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Register a new userNumerical simulation of time delays in light induced ionization
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We apply a fundamental definition of time delay, as the difference between the time a particle spends within a finite region of a potential and the time a free particle spends in the same region, to determine results for photoionization of an electron by an extreme ultraviolet (XUV) laser field using numerical simulations on a grid. Our numerical results are in good agreement with those of the Wigner-Smith time delay, obtained as the derivative of the phase shift of the scattering wave packet with respect to its energy, for the short-range Yukawa potential. In case of the Coulomb potential we obtain time delays for any finite region, while - as expected - the results do not converge as the size of the region increases towards infinity. The impact of an ultrashort near-infrared probe pulse on the time delay is analyzed for both the Yukawa as well as the Coulomb potential and is found to be small for intensities below $10^{13}$ W/cm$^2$.
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Measuring the photoionization time delay between electrons from different orbitals is one of the most important accomplishments of attosecond science. These measurements are typically done using attosecond pulses to photoionize a target inside a photoelectron spectrometer. In such experiments, the measured delay corresponds to the superposition of all possible paths to ionization and can include multiple sources of delay. These effects can be difficult to deconvolve. Here, we exploit the collision physics nature of recollision and show that, by perturbing recollision dynamics, photorecombination time delays due to electron dynamics and structure can be measured entirely optically and without obfuscation from molecular structure and propagation effects. While we concentrate on photorecombination delays in argon around the Cooper minimum our approach is general. Therefore, our work holds the potential to fundamentally change how attosecond measurement is performed and 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.
This tutorial presents an introduction to the interaction of light and matter on the attosecond timescale. Our aim is to detail the theoretical description of ultra-short time-delays, and to relate these to the phase of extreme ultraviolet (XUV) light pulses and to the asymptotic phase-shifts of photoelectron wave packets. Special emphasis is laid on time-delay experiments, where attosecond XUV pulses are used to photoionize target atoms at well-defined times, followed by a probing process in real time by a phase-locked, infrared laser field. In this way, the laser field serves as a clock to monitor the ionization event, but the observable delays do not correspond directly to the delay associated with single-photon ionization. Instead, a significant part of the observed delay originates from a measurement induced process, which obscures the single-photon ionization dynamics. This artifact is traced back to a phase-shift of the above-threshold ionization transition matrix element, which we call the continuum-continuum phase. It arises due to the laser-stimulated transitions between Coulomb continuum states. As we shall show here, these measurement-induced effects can be separated from the single-photon ionization process, using analytical expressions of universal character, so that eventually the attosecond time-delays in photoionization can be accessed.
Electrons in atoms and molecules can not react immediately to the action of intense laser field. A time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum emerges. This lag characterizes the response time of the electronic wave function to the strong-field ionization event and has important effects on subsequent ultrafast dynamics of the ionized electron. The absolute time lag is not accessible in experiments. Here, a calibrated attoclock procedure, which is related to a simple Coulomb-induced temporal correction to electron trajectories, is proposed to measure the relative lag of two different ionization events. Using this procedure,the difference (i.e., the relative lag) between the ionization time lags of polar molecules in two consecutive half laser cycles can be probed with a high accuracy.
We study the behavior of the Eisenbud-Wigner collisional time delay around Feshbach resonances in cold and ultracold atomic and molecular collisions. We carry out coupled-channels scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length, so exhibits a pole as a function of applied field. At high energy, it exhibits a Lorentzian peak as a function of either energy or field. For narrow resonances, the crossover between these two regimes occurs at an energy proportional to the square of the resonance strength parameter $s_textrm{res}$. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.
We apply a recently proposed theoretical concept and numerical approach to obtain time delays in extreme ultraviolet (XUV) photoionization of an electron in a short- or long-range potential. The results of our numerical simulations on a space-time grid are compared to those for the well-known Wigner-Smith time delay and different methods to obtain the latter time delay are reviewed. We further use our numerical method to analyze the effect of a near-infrared streaking field on the time delay obtained in the numerical simulations.
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