydberg electron that is in a superposition of high angular momentum states. This results in a homonuclear molecule with a permanent electric dipole moment in the kilo-debye range. Trilobite molecules have previously been observed only with admixtures of low-l states. Here we report on the observation of two vibrational series of pure trilobite Rubidium-Rydberg molecules that are nearly equidistant. They are produced by three-photon photoassociation and lie energetically more than 15 GHz below the atomic 22F state of rubidium. We show that these states can be used to measure the electron-atom scattering length at low energies in order to benchmark current theoretical calculations. In addition to measuring their kilo-Debye dipole moments, we also show that the molecular lifetime is increased compared to the 22F state due to the high-l character. The observation of an equidistant series of vibrational states opens the way to observe coherent molecular wave packet dynamics.

Strong Laser Field-Driven Coupled Electron-Nuclear Dynamics: Quantum vs Classical Description.

We have performed a coupled electron-nuclear dynamics study of H2+ molecular ions under the influence of an intense few-cycle 4.5 fs laser pulse with an intensity of 4 × 1014 W/cm2 and a central wavelength of 750 nm. Both quantum and classical dynamical methods are employed in the exact similar initial conditions with the aim of head-to-head comparison of two methodologies. A competition between ionization and dissociation channel is explained under the framework of quantum and classical dynamics. The origin of the electron localization phenomena is elucidated by observing the molecular and electronic wave packet evolution pattern. By probing with different carrier envelope phase (CEP) values of the ultrashort pulse, the possibility of electron localization on either of the two nuclei is investigated. The effects of initial vibrational states on final dissociation and ionization probabilities for several CEP values are studied in detail. Finally, asymmetries in the dissociation probabilities are calculated and mutually compared for both quantum and classical dynamical methodologies, whereas Franck-Condon averaging over the initial vibrational states is carried out in order to mimic the existing experimental conditions.

High resolution metrology of autoionizing states through Raman interferences

Metrology of electron wavepackets is often conducted with the technique of photoelectron interferometry. However, the ultrashort light pulses employed in this method place a limit on the energy resolution. Here, weadvance ultrafast photoelectron interferometry access both high temporal and spectral resolution. The key to our approach lies in stimulating Raman interferences with a probe pulse and while monitoring the modification of the autoionizing electron yield in a separate delayed detection step. As a proof of the principle, we demonstrated this technique to obtain the components of an autoionizing nf′ wavepacket between the spin-orbit split ionization thresholds in argon. We extracted the amplitudes and phases from the interferogram and compared the experimental results with second-order perturbation theory calculations. This high resolution probing and metrology of electron dynamics opens the path for study of molecular wavepackets.

Role of the Cohen-Fano interference in recoil-induced rotation.

We study the rotational dynamics induced by the recoil effect in diatomic molecules using time-resolved two-color x-ray pump-probe spectroscopy. A short pump x-ray pulse ionizes a valence electron inducing the molecular rotational wave packet, whereas the second time-delayed x-ray pulse probes the dynamics. An accurate theoretical description is used for analytical discussions and numerical simulations. Our main attention is paid to the following two interference effects that influence the recoil-induced dynamics: (i) Cohen-Fano (CF) two-center interference between partial ionization channels in diatomics and (ii) interference between the recoil-excited rotational levels manifesting as the rotational revival structures in the time-dependent absorption of the probe pulse. The time-dependent x-ray absorption is computed for the heteronuclear CO and homonuclear N2 molecules as showcases. It is found that the effect of CF interference is comparable with the contribution from independent partial ionization channels, especially for the low photoelectron kinetic energy case. The amplitude of the recoil-induced revival structures for the individual ionization decreases monotonously with a decrease in the photoelectron energy, whereas the amplitude of the CF contribution remains sufficient even at the photoelectron kinetic energy below 1eV. The profile and intensity of the CF interference depend on the phase difference between the individual ionization channels related to the parity of the molecular orbital emitting the photoelectron. This phenomenon provides a sensitive tool for the symmetry analysis of molecular orbitals.

Coincidence spectroscopy of molecular normal Auger decay by ultrashort x-ray pulses

When a core-shell electron is ionized by coherent ultrashort x-ray pulses with varied duration, different nuclear wave packets of a cationic molecule are formed, which can be effectively studied by detecting the photoelectron-Auger electron-ion fragment as it is proposed in the present paper. We develop the theory for the photoelectron, i.e., Auger electron, ion fragment three-body coincidence spectroscopy, where dissociative Auger final states are considered. Simulations to display the HF molecule show that the coincidence spectra encode the detailed information of coherent nuclear wave-packet dynamics. Our work paves the way for using currently available coherent ultrashort x-ray pulses to investigate and manipulate molecular nuclear wave packets. Moreover, we discuss possibilities for high-resolution coincidence experimental techniques.

Structure and lattice thermal conductivity of grain boundaries in silicon by using machine learning potential and molecular dynamics

In silicon, lattice thermal conductivity plays an important role in a wide range of applications such as thermoelectric and microelectronic devices. Grain boundaries (GBs) in polycrystalline silicon can significantly reduce lattice thermal conductivity, but the impact of GB atomic structures on it remains to be elucidated. This study demonstrates accurate predictions of the GB structures, GB energies, and GB phonon properties in silicon using machine learning potentials (MLPs). The results indicate that the MLPs enable robust GB structure searches owing to the fact that the MLPs were developed from a training dataset covering a wide variety of structures. We also investigate lattice thermal conduction at four GB atomic structures using large-scale perturbed molecular dynamics and phonon wave-packet simulations. The comparison of these results indicates that the GB structure dependence of thermal conductivity stems from anharmonic vibrations at GBs rather than from the phonon transmission behavior at GBs. The advantages of the MLPs compared with a typical empirical potential of silicon are also thoroughly investigated.

Expansive Quantum Mechanical Exploration of Chemical Reaction Paths.

Quantum mechanical methods have been well-established for the elucidation of reaction paths of chemical processes and for the explicit dynamics of molecular systems. While they are usually deployed in routine manual calculations on reactions for which some insights are already available (typically from experiment), new algorithms and continuously increasing capabilities of modern computer hardware allow for exploratory open-ended computational campaigns that are unbiased and therefore enable unexpected discoveries. Highly efficient and even automated procedures facilitate systematic approaches toward the exploration of uncharted territory in molecular transformations and dynamics. In this work, we elaborate on such explorative approaches that range from reaction network explorations with (stationary) quantum chemical methods to explorative molecular dynamics and migrant wave packet dynamics. The focus is on recent developments that cover the following strategies. (i) Pruning search options for elementary reaction steps by heuristic rules based on the first-principles of quantum mechanics: Rules are required for reducing the combinatorial explosion of potentially reactive atom pairings, and rooting them in concepts derived from the electronic wave function makes them applicable to any molecular system. (ii) Enforcing reactive events by external biases: Inducing a reaction requires constraints that steer and direct elementary-step searches, which can be formulated in terms of forces, velocities, or supplementary potentials. (iii) Manual steering facilitated by interactive quantum mechanics: As ultrafast quantum chemical methods allow for real-time manual interactions with molecular systems, human-intuition-guided paths can be easily explored with suitable human-machine interfaces. (iv) New approaches for transition-state optimization with continuous curve representations can provide stable schemes to be driven in an automated way by allowing for an efficient tuning of the curve's parameters (instead of a manipulation of a collection of structures along the path), and (v) reactive molecular dynamics and direct wave packet propagation exploit the equations of motion of an underlying mechanical theory (usually, classical Newtonian mechanics or Schrödinger quantum mechanics). Explorative approaches are likely to replace the current state of the art in computational chemistry, because they reduce the human effort to be invested in reaction path elucidations, they are less prone to errors and bias-free, and they cover more extensive regions of the relevant configuration space. As a result, computational investigations that rely on these techniques are more likely to deliver surprising discoveries.

Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules.

Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

Effect of interfacial structures on phonon transport across atomically precise Si/Al heterojunctions

Phonons are important carriers of energy and information in many cryogenic devices used for quantum information science and in fundamental physics experiments such as dark matter detectors. In these systems phonon behaviors can be dominated by interfaces and their atomic structures; hence, there is increasing demand for a more detailed understanding of interfacial phonon transport in relevant material systems. Previous studies have focused on understanding thermal transport over the entire phonon spectrum at and above room temperature. At ultralow temperatures, however, knowledge is missing regarding athermal phonon behavior due to the challenge in modeling the extreme conditions in microscale, heterogeneous cryogenic systems, as well as extracting single-phonon information from a large ensemble. In this paper, we delineate the effects of interfacial atomic structures on phonon transport using a combination of classical molecular dynamics (MD) and phonon wave-packet simulations, to illustrate the consistency and differences between the ensemble- and single-phonon dynamics. We consider three single-crystal Si surface reconstructions---$(1\ifmmode\times\else\texttimes\fi{}1), (\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})$ and $(7\ifmmode\times\else\texttimes\fi{}7)$---and model both experimentally observed $\mathrm{Si}(1\ifmmode\times\else\texttimes\fi{}1)/\mathrm{Al}$ interfaces and hypothesized $\mathrm{Si}(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})$/Al and $\mathrm{Si}(7\ifmmode\times\else\texttimes\fi{}7)/\mathrm{Al}$ interfaces. The overall interfacial thermal conductance calculated from non-equilibrium MD shows that for the $\mathrm{Si}(1\ifmmode\times\else\texttimes\fi{}1)/\mathrm{Al}$ system, the presence of Al twin boundaries can hinder phonon transport and reduce thermal conductance by 2--12% relative to single-crystal Al; whereas the Si $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})$ and $(7\ifmmode\times\else\texttimes\fi{}7)$ reconstructions can enhance it by 6--19%. Normal mode decomposition reveals that both the increase and decrease in conductance are related to inelastic phonon scattering. Single-phonon wave-packet simulations predict phonon transport properties consistent with non-equilibrium MD, while further suggesting that phonon polarization conversion is significant even when elastic transmission dominates, and that the interfacial structures have anisotropic impacts on atomic vibrations along different lattice directions. Our findings suggest avenues for achieving selective phonon transport via controlling interfacial structures of materials using atomically precise fabrication techniques, and that the phonon wave-packet formalism is a potentially powerful method for developing a detailed understanding of non-equilibrium phenomena in the low-temperature limit.

On the molecular electronic flux: Role of nonadiabaticity and violation of conservation

Analysis of electron flux within and in between molecules is crucial in the study of real-time dynamics of molecular electron wavepacket evolution such as those in attosecond laser chemistry and ultrafast chemical reaction dynamics. We here address two mutually correlated issues on the conservation law of molecular electronic flux, which serves as a key consistency condition for electron dynamics. The first one is about a close relation between "weak" nonadiabaticity and the electron dynamics in low-energy chemical reactions. We show that the electronic flux in adiabatic reactions can be consistently reproduced by taking account of nonadiabaticity. Such nonadiabaticity is usually weak in the sense that it does not have a major effect on nuclear dynamics, whereas it plays an important role in electronic dynamics. Our discussion is based on a nonadiabatic extension of the electronic wavefunction similar in idea to the complete adiabatic formalism developed by Nafie [J. Chem. Phys. 79, 4950 (1983)], which has also recently been reformulated by Patchkovskii [J. Chem. Phys. 137, 084109 (2012)]. We give straightforward proof of the theoretical assertion presented by Nafie using a time-dependent mixed quantum-classical framework and a standard perturbation expansion. Explicitly taking account of the flux conservation, we show that the nonadiabatically induced flux realizes the adiabatic time evolution of the electronic density. In other words, the divergence of the nonadiabatic flux equals the time derivative of the electronic density along an adiabatic time evolution of the target molecule. The second issue is about the accurate computationability of the flux. The calculation of flux needs an accurate representation of the (relative) quantum phase, in addition to the amplitude factor, of a total wavefunction and demands special attention for practical calculations. This paper is the first one to approach this issue directly and show how the difficulties arise explicitly. In doing so, we reveal that a number of widely accepted truncation techniques for static property calculations are potential sources of numerical flux non-conservation. We also theoretically propose alternative strategies to realize better flux conservation.

THz birefringence inside femtosecond laser filament in air

Large birefringence of THz wave inside a femtosecond laser filament in air has been found in this work. By varying the laser pulse energy, the filament length is changed, inducing variation in the phase delay between two perpendicularly polarized THz pulses. The birefringence could be explained by the delayed rotational molecular wave packet of air molecules inside the femtosecond laser-induced filament. The newly discovered THz birefringence is essentially attributed to the strong confinement of the THz pulse inside the filament. This phenomenon has opened a new way to freely control the polarization of THz pulses emitted from an optical filament and significantly benefits polarization-sensitive THz spectroscopy and control of matter.

Correlated variational treatment of ionization coupled to nuclear motion: Ultrafast pump and ionizing probe of electronic and nuclear dynamics in LiH

Author(s): Bello, RY; Lucchese, RR; Rescigno, TN; McCurdy, CW | Abstract: We demonstrate a theoretical treatment of dissociative single ionization of the LiH molecule using two-color UV-UV pulse sequences that makes use of a highly correlated description of both the ionization continuum and target molecular ion and neutral states to which it is coupled. The present results emphasize how the details of the ionization process at various internuclear distances combine to form a lens through which such experiments image the dynamics of intermediate electronic states populated by the pump pulse. While ionization yields (dissociative and nondissociative) provide information about the amplitudes and phases that build up the molecular wave packet in the neutral states, molecular frame photoelectron angular distributions exhibit the changing character of those states, i.e., from ionic to covalent. In addition, the time-dependent mean kinetic energy of the wave packet on neutral states is clearly mapped onto the kinetic energy release of the atomic fragments produced by the probe ionization pulse.

Dynamics of the femtosecond laser-triggered spark gap.

We present space and time resolved measurements of the air hydrodynamics induced by femtosecond laser pulse excitation of the air gap between two electrodes at high potential difference. We explore both plasma-based and plasma-free gap excitation. The former uses the plasma left in the wake of femtosecond filamentation, while the latter exploits air heating by multiple-pulse resonant excitation of quantum molecular wavepackets. We find that the cumulative electrode-driven air density depression channel plays the dominant role in the gap evolution leading to breakdown. Femtosecond laser heating serves mainly to initiate the depression channel; the presence of filament plasma only augments the early heating.

Quantum state holography to reconstruct the molecular wave packet using an attosecond XUV\u2013XUV pump-probe technique

An attosecond molecular interferometer is proposed by using a XUV–XUV pump-probe scheme. The interferograms resulting in the photoelectron distributions enable the full reconstruction of the molecular wave packet associated to excited states using a quantum state holographic approach that, to our knowledge, has only been proposed for simple atomic targets combining attosecond XUV pulses with IR light. In contrast with existing works, we investigate schemes where one- and two-photon absorption paths contribute to ionize the hydrogen molecule and show that it is possible to retrieve the excitation dynamics even when imprinted in a minority channel. Furthermore, we provide a systematic analysis of the time-frequency maps that reveal the distinct, but tightly coupled, motion of electrons and nuclei.

Retrieval of full angular- and energy-dependent complex transition dipoles in the molecular frame from laser-induced high-order harmonic signals with aligned molecules

High-order harmonic signals generated in molecules are the consequence of coherent summation of complex laser-induced transition dipoles $d(\ensuremath{\theta},\ensuremath{\omega})$ with each fixed-in-space molecule; here $\ensuremath{\theta}$ is the angle of the molecular axis with respect to the laser polarization axis and $\ensuremath{\omega}$ is the harmonic energy. In the so-called rotational coherent spectroscopy, it is proposed to extract the fixed-in-space $d(\ensuremath{\theta},\ensuremath{\omega})$ in the molecular frame by measuring harmonics generated by a probing laser from the rotational molecular wave packets that have been prepared by a prior pump laser. By varying the time delay between the two lasers, methods have been utilized to extract the $\ensuremath{\theta}$ dependence of both the amplitude and phase of each individual harmonic, but the relative phase between harmonics cannot be retrieved. Here we report that this limitation can be removed. It requires the additional measurement of harmonic spectra versus the pump-probe angles at one fixed time delay. The two-dimensional input harmonic data (time-delay and pump-probe angle) are then used to retrieve the full complex transition dipole $d(\ensuremath{\theta},\ensuremath{\omega})$ using a retrieval method based on machine learning algorithms. We demonstrate this method on ${\mathrm{N}}_{2}$ and ${\mathrm{CO}}_{2}$ molecules.

Transfer-matrix theory of surface spin-echo experiments with molecules

${}^3$He beam spin-echo experiments have been used to study surface morphology, molecular and atomic surface diffusion, phonon dispersions, phason dispersions and phase transitions of ionic liquids. However, the interactions between ${}^3$He atoms and surfaces or their adsorbates are typically isotropic and weak. To overcome these limitations, one can use molecules instead of ${}^3$He in surface spin-echo experiments. The molecular degrees of freedom, such as rotation, may be exploited to provide additional insight into surfaces and the behaviour of their adsorbates. Indeed, a recent experiment has shown that $\textit{ortho}$-hydrogen can be used as a probe that is sensitive to the orientation of a Cu(115) surface [Godsi et al., Nat. Comm. $\textbf{8}$, 15357 (2017)]. However, the additional degrees of freedom offered by molecules also pose a theoretical challenge: a large manifold of molecular states and magnetic field-induced couplings between internal states. Here, we present a fully quantum mechanical approach to model molecular surface spin-echo experiments and connect the experimental signal to the elements of the time-independent molecule-surface scattering matrix. We present a one-dimensional transfer matrix method that includes the molecular hyperfine degrees of freedom and accounts for the spatial separation of the molecular wavepackets due to the magnetic control fields. We apply the method to the case of $\textit{ortho}$-hydrogen, show that the calculated experimental signal is sensitive to the scattering matrix elements, and perform a preliminary comparison to experiment. This work sets the stage for Bayesian optimization to determine the scattering matrix elements from experimental measurements and for a framework that describes molecular surface spin-echo experiments to study dynamic surfaces.