Photoionization Time Delay Research Articles

Photo-Ionization Time Delay in Linearly Extended π-Conjugated Molecular Systems

We calculate the photo-ionization time delay for extended, linear, π-conjugated molecules. Ionization can be realized as scattering of an electron from bound to continuum states due to interaction with an ionizing radiation field. This allows us to use the Wigner method, whereby the rate of change in phase of the scattered electron wave packet with respect to the electron energy gives a measure of the ionization time delay. An analytical expression for ionization time delay is obtained using a model system that shows how interference between different ionization pathways leads to a finite time delay, even if there is a zero time delay corresponding to individual pathways. It is observed that the ionization time delay increases linearly as the size of the chain increases. We compute the ionization time delay also using computational chemistry and compare the results with those obtained from the model system. In qualitative agreement with the model calculation, we find that the ionization time delay increases linearly with increasing conjugation.

Molecular-Frame Photoelectron Angular Distributions of CO in the Vicinity of Feshbach Resonances: An XCHEM Approach.

The advent of ultrashort XUV pulses is pushing for the development of accurate theoretical calculations to describe ionization of molecules in regions where electron correlation plays a significant role. Here, we present an extension of the XCHEM methodology to evaluate laboratory- and molecular-frame photoelectron angular distributions in the region where Feshbach resonances are expected to appear. The performance of the method is demonstrated in the CO molecule, for which information on Feshbach resonances is very scarce. We show that photoelectron angular distributions are dramatically affected by the presence of resonances, to the point that they can completely reverse the preferred electron emission direction observed in direct nonresonant photoionization. This is the consequence of significant changes in the electronic structure of the molecule when resonances decay, an effect that is mostly driven by electron correlation in the ionization continuum. The present methodology can thus be helpful for the interpretation of angularly resolved photoionization time delays in this and more complex molecules.

Quantitative uncertainty determination of phase retrieval in RABBITT.

Reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is one of the most widely used approaches to measure the time delays in photoionization. The time delay, which corresponds to a phase difference of two oscillating signals, is usually retrieved by cosine fitting or fast Fourier transform (FFT). We propose two estimators for the phase uncertainty of cosine fitting from the signal per se of an individual experiment: (i) σ(φ fit)≈B A2N, where B/A is the mean-value-to-amplitude ratio, and N is the total count number, and (ii) σ(φ fit)≈1-R 2 R 2 n bins, where nbins is the total number of bins in the time domain, and R2 is the coefficient of determination. The former estimator is applicable for the statistical fluctuation, while the latter includes the effects from various uncertainty sources, which is mathematically proven and numerically validated. This leads to an efficient and reliable approach to determining quantitative uncertainties in RABBITT experiments and evaluating the observed discrepancy among individual measurements, as demonstrated on the basis of experimental data.

Two-center interference and stereo Wigner time delay in photoionization of asymmetric molecules

We present numerical simulations of the time delay in photoemission of asymmetric diatomic molecules using the technique of reconstruction of attosecond beating by interference of two-photon transitions (RABITT) by solving the time-dependent Schr\"odinger equation. Our results show an obvious time delay between photoelectrons emitted to the left and right and this relative time delay oscillates as the photoelectron energy changes. More interestingly, the amplitude of this oscillation increases when the asymmetry degree of diatomic molecules decreases. With the method of the selected continuum wave functions, we calculate the Wigner time delay in photoionization. The obtained stereo Wigner time delay also oscillates with photoelectron energy. This oscillation is traced back to two-center interferences and it could explain the relative time delay in the RABITT measurement. Furthermore, our results indicate that the continuum-continuum time delay in photoemission of heteronuclear molecules is asymmetric.

Attosecond photoionization dynamics in the vicinity of the Cooper minima in argon

Using a spectrally resolved electron interferometry technique, we measure photoionization time delays between the $3s$ and $3p$ subshells of argon over a large 34-eV energy range covering the Cooper minima in both subshells. The observed strong variations of the $3s-3p$ delay difference, including a sign change, are well reproduced by theoretical calculations using the Two-Photon Two-Color Random Phase Approximation with Exchange. Strong shake-up channels lead to photoelectrons spectrally overlapping with those emitted from the $3s$ subshell. These channels need to be included in our analysis to reproduce the experimental data. Our measurements provide a stringent test for multielectronic theoretical models aiming at an accurate description of inter-channel correlation.

The Coulomb effects in laser-assisted single photoionization

Attosecond photoionization time delays reveal information about an outgoing electron getting away from the Coulomb potential. In this study, we improve the eikonal approximation model that overestimates the laser-Coulomb coupling effect in the laser-assisted photoionization of atoms. The improved eikonal approximation model can be accurate on about the 2 asec level relative to the time-dependent Schrödinger equation results. The improvement of photoionization time delays demonstrates that the electrons ionized by extreme ultraviolet attosecond pulse possesses momentum larger than the asymptotical momentum due to the attractive Coulomb potential of the parent ion. These results will give a deeper insight into understanding the laser-assisted single photoionization.

Zeptosecond Dynamics in Atoms: Fact or Fiction?

Photon exchange due to nuclear bremsstrahlung during nuclear collisions can cause Coulomb excitation in the projectile and the target nuclei. The corresponding process originated in nuclear timescales can also be observed in atomic phenomenon experimentally if it delayed by at least with an attosecond or longer timescales. We have found that this happens due to a mechanism involving the Eisenbud-Wigner-Smith time delay process. We have estimated photoionization time delays in atomic collisions utilizing the nonrelativistic version of random phase approximation with exchange and Hartree-Fock methods. We present three representative processes in which we can observe the phenomena in attosecond timescales even though they originate from excitations in the zeptosecond timescales. Thus the work represents an investigation of parallels between two neighboring areas of physics. Furthermore the present work suggests new possibilities for atomic physics research near the Coulomb barrier energy, where the laser is replaced by nuclear bremsstrahlung.

Photoionization of Xe 5s: angular distribution and Wigner time delay in the vicinity of the second Cooper minimum

The angular distribution and photoionization Wigner time delay of Xe 5s photoelectrons are studied in the region of the second Cooper minimum (SCM) using (i) the relativistic multiconfiguration Tamm–Dancoff approximation, (ii) the relativistic-random-phase approximation (RRPA) and (iii) the RRPA-with-relaxation to demonstrate how differing treatments of correlation, and the relativistic interactions, affect the results. The results of the three methods are compared with each other and with available experimental data. The comparison reveals the importance of electron correlations for which a multiconfiguration description of the initial state is essential. The spin-resolved and spin-averaged photoionization time delay results show important signatures in the region of the SCM in the Xe 5s photoionization cross-section.

Angle-resolved time delays for shake-up ionization of helium

Recent angle-resolved RABBITT experiments have shown that the photoionization time delay depends on the emission angle of the photoelectron. In this work we demonstrate that for photoemission from helium accompanied by shake-up (correlation satellites), the angular variation of the time delay is dramatically enhanced by the dipolar coupling between the photoelectron and the highly polarizable bound electron in the IR field. We show that the additivity rule for the time delays due to the atomic potential, the continuum-continuum (cc) coupling by the IR field, and due to this two-electron process remains valid for angle-resolved RABBITT. Our results are expected to be also applicable to other multi-electron systems that are highly polarizable or feature a permanent dipole moment.

Photoionization phase shift and Wigner time delay of endohedrally confined atoms using transient phase methods

In contrast to the conventional finite difference methods, two transient phase methods have been effectively used in the present work to directly compute the photoionization phase shift and Wigner time delay of confined atoms (A@C60) in the single-active electron (SAE) approximation. The different phase methods: (A) employing logarithmic derivatives at shell boundaries, and (B) Born approximation are verified with the help of well-established finite difference methods in SAE approximation and sophisticated many-electron techniques. In this work, confinement oscillations on the dipole phase and photoelectron group delay following ionization from 1s subshell of H@C60, 3p subshell of Ar@C60 and 5p subshell of Xe@C60 are analyzed. The comparison with many-body calculation shows that the features in the time delay of a confined system are governed mainly by the effects of screening apart from that due to the external potential. A systematic study and comparison of the results from phase methods and many-electron techniques indicate that these techniques can be effectively used in the analysis of photoionization phase shift and time delay in confined atoms.

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.

Time delays from one-photon transitions in the continuum

Attosecond photoionization time delays reveal information about the potential energy landscape that an outgoing electron wavepacket probes upon ionization. In this study, we experimentally quantify the dependence of the time delay on the angular momentum of the liberated photoelectrons. For this purpose, we resolved electron quantum-path interference spectra in energy and angle using a two-color attosecond pump–probe photoionization experiment in helium. A fitting procedure of the angle-dependent interference pattern allows us to disentangle the relative phase of all four quantum pathways that are known to contribute to the final photoelectron signal. In particular, we resolve the dependence on angular momentum of the delay of one-photon transitions between continuum states, which is an essential and universal contribution to the total photoionization delay observed in attosecond pump–probe measurements. For such continuum–continuum transitions, we measure a delay between outgoing s and d electrons as large as 12 attoseconds, close to the ionization threshold in helium. Both single-active-electron and first-principles ab initio simulations confirm this observation for helium and hydrogen, demonstrating the universality of the observed delays.

Effect of SOIAIC on photoionization time delay of the Xe 3d subshell

SynopsisThe effect of spin-orbit activated interchannel coupling (SOIAIC) has been studied on the time delay spectrum of 3d photoionization in xenon. The relativistic-random-phase-approximation with relaxation (RRPA-R) has been used to calculate the Wigner-Eisenbud-Smith (WES) time delay in photoionization. SOIAIC has a strong influence on the WES time delay for all ejection angles of the photoelectrons with respect to the incident direction and the polarization vector of the photon absorbed.

Angle-resolved time delays in photoionization with a high repetition rate laser source

SynopsisComplete measurements of photoionization include both time-resolved and angle-resolved mapping of the atomic and molecular dynamics. The setup described in this work is suited to be used for attosecond pump-probe experiments as well as providing insights into the angular dependencies of photoionization.

Fano's Propensity Rule in Angle-Resolved Attosecond Pump-Probe Photoionization.

In a seminal article, Fano predicts that absorption of light occurs preferably with increase of angular momentum. We generalize Fano's propensity rule to laser-assisted photoionization, consisting of absorption of an extreme-ultraviolet photon followed by absorption or emission of an infrared photon. The predicted asymmetry between absorption and emission leads to incomplete quantum interference in attosecond photoelectron interferometry. It explains both the angular dependence of the photoionization time delays and the delay dependence of the photoelectron angular distributions. Our theory is verified by experimental results in Ar in the 20-40eV range.

Strong dependence of photoionization time delay on energy and angle in the neighborhood of Fano resonances

We uncover dramatic variations of the Wigner photoemission time delay with energy and angle in the vicinity of a Fano resonance with the time delay taking opposite signs at different angles at the same energy as well as at the opposite sides of the resonance at the same angle. These variations are illustrated by choosing the Ne $2s\ensuremath{\rightarrow}3p$ autoionizing state as a case study. Moreover, we demonstrate the existence of strikingly significant changes in time delay due to relativistic effects despite Ne being a low-$Z$ atom. This finding shows the possibility for utilizing time delay chronoscopy as a route towards experimental probing of relativistic interactions and the phases of individual transition matrix elements upon atomic photoionization of low-$Z$ atoms. Finally, we develop a practical parametrization to model and explain the angle and energy variation of the autoionizing resonance time delay in the nonrelativistic limit.

Validity of extracting photoionization time delay from the first moment of streaking spectrogram**Project supported by the Talent Introduction Foundation of Qiannan Normal University of Nationalities, China (Grant No. qnsyrc201619), Natural Science Foundation of Guizhou Provincial Education Department for Young Talents, China (Grant No. Qian Education Contract KY[2017]339), and Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office

Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the methods of extracting the time delay from the streaking spectrogram, the simplest one is to calculate the first moment of the spectrogram and to measure its offset relative to the vector potential of the infrared field. The first moment method has been used in many theoretical simulations and analysis of experimental data, but the meaning of this offset needs to be investigated. We simulate the spectrograms and compare the extracted time delay from the first moment with the input Wigner delay. In this study, we show that the first moment method is valid only when the group delay dispersions corresponding to both the spectral phase of the attosecond pulse and the phase of the single-photon transition dipole matrix element of the target are small. Under such circumstance, the electron wave packet behaves like a classical particle and the extracted time delay can be related to a group delay in the photoionization process. To avoid ambiguity and confusion, we also suggest that the photoionization time delay be replaced by photoionization group delay and the Wigner time delay be replaced by Wigner group delay.

Intershell-correlation-induced time delay in atomic photoionization

We predict an observable Wigner time delay in outer atomic shell photoionization near inner shell thresholds. The near-threshold increase of time delay is caused by intershell correlation and serves as a sensitive probe of this effect. The time delay increase is present even when the inner and outer shell thresholds are hundreds of electron volts apart. We illustrate this observation by several prototypical examples in noble gas atoms from Ne to Kr. In our study, we employ the random phase approximation with exchange and its relativistic generalization. We also support our findings by a simplified, yet quite insightful, treatment within the lowest-order perturbation theory.

Wigner–Eisenbud–Smith photoionization time delay due to autoioinization resonances

An empirical ansatz for the complex photoionization amplitude and Wigner–Eisenbud–Smith time delay in the vicinity of a Fano autoionization resonance are proposed to evaluate and interpret the time delay in the resonant region. The utility of this expression is evaluated in comparison with accurate numerical calculations employing the ab initio relativistic random phase approximation and relativistic multichannel quantum defect theory. The indisputably good qualitative agreement (and semiquantitative agreement) between corresponding results of the proposed model and results produced by the ab initio theories proves the usability of the model. In addition, the phenomenology of the time delay in the vicinity of multichannel autoionizing resonances is detailed.

Attosecond Time Delay in Photoionization of Noble-Gas and Halogen Atoms

Ultrafast processes are now accessible on the attosecond time scale due to the availability of ultrashort XUV laser pulses. Noble-gas and halogen atoms remain important targets due to their giant dipole resonance and Cooper minimum. Here, we calculate photoionization cross section, asymmetry parameter and Wigner time delay using the time-dependent local-density approximation (TDLDA), which includes the electron correlation effects. Our results are consistent with experimental data and other theoretical calculations. The asymmetry parameter provides an extra layer of access to the phase information of the photoionization processes. We find that halogen atoms bear a strong resemblance on cross section, asymmetry parameter and time delay to their noble-gas neighbors. Our predicted time delay should provide a guidance for future experiments on those atoms and related molecules.