Session S08: Dynamics at the Attosecond Timescale

Two-photon double-ionization of polyelectronic atoms with a virtual sequential model

Pump-probe experiments with new XUV sources [1] permit to observe correlated electron dynamics with attosecond resolution. The quantitative description of two-photon double ionization (2PDI) dynamics in these experiments is numerically expensive [2,3]. Still, a virtual sequential model (VSM) with only single-ionization intermediate states and no final-state interaction can capture qualitative aspects of this process even below the sequential regime [4]. In this work, we extend the VSM to finite pulses [5] and polyelectronic atoms. The photoionization cross section of the ground state and of the intermediate ionic states are computed ab initio with the NewStock close-coupling code. This model includes the contribution from final autoionizing states as well as finite-pulse effects. The joint energy distribution for the 2PDI of helium compares well with available results in the literature for both single and sequences of multiple ultrashort pulses. Preliminary results for the application of this approach to the neon atom will be presented. 

[1] Duris et al, Nat. Phot. 14, 30 (2020); Saito et al, Optica 6, 1542 (2019).

[2] Feist et al, PRA 77, 043420 (2008).

[3] Palacios et al, PRA 79, 033402 (2009).

[4] Horner et al., PRA 76, 030701(R) (2007).

[5] Jimenez et al, PRA 93, 023429 (2016).   

Strong-field dissociation of CO2+ Van-Hung Hoang1 and Uwe Thumm1 1Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA

We theoretically investigated strong-field XUV-IR pump-probe dissociative ionization of CO₂. Employing the multi-configurational self-consistent-field quantum-chemistry code GAMESS to ab initio calculate CO₂⁺ adiabatic potential energy surfaces and dipole couplings, we numerically propagated the time-dependent Schrödinger equation for the nuclear motion. Distinguishing the effects of (velocity-dependent) non-adiabatic and external IR-field dipole couplings, we (A) calculated the population of the predissociative C ²Σ_g⁺ state and kinetic energy release (KER) in the O + CO⁺ dissociation channel and (B) investigated the imprint on KER spectra of the nuclear dynamics near the A²Π_u and B²Σ_u⁺ conical intersection. Accounting for all vibrational normal modes (bending, symmetrical and anti-symmetrical stretch), our simulated fragment KER spectra and pump-probe-delay dependent CO⁺ yield oscillation period are in good agreement with the experiment of Timmers et al., Phys. Rev. Lett. 113, 113003 (2014). This agreement persists for reduced-dimensionality calculations with linear molecules (disregarding bending).   

Angle-Dependent Continuum Transitions in Multi-Sideband RABBITT on Argon: Experiment and Theory

The reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) [1,2] is a commonly used technique for the study of photoionization dynamics in atomic, molecular, and solid systems with attosecond pulses [3]. Recently, a three-sideband (3-SB) scheme was suggested [4] and analyzed in detail theoretically for atomic hydrogen [5]. We present recently obtained results from a 3-SB RABBITT experiment with argon as the target gas. The dependence of the continuum-continuum transition phase on the orbital angular momenta of the continuum states is revealed in the angular variation of the three sideband phases. We also directly show an effect of Fano resonances on these phases. Argon is experimentally more readily accessible than atomic hydrogen, but its multi-electron character presents a major challenge to theory. Since single-active electron (SAE) calculations do not adequately reproduce the photoionization cross section of argon, we use the multi-electron R-matrix with time dependence (RMT) method [6] to generate theoretical predictions. These are compared with the latest experimental data.

[1] P. Paul et al., Science 292 (2001) 1689.

[2] H. Muller, Appl. Phys. B 74 (2002) S17.

[3] J. Dahlström et al., Chem. Phys. 414 (2013) 53.

[4] A. Harth et al.,Phys. Rev. A 99 (2019) 023410.

[5] D. Bharti et al., Phys. Rev. A 103 (2021) 022834.

[6] A. C. Brown et al., Comput. Phys. Comm. 250 (2020) 107062.   

Time delay in XUV photon driven ionization of C60 giant plasmon

Large scale coherent electron correlations play the dominant role to induce a giant plasmon excitation in fullerenes driven by extreme ultra-violet (XUV) light absorption. This excitation primarily decays via the single-electron continuum channels to create a broad resonance in the ionization spectrum. The underlying many-body mechanism induces a temporary attractive force to affect the time delay of the photoelectrons to reach the detector. In order to determine this delay, the so-called Eisenbud-Wigner-Smith delay, for the C₆₀ fullerene molecule, we apply a scheme of linear response time-dependent density functional theory [1] where the C₆₀ ion-core is frozen in a spherical jellium charge distribution. We find a delay approximately within the range of 100-200 attoseconds over the plasmon resonance energy range. This is comparable to the average dephasing time obtained from the linewidth of the resonance. The result served as an essential ingredient to describe recent real time measurements by photoelectron chronoscopy [2]. [1] Choi et al., Phys. Rev. A, 95, 023404 (2017); [2] Biswas et al., arXiv:2111.14464 [physics.atom-ph]   

ASTRA, a transition-density-matrix method for attosecond molecular dynamics

The push of ultrashort light sources to and beyond the water window [1], to high intensity [2], and to ever shorter durations has opened the way to the site-specific x-ray-pump x-ray-probe study of electron dynamics in molecules of chemical relevance. Theoretical tools able to quantitatively resolve in time the correlated and entangled character of molecular ionization processes are necessary to guide these experiments. Here we present ASTRA (AttoSecond TRAnsitions), a program based on an innovative approach to the close-coupling method for molecular ionization. ASTRA makes use of high-order transition density matrices between large-scale-CI ionic states with arbitrary symmetry and multiplicity, obtained with an extension of the LUCIA code [3], and on hybrid Gaussian-B-spline integrals [4,5]. These essential features allow ASTRA to reach core-excitation/decay energies, to account for exchange effects exactly, and to scale independently of the size of the parent-ion configuration space. The talk will focus on ASTRA theory, its current applications, and its future directions.

[1] Duris J et al, Nat. Phot. 14, 30 (2020)

[2] Saito N et al, Optica 6, 1542 (2019)

[3] Olsen J et al, JCP 104, 8007 (1996)

[4] Masin Z et al, CPC 249, 107092 (2020)

[5] Gharibnejad H et al, CPC 263, 107889 (2021)   

Photoelectron – ion entanglement in streaked direct and shake-up photoemission from helium: an ab initio approach

We applied our FE-DVR code for the ab initio calculation of single- and double-ionization of gaseous helium atoms [1] to explore the effects of electronic correlation on attosecond time- and angle-resolved photoemission. Our calculated spectra and relative photoemission time delays for IR streaked direct and He+ (n=2) shake-up XUV emission agree well with experimental and theoretical data in [2]. To scrutinize the influence of the transient induced oscillating residual excited He+ (n=2,3) charge distribution, we compared our ab-initio streaking calculations with single active electron (SAE) calculations. By adjusting effective multipole SAE potentials to ab initio calculated He+* charge distributions, we assessed to role of individual multipole components of the residual He+* ion on spectra and photoemission delays.

[1] A. Liu and U. Thumm, “Laser-assisted XUV double ionization of helium: Energy-sharing dependence of joint angular distributions”, Phys. Rev. A 91, 043416 (2015).

[2] M. Ossiander et al., “Attosecond correlation dynamics” Nat. Phys. 13, 280 (2017).

    

Direct Electric Field Measurement of Femtosecond Time-Resolved Four-Wave Mixing Signals in Molecules

We measure the third order nonlinear response in molecules such as CO₂ and ethylene, by fully reconstructing the emitted signal electric field. Using a spectral interferometry-based technique for measuring ultraweak femtosecond pulses, called TADPOLE, we measure the real and imaginary parts of the nonlinear response in a single measurement. The nonlinear signal is generated using the Optical Kerr-effect (OKE), where a pair of femtosecond pulses (gate and probe) generate a signal that co-propagates with the probe beam having a polarization orthogonal to the probe polarization. Properties of the reconstructed signal electric field, such as the pulse envelope full-width half maximum and chirp of the temporal phase, can provide detailed information about ultrafast dynamics in these systems. We present results from measurement of nonlinear signal electric fields generated from purely electronic response in neutral CO₂ molecules and ionized ethylene molecules. A further extension of these experiments to measure higher order nonlinear response, such as the fourth order non-linear response in chiral molecules will be discussed.

    

Measurement of molecular-frame electronic nonlinear response in aligned carbon dioxide and nitrogen molecules

We report the measurement of the molecular frame third-order nonlinear response tensor (second hyper-polarizability) in impulsively aligned carbon dioxide and nitrogen molecules. A moderately strong femtosecond near-infrared laser pulse is used to impulsively align gas molecules, and a set of weaker femtosecond pulses subsequently probe the nonlinear response using non-degenerate four-wave mixing (N-DFWM). The emitted electric field is directly measured, using a spectral interferometry technique for measuring ultraweak femtosecond pulses, called TADPOLE. The measured amplitude and phase of the signal electric field is combined to get the real and imaginary parts of the signal in a single measurement. By suppressing the rotational and ionization grating contributions, N-DFWM exclusively measures the electronic-only nonlinearity. By analyzing the nonlinear signal as a function of time delay between the alignment pulse and the four-wave mixing pulses, the molecular frame nonlinear response is extracted using the previously established technique of Orientation Resolution through Rotational Coherence Spectroscopy (ORRCS). Using the transformation properties of a tensor under rotation, a few tensor components measured as a function of the molecular alignment angle can be converted into multiple tensor components for a fixed molecular orientation. Knowledge of these multiple tensor components are used to distinguish the symmetries of the ground state electronic character in different molecules. We discuss these results for carbon dioxide and nitrogen. The roadmap for extending these nonlinear response tensor measurements to study ultrafast dynamics on electronically excited states in molecules is discussed.   

Improved initial conditions of the electron ionized by a strong, linearly polarized laser field and their reconstruction from the detected momentum of the electron

Tunneling time and exit momentum are of outstanding importance regarding both quantum theory and attosecond metrology. Several research groups published relevant experimental results, and the explanatory theoretical models often employ classical dynamics, where the choice of proper initial conditions is an important open question.

We focus on atomic hydrogen driven by a linearly polarized few-cycle near-infrared laser pulse having a peak intensity that ensures tunneling. We show the real classical picture associated with the exact quantum process of strong-field ionization in the parameter range relevant to state-of-the-art experimental techniques [Sz. Hack et al. Phys. Rev. A, 104, L031102 (2021)]. This classical model follows the quantum evolution very well; it accounts for direct ionization, rescattering and the blurred nature of the liberation process; it solves and explains the problem of the non-zero initial momentum in models assuming traditional tunneling.

Using the improved initial conditions, we show a simple procedure to reconstruct the starting time from the detected momentum of a directly escaping electron. We tested this method with numerical experiments resulting the accuracy of the reconstructed starting time less than 5 as for the most probable trajectories.   

On-the-fly ab initio semiclassical evaluation of electronic coherences in polyatomic molecules reveals a simple mechanism of decoherence

Irradiation of a molecular system by an intense laser field can trigger dynamics of both electronic and nuclear subsystems. The lighter electrons usually move on much faster, attosecond time scale but the slow nuclear rearrangement damps ultrafast electronic oscillations, leading to the decoherence of the electronic dynamics within a few femtoseconds. We show that a simple, single-trajectory semiclassical scheme can evaluate the electronic coherence time in polyatomic molecules accurately by demonstrating an excellent agreement with full-dimensional quantum calculations. In contrast to numerical quantum methods, the semiclassical one reveals the physical mechanism of decoherence beyond the general blame on nuclear motion. In the propiolic acid, the rate of decoherence and the large deviation from the static frequency of electronic oscillations are quantitatively described with just two semiclassical parameters---the phase space distance and signed area between the trajectories moving on two electronic surfaces. Because it evaluates the electronic structure on the fly, the semiclassical technique avoids the "curse of dimensionality" and should be useful for preselecting molecules for experimental studies.