Multielectron Dynamics Research Articles

Multielectron Dynamics in the Condensed Phase: Quantum Structure-Function Relationships.

Quantum information promises dramatic advances in computing last seen in the digital revolution, but quantum hardware is fragile, noisy, and resource intensive. Chemistry has a role in developing new materials for quantum information that are robust to noise, scalable, and operable in ambient conditions. While molecular structure is the foundation for understanding mechanism and reactivity, molecular structure/quantum function relationships remain mostly undiscovered. Using singlet fission as a specific example of a multielectron process capable of producing long-lived spin-entangled electronic states at high temperatures, I describe how to exploit molecular structure and symmetry to gain quantum function and how some principles learned from singlet fission apply more broadly to quantum science.

Efficient simulation of multielectron dynamics in molecules under intense laser pulses: implementation of the multiconfiguration time-dependent Hartree–Fock method based on the adaptive finite element method

We present an implementation of the multiconfiguration time-dependent Hartree–Fock method based on the adaptive finite element method for molecules under intense laser pulses. For efficient simulations, orbital functions are propagated by a stable propagator using the short iterative Arnoldi scheme and our implementation is parallelized for distributed memory computing. This is demonstrated by simulating high-harmonic generation from a water molecule and achieves a simulation of multielectron dynamics with overwhelmingly less computational time, compared to our previous work [Sawada, R. et al. Phys. Rev. A, 2016, 93, 023434].

Time-dependent multiconfiguration self-consistent-field and time-dependent optimized coupled-cluster methods for intense laser-driven multielectron dynamics

We reviewed the time-dependent multiconfiguration self-consistent-field (TD-MCSCF) method and the time-dependent optimized coupled-cluster (TD-OCC) method for first-principles simulations of high-field phenomena such as tunneling ionization and high-order harmonic generation in atoms and molecules irradiated by a strong laser field. These methods provide a flexible and systematically improvable description of the multielectron dynamics by expressing the all-electron wavefunction by configuration interaction expansion or coupled-cluster expansion, using time-dependent one-electron orbital functions. The time-dependent variational principle plays a key role in deriving these methods while satisfying gauge invariance and Ehrenfest theorem. The real-time/real-space implementation with an absorbing boundary condition enables the simulation of high-field processes involving multiple excitation and ionization. We present a detailed, comprehensive discussion of such features of the TD-MCSCF and TD-OCC methods.

Optical Measurement of Photorecombination Time Delays

Recollision physics and attosecond pulse generation meld the precision of optics with collision physics. As a follow-up to our previous work, we reveal a new direction for the study of electronic structure and multielectron dynamics by exploiting the collision-physics nature of recollision. We show experimentally that, by perturbing recollision trajectories with an infrared field, photorecombination time delays can be measured entirely optically using the Cooper minimum in argon as an example. In doing so, we demonstrate the relationship between recollision trajectories and the transition moment coupling the ground and continuum states. In particular, we show that recollision trajectories are influenced by their parent ion, while it is commonly assumed they are not. Our work paves the way for the entirely optical measurement of ultrafast electron dynamics and photorecombination delays due to electronic structure, multielectron interaction, and strong-field-driven dynamics in complex molecular systems and correlated solid-state systems.

Postcollision-interaction effects in multistep Auger transitions following Ar 1s photoionization

Postcollision-interaction (PCI) effects involving multistep decay processes following Ar $1s$ photoionization has been studied by Auger electron spectroscopy. The experiment focused on $LMM$ Auger electrons measured in small photon energy steps across the Ar $1s$ photoionization threshold. Decay pathways that we studied include (1) the ${\mathrm{Ar}}^{+*}2{p}^{--1}\ensuremath{\rightarrow}{\mathrm{Ar}}^{2+}3{p}^{--2}$ LMM\ensuremath{\alpha} Auger process due to a single $L$ hole created by $KL$ fluorescence, (2) the ${\mathrm{Ar}}^{2+*}2{p}^{--2}\ensuremath{\rightarrow}{\mathrm{Ar}}^{3+*}2{p}^{--1}3{p}^{--2}$ ${LMM}_{1}$ Auger process following double $L$ shell hole states produced by a $KLL$ Auger processes, and (3) the subsequent ${\mathrm{Ar}}^{3+*}2{p}^{--1}3{p}^{--2}\ensuremath{\rightarrow}{\mathrm{Ar}}^{4+}3{p}^{--4}$ ${LMM}_{2}$ Auger transitions. Particularly pronounced PCI shifts and unusual line shapes compared to the ordinary one-step PCI process were found in the spectra of Auger processes following a $KLL$ Auger first step. The experimental results were compared with calculations based on the semiclassical approach to PCI. Good agreement was found between the calculated and experimental PCI shifts. The result opens possibilities for further studies of the multielectron dynamics between Auger electrons mediated through the photoelectron in these and similar systems.

Investigation of the multielectron dynamics of CO in intense laser fields by the effective potential analysis of natural orbitals

We simulated the multielectron dynamics of CO in multicolor pulses of a near-IR fundamental ω and harmonics up to 4ω by using the multiconfiguration time-dependent Hartree-Fock method. The dynamics were analyzed in terms of effective potentials that govern the time evolution of molecular orbitals. The effective potential for the highest occupied orbital has a hump barrier responsible for anisotropic ionization of CO and the shape of a hump significantly changes at different internuclear distances. The electronic response became nonadiabatic when a 4ω-field was included, resulting in the enhancement in ionization and the extension of the high-order harmonic generation cutoff.

Time-dependent optimized coupled-cluster method with doubles and perturbative triples for first principles simulation of multielectron dynamics.

We report the formulation of a new, cost-effective approximation method in the time-dependent optimized coupled-cluster (TD-OCC) framework [T. Sato et al., J. Chem. Phys. 148, 051101 (2018)] for first-principles simulations of multielectron dynamics in an intense laser field. The method, designated as TD-OCCD(T), is a time-dependent, orbital-optimized extension of the “gold-standard” CCSD(T) method in the ground-state electronic structure theory. The equations of motion for the orbital functions and the coupled-cluster amplitudes are derived based on the real-valued time-dependent variational principle using the fourth-order Lagrangian. The TD-OCCD(T) is size extensive and gauge invariant, and scales as O(N 7) with respect to the number of active orbitals N. The pilot application of the TD-OCCD(T) method to the strong-field ionization and high-order harmonic generation from a Kr atom is reported in comparison with the results of the previously developed methods, such as the time-dependent complete-active-space self-consistent field (TD-CASSCF), TD-OCC with double and triple excitations (TD-OCCDT), TD-OCC with double excitations (TD-OCCD), and the time-dependent Hartree-Fock (TDHF) methods.

Attosecond investigation of extreme-ultraviolet multi-photon multi-electron ionization

Multi-electron dynamics in atoms and molecules very often occur on sub- to few-femtosecond time scales. The available intensities of extreme-ultraviolet (XUV) attosecond pulses have previously allowed the time-resolved investigation of two-photon, two-electron interactions. Here we study double and triple ionization of argon atoms involving the absorption of up to five XUV photons using a pair of intense attosecond pulse trains (APTs). By varying the time delay between the two APTs with attosecond precision and the spatial overlap with nanometer precision, we obtain information on complex nonlinear multi-photon ionization pathways. Our experimental and numerical results show that A r 2 + is predominantly formed by a sequential two-photon process, whereas the delay dependence of the A r 3 + ion yield exhibits clear signatures of the involvement of a simultaneous two-photon absorption process. Our experiment suggests that it is possible to investigate multi-electron dynamics using attosecond pulses for both pumping and probing the dynamics.

Dynamical effects of Pauli blocking on resonant multielectron ionization

We examine the dynamical role of the Pauli exclusion principle on resonant multielectron ionization. Using a simple essential-state model that permits us approximate but analytical solutions, we show that this principle can lead to several unexpected consequences. It has only a transient effect on the resonant multielectron dynamics and its dynamical impact decreases with increasing Rabi frequency. Due to mutually competing mechanisms, this principle can enhance the ionization probability, while at the same time it also decreases the probability for double ionization. Furthermore, it can also manifest itself in the energy distribution of the ionized electrons, but only if the energy accumulation range of the electronic detector is chosen to be sufficiently wide.

Near-field imaging of dipole emission modulated by an optical grating

Attosecond measurements have been achieved in technically demanding pump-probe experiments by photoelectron streaking with stable infrared lasers and extreme-ultraviolet (XUV) instruments. Here, we demonstrate an efficient single-image all-optical measurement of an isolated attosecond pulse for its complete temporal characterization. We create the attosecond pulse with a 0.1-mJ, few-cycle, infrared pump beam and modulate it with an obliquely incident same-frequency weak beam. By refocusing the XUV beams, we obtain a spectrally resolved XUV image, showing the spectral phase of the attosecond pulse. Near-field imaging allows us to measure our pulse in 150 shots. This efficiency will be important for attosecond pulses in the water-window region. For complex systems, multi-electron dynamics is encoded in the temporal structure of attosecond pulses.

Manipulation of Multielectron Dynamics of Molecules by Fourier-Synthesized Intense Laser Pulses: Effective Potential Analysis of CO

We present a theoretical investigation as to how multielectron dynamics of CO are manipulated by Fourier-synthesized intense laser pulses. The pulses used are assumed to be comprised of harmonics up to the fourth order. The multiconfiguration time-dependent (TD) Hartree-Fock (MCTDHF) method, where the multielectron wavefunction Ψ(t) is expressed as a linear combination of various electron configurations, is employed to simulate the dynamics of CO interacting with Fourier-synthesized pulses. The multielectron nature such as electron correlation is quantified by using our effective potential approach. To begin with, the time-dependent natural orbitals {ϕj(r,t)} which diagonalize the first order reduced density matrix are obtained from Ψ(t), where r is the one-electron coordinate. The effective potentials υjeff(r,t) that determine the dynamics of ϕj(r,t) are then derived from the equations of motion for {ϕj(r,t)}. υjeff(r,t) consists of the one-body part υ1(t) including the interaction with the laser electric field ε(t) and the two-body part υ2,j(t) originating from electron-electron interaction. In this way, the role of electron correlation can be quantified by comparing υjeff(r,t) with those obtained by the TDHF method, where Ψ(t) is approximated by a single Slater determinant. We found a very similar profile in υ5σeff(r,t) of the 5σ highest occupied molecular orbital for both near-infrared one-color (ω) and directionally asymmetric ω+2ω two-color pulses; when ε(t) points from the nucleus C to O, a hump appears in υ5σeff(r,t) only 2 bohrs outward from C. The hump formation, which originates from the field-induced change in υ2,5σ(t) (especially, due to electron correlation), is responsible for preferential electron ejection from the C atom side (experimentally observed anisotropic ionization). A coherent superposition of ω and 2ω fields with an appropriate relative phase thus works as a one-color pulse of which either positive or negative peaks are filtered out. More sophisticated manipulation is possible by adding higher harmonics to a synthesized field. We show that the 5σ orbital can be squeezed toward the inside of the potential valley in υ5σeff(r,t), which encloses the molecule at a radius of ∼7 bohrs (semicircle in the region of z <0), by adjusting the phases of a ω+2ω+3ω+4ω field. The hump and valley formation in υ5σeff(r,t) are closely correlated with domains of increasing and decreasing electron density, respectively.

Time-dependent optimized coupled-cluster method for multielectron dynamics. IV. Approximate consideration of the triple excitation amplitudes.

We present a cost-effective treatment of the triple excitation amplitudes in the time-dependent optimized coupled-cluster (TD-OCC) framework called TD-OCCDT(4) for studying intense laser-driven multielectron dynamics. It considers triple excitation amplitudes correct up to the fourth-order in many-body perturbation theory and achieves a computational scaling of O(N7), with N being the number of active orbital functions. This method is applied to the electron dynamics in Ne and Ar atoms exposed to an intense near-infrared laser pulse with various intensities. We benchmark our results against the TD complete-active-space self-consistent field (TD-CASSCF), TD-OCC with double and triple excitations (TD-OCCDT), TD-OCC with double excitations (TD-OCCD), and TD Hartree-Fock (TDHF) methods to understand how this approximate scheme performs in describing nonperturbatively nonlinear phenomena, such as field-induced ionization and high-harmonic generation. We find that the TD-OCCDT(4) method performs equally well as the TD-OCCDT method, almost perfectly reproducing the results of the fully correlated TD-CASSCF with a more favorable computational scaling.

Decoherence-Induced Universality in Simple Metal Cluster Photoelectron Angular Distributions

Measured angular distributions of photoelectrons from size-selected copper and sodium cluster anions are demonstrated to exhibit a universal behavior independent of the initial electron state, cluster size, or material, which can be traced back to momentum conservation upon photoemission. Quantum simulations reproduce the universality under the assumption that multielectron dynamics localizes the emission on the cluster surface and renders the cluster opaque to photoelectrons, thereby quenching interference effects that would otherwise obscure this almost classical behavior.

Electron correlation effects in attosecond photoionization of CO2

A technique for measuring photoionization time delays with attosecond precision is combined with calculations of photoionization matrix elements to demonstrate how multi-electron dynamics affect photoionization time delays in carbon dioxide. Electron correlation is observed to affect the time delays through two mechanisms: autoionization of molecular Rydberg states and accelerated escape from a continuum shape resonance.

Analysis of the multielectron dynamics in intense laser-induced ionization of CO by the time-dependent effective potentials for natural orbitals

We simulated the multielectron dynamics of a CO molecule irradiated by near-IR λ = 760 nm two-cycle pulses with different carrier envelope phases by using the multiconfiguration time-dependent (TD) Hartree–Fock (MCTDHF) method. The ionization rate estimated from the simulations is higher when the laser electric field ɛ(t) points from C to O than in the opposite case, in agreement with the results of two-color experiments. The mechanism of the directional anisotropy in tunnel ionization of CO was examined by converting the obtained multielectron dynamics to the representation in terms of TD natural orbitals {ϕj(t)}. Within the framework of MCTDHF, we derived the equations of motion for {ϕj(t)}. From the derived equations, we defined the TD effective potentials that govern the dynamics of ϕj(t). consists of the one-body part v1(t) including the interaction with ɛ(t) and the two-body part v2,j(t) originating from electron–electron interaction. In for the 5σ HOMO, a narrow hump associated with the increase in v2,5σ(t) is surmounted on the field-distorted barrier of v1(t) + v2,5σ(0) near the nucleus C when ɛ(t) points from C to O, which results in the anisotropic ionization of CO. For 4σ, a high barrier that suppresses ionization is formed in when ɛ(t) points from C to O, which suggests that dynamical correlation exists between 4σ and 5σ electrons on route to ionization. For the opposite phase, becomes barrierless, enhancing high-harmonic generation through 4σ. We also simulated the dynamics for a λ = 380 nm pulse to investigate how reflects the nonadiabatic electronic response to the pulse. We found that the height of the hump in v1(0) + v2,5σ(t) is nearly proportional to the induced dipole moment of ϕ5σ(t), irrespective of whether the response is adiabatic or not. The for LiH is also presented to demonstrate the ubiquity of hump structures.

Time-dependent optimized coupled-cluster method for multielectron dynamics. III. A second-order many-body perturbation approximation.

We report successful implementation of the time-dependent second-order many-body perturbation theory using optimized orthonormal orbital functions called time-dependent optimized second-order many-body perturbation theory to reach out to relatively larger chemical systems for the study of intense-laser-driven multielectron dynamics. We apply this method to strong-field ionization and high-order harmonic generation of Ar. The calculation results are benchmarked against ab initio time-dependent complete-active-space self-consistent field, time-dependent optimized coupled-cluster double, and time-dependent Hartree-Fock methods, as well as a single active electron model to explore the role of electron correlation.

Spectral signature of back reaction in correlated electron dynamics in intense electromagnetic fields

This paper reports a back-reaction mechanism in multielectron correlation dynamics of helium atoms irradiated by strong laser fields. The signature of back-reaction in high harmonic spectroscopy is a secondary plateau of high-order harmonics extending the emission towards higher frequencies, beyond the standard cut-off frequency.

Strong-field control and attosecond probing of multielectron dynamics

The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.

Complete phase retrieval of photoelectron wavepackets

Coherent, broadband pulses of extreme ultraviolet light provide a new and exciting tool for exploring attosecond electron dynamics. Using photoelectron streaking, interferometric spectrograms can be generated that contain a wealth of information about the phase properties of the photoionization process. If properly retrieved, this phase information reveals attosecond dynamics during photoelectron emission such as multielectron dynamics and resonance processes. However, until now, the full retrieval of the continuous electron wavepacket phase from isolated attosecond pulses has remained challenging. Here, after elucidating key approximations and limitations that hinder one from extracting the coherent electron wavepacket dynamics using available retrieval algorithms, we present a new method called absolute complex dipole transition matrix element reconstruction (ACDC). We apply the ACDC method to experimental spectrograms to resolve the phase and group delay difference between photoelectrons emitted from Ne and Ar. Our results reveal subtle dynamics in this group delay difference of photoelectrons emitted form Ar. These group delay dynamics were not resolvable with prior methods that were only able to extract phase information at discrete energy levels, emphasizing the importance of a complete and continuous phase retrieval technique such as ACDC. Here we also make this new ACDC retrieval algorithm available with appropriate citation in return.

Time-dependent optimized coupled-cluster method for multielectron dynamics. II. A coupled electron-pair approximation.

We report the implementation of a cost-effective approximation method within the framework of the time-dependent optimized coupled-cluster (TD-OCC) method [T. Sato et al., J. Chem. Phys. 148, 051101 (2018)] for real-time simulations of intense laser-driven multielectron dynamics. The method, designated as TD-OCEPA0, is a time-dependent extension of the simplest version of the coupled-electron pair approximation with optimized orbitals [U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 139, 054104 (2013)]. It is size extensive, gauge invariant, and computationally much more efficient than the TD-OCC method with double excitations. We employed this method to simulate the electron dynamics in Ne and Ar atoms exposed to intense near infrared laser pulses with various intensities. The computed results, including high-harmonic generation spectra and ionization yields, are compared with those of various other methods ranging from uncorrelated time-dependent Hartree-Fock to fully correlated (within the active orbital space) time-dependent complete-active-space self-consistent field (TD-CASSCF). The TD-OCEPA0 results show good agreement with TD-CASSCF ones for moderate laser intensities. For higher intensities, however, TD-OCEPA0 tends to overestimate the correlation effect, as occasionally observed for CEPA0 in the ground-state correlation energy calculations.