Wigner Time Delay Research Articles

Photoionization dynamics of endohedrally confined atomic H and Ar: a contrasting study between compact versus diffused model potential

Photoionization from H@C60 and Ar@C60 is studied by employing two different model potentials to simulate the endohedral environment. The contrast between the diffusive Gaussian annular square well (GASW) and the compact annular square well (ASW) model potential on the photoionization dynamics is explored by studying the cross-section, phase shift, and Wigner time delay. A realistic description of the fullerene environment requires the right amount of diffuseness and compactness, and the proposed GASW model has both of these attributes. The dynamical properties of an encapsulated atom are studied systematically as a function of the well depth, and it is found that the GASW model induces mild and realistic confinement oscillations on the photoionization parameters in comparison with the ASW case. In addition, the present work brings out a few other interesting features. For a confining well depth of 1.03 a.u., the phase of the dipole matrix elements takes sharp jumps akin to the behavior of dipole phases at the Cooper minimum. In the case of free Ar, the correlation effects contribute less to the time delay in comparison with screening effects near the Cooper minimum. In search of a realistic potential to mimic confinement, the GASW model potential is recommended.

Dominance of correlation and relativistic effects on photodetachment time delay well above threshold

Wigner time delay in photodetachment from the $3{p}_{3/2}$ and $3{p}_{1/2}$ subshells of ${\mathrm{Cl}}^{\ensuremath{-}}$ has been studied in the vicinity of the $2{p}_{3/2}$ and $2{p}_{1/2}$ thresholds, using the relativistic random phase approximation (RRPA). The results show time delay spectra dominated by many-body correlations along with very complicated dependence on the energy over a broad spectral range. In addition, the time delay spectra of the two spin-orbit split $3p$ subshells differ significantly from one another, thereby revealing the importance of relativistic effects even in the case of a low-$Z$ system.

Effects of disorder in frozen-mode light

We employ renormalization ideas in order to describe the interplay between a frozen mode regime—a scattering feature associated with the presence of stationary inflection point (SIP) singularities—and disorder in photonic systems. Specifically, we demonstrate the existence of a β-function for a (rescaled) Wigner delay time PL at SIP frequencies which depends on PL itself and controls its variation with the system size L and disorder strength.

Wigner time delay in photodetachment

This work was supported by the infrastructure and hospitality provided by the Director, IIT Tirupati. S.S. is thankful to IIT Patna for the hospitality and support he received during his visit to IIT Patna to do one part of the work. J.J. acknowledges the support provided by SERB through Project No. ECR/2016/001564. S.T.M. acknowledges the support provided by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, Grant No. DE-FG02- 03ER15428.

Peculiarities of Wigner Time Delay in Slow-Electron Elastic Scattering by a Potential Well with Arising Discrete Levels

We generalize here the one-level consideration in our recent paper arXiv:1901.00411 [1] to the case when an electron collides with a potential that have any number of s bound states. We investigate peculiarities in the Wigner time delay behavior for slow electron elastic s-scattering by spherically symmetric square-potential well. We have considered potential wells, the variation of parameters of which (potential depth U and its radius R) lead to arising arbitrary number of s bound states. We demonstrate that while the time delay for potential wells with no discrete s-levels always has a positive value for small electron energies, it changes sign after level arising. We found that at the moments of arising in the well not only of the first but also following s-levels as well, the time delay as a function of U experiences instant jumps from a positive value to a negative one. The amplitudes of these jumps increases with decrease of the electron wave vector k. The times delay for potential well, the variation of the radius of which R leads to the appearance of discrete levels, also change sign at these critical radii.

Wigner Time Delay Induced by a Single Quantum Dot

Resonant scattering of weak coherent laser pulses on a single two-level system realized in a semiconductor quantum dot is investigated with respect to a time delay between incoming and scattered light. This type of time delay was predicted by Wigner in 1955 for purely coherent scattering and was confirmed for an atomic system in 2013 [R. Bourgain etal., Opt. Lett. 38, 1963 (2013)OPLEDP0146-959210.1364/OL.38.001963]. In the presence of electron-phonon interaction, we observe deviations from Wigner's theory related to incoherent and strongly non-Markovian scattering processes which are hard to quantify via a detuning-independent pure dephasing time. We observe detuning-dependent Wigner delays of up to 530ps in our experiments which are supported quantitatively by microscopic theory allowing for pure dephasing times of up to 950ps.

Magic Number Theory of Superconducting Proximity Effects and Wigner Delay Times in Graphene-Like Molecules

When a single molecule is connected to external electrodes by linker groups, the connectivity of the linkers to the molecular core can be controlled to atomic precision by appropriate chemical synthesis. Recently, the connectivity dependence of the electrical conductance and Seebeck coefficient of single molecules has been investigated both theoretically and experimentally. Here we study the connectivity dependence of the Wigner delay time of single-molecule junctions and the connectivity dependence of superconducting proximity effects, which occur when the external electrodes are replaced by superconductors. Although absolute values of transport properties depend on complex and often uncontrolled details of the coupling between the molecule and electrodes, we demonstrate that ratios of transport properties can be predicted using tables of 'magic numbers,' which capture the connectivity dependence of superconducting proximity effects and Wigner delay times within molecules. These numbers are calculated easily, without the need for large-scale computations. For normal-molecule-superconducting junctions, we find that the electrical conductance is proportional to the fourth power of their magic numbers, whereas for superconducting-molecule-superconducting junctions, the critical current is proportional to the square of their magic numbers. For more conventional normal-molecule-normal junctions, we demonstrate that delay time ratios can be obtained from products of magic number tables.

Ultrafast time-domain wave packet evolution of atomic photoionization

We present a combined numerical and theoretical study of atomic photoionization in the time domain. We show how a photoelectron wave packet rapidly changes its shape after being emitted, from a complex multipeak structure to eventually a relatively simple single-peak structure. This time-domain shape evolution provides information beyond the time-dependent average position of the wave packet, which for example has been used to retrieve the Wigner time delay. For few-cycle laser pulses, the asymptotic velocity of the photoelectron can be different from long-pulse-based expectations due to non-negligible changes of the dipole matrix element within the spectra of the laser pulses.

Orientation-dependent stereo Wigner time delay and electron localization in a small molecule

We present orientation-dependent stereo Wigner time delays of CO molecules, which reveal the electron localization at the ionization moment. Together with theoretical calculations this constitutes a spatially-and temporally-resolved reconstruction of the molecular photoelectric effect.

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.

Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, related to the energy (or frequency) derivative of the scattering matrix . We develop a random matrix approach to study the statistical properties of the symmetrised Wigner–Smith time-delay matrix , and obtain the joint distribution of and for the system with non-ideal contacts, characterised by a finite transmission probability (per channel) . We derive two representations of the distribution of in terms of matrix integrals specified by the Dyson symmetry index (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay , which is an important quantity providing the density of states of the open system. Using the obtained results, we determine the distribution of the Wigner time delay in the weak coupling limit and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour for . (ii) The distribution shows the universal behaviour in some intermediate range . (iii) It has a power law decay for large .

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.

How Long Does a Quantum Particle or Wave Stay in a Given Region of Space?

The delay time associated with a scattering process is one of the most important dynamical aspects in quantum mechanics. A common measure of this is the Wigner delay time based on the group velocity description of a wave packet, which may easily indicate superluminal or even negative times of interaction that are unacceptable. Many other measures such as dwell times have been proposed, but also suffer from serious deficiencies, particularly for evanescent waves. One important way of realising timescales that are causally connected to the spatial region of interest relies on utilising the dynamical evolution of extra degrees of freedom, called quantum clocks, such as the precession of the spin of an electron in an applied magnetic field or the coherent decay or growth of light in an absorptive or amplifying medium placed within the region of interest. Here we provide a review the several approaches developed to answer the basic question “how much time does a quantum particle (or wave) spend in a specified region of space?” While a unique answer still evades us, important progress has been made in understanding the timescales and obtaining positive definite times of interaction by noting that all such clocks are affected by spurious scattering concomitant with the very clock potentials, however, weak they be, and by eliminating the spurious scattering.

Orientation-dependent stereo Wigner time delay and electron localization in a small molecule.

Attosecond metrology of atoms has accessed the time scale of the most fundamental processes in quantum mechanics. Transferring the time-resolved photoelectric effect from atoms to molecules considerably increases experimental and theoretical challenges. Here we show that orientation- and energy-resolved measurements characterize the molecular stereo Wigner time delay. This observable provides direct information on the localization of the excited electron wave packet within the molecular potential. Furthermore, we demonstrate that photoelectrons resulting from the dissociative ionization process of the CO molecule are preferentially emitted from the carbon end for dissociative 2Σ states and from the center and oxygen end for the 2Π states of the molecular ion. Supported by comprehensive theoretical calculations, this work constitutes a complete spatially and temporally resolved reconstruction of the molecular photoelectric effect.

Simulation of angular-resolved RABBITT measurements in noble-gas atoms

We simulate angular resolved RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) measurements on valence shells of noble gas atoms (Ne, Ar, Kr, and Xe). Our non-perturbative numerical simulation is based on solution of the time-dependent Schr\"odinger equation for a target atom driven by an ionizing XUV and dressing IR fields. From these simulations we extract the angular dependent magnitude and phase of the RABBITT oscillations and deduce the corresponding angular anisotropy {\beta} parameter and Wigner time delay ${\tau}_W$ for the single XUV photon absorption which initiates the RABBITT process. Said {\beta} and ${\tau}_W$ parameters are compared with calculations in the random phase approximation with exchange (RPAE) which includes inter-shell correlation. This comparison is used to test various effective potentials employed in the one-electron TDSE. In lighter atoms (Ne and Ar), several effective potentials are found to provide accurate simulation of RABBITT measurements for a wide range of photon energies up to 100 eV above the valence shell threshold. In heavier atoms (Kr and Xe), the onset of strong correlation with the d-shell restricts the validity of the single active electron approximation to several tens of eV above the valence shell threshold.

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.

Attosecond delay in the molecular photoionization of asymmetric molecules.

We report theoretical calculations of the delay in photoemission from CO with particular emphasis on the role of the ultrafast electronic bound dynamics. We study the delays in photoionization in the HOMO and HOMO-1 orbitals of the CO molecule by looking into the stereo Wigner time delay technique. That compares the delay in photoemission from electrons emitted to the left and right to extract structural and dynamical information of the ionization process. For this we apply two techniques: The attosecond streak camera and the time of flight technique. Although they should provide the same results we have found large discrepancies of up to 36 in the case of HOMO, while for the HOMO-1 we obtain the same results with the two techniques. We have found that the large time delays observed in the HOMO orbital with the streaking technique are a consequence of the resonant transition triggered by the streaking field. This resonant transition produces a bound electron wavepacket that modifies the measurements of delay in photoionization. As a result of this observation, our technique allows us to reconstruct the bound wavepacket dynamics induced by the streaking field. By measuring the expected value of the electron momentum along the polarization direction after the streaking field has finished, we can recover the relative phase between the complex amplitudes of the HOMO and LUMO orbitals. These theoretical calculations pave the way for the measurement of ultrafast bound-bound electron transitionsand its crucial role for the delay in photoemission observation.

Wigner time delay and spin–orbit activated confinement resonances

A study of the photoionization of spin–orbit split subshells of high-Z atoms confined in C60 has been performed using the relativistic-random-phase approximation. Specifically, Hg@C60 5p, Rn@C60 6p and Ra@C60 5d were investigated and the near-threshold confinement resonances in the j = l − 1/2 channels were found to engender structures in the j = l + 1/2 cross sections via correlation in the form of interchannel coupling. These structures are termed spin–orbit induced confinement resonances and they are found to profoundly influence the Wigner time delay spectrum resulting in time delays of tens or hundreds of attoseconds along with dramatic swings in time delay over small energy intervals. Pronounced relativistic effects in time delay are also found. These structures, including their manifestation in time delay spectra, are expected to be general phenomena in the photoionization of spin–orbit doublets in confined high-Z atoms.

Impact of fullerene polarizability on Wigner time delay in photodetachment of fullerene anions

SynopsisThe initial insight into the impact of fullerene polarizability on photodetachment time delay from fullerene anions is exposed. The impact is demonstrated to be significant.

Spin polarization in photoemission from the cuprate superconductor Bi2Sr2CaCu2O8+δ

Photoelectrons produced from the excitation of spin-degenerate states in solids can have a sizable spin polarization, which is related to the phase of interfering channels in the photoemission matrix elements. Such spin polarization can be measured by spin-resolved photoemission spectroscopy to gain information about the transitions and the Wigner time delay of the process. Incorporating strongly correlated electron systems into this paradigm could yield a novel means of extracting phase information crucial to understanding the mechanism of their emergent behavior. In this work, we present, as a case study, experimental measurements of the cuprate superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ by spin-resolved photoemission while maintaining full angular and energy resolution. A spin polarization of at least $10%$ is observed, which is related to the phase of the photoelectron wave function.