We consider the time delay of electron detachment from a Coulomb center and two-center systems in the process of ionization. It is shown that the attosecond streaking, most usual method of time delay measure, can be formally described by placing a virtual detector of the arrival time delay at a certain distance from the center of the system. This approach allows derivation of a simple formula for Coulomb-laser coupling that perfectly agrees with the results of numerical solution of the time-dependent Schrödinger equation. The dependence of the time delay upon the energy, the angular momentum projection, and the azimuthal quantum number is studied for the ionization of molecular hydrogen ion. Finally, we propose a physical interpretation of singularities, arising when the formal expression for the time delay is applied to the ionization of molecular hydrogen.
A method is proposed for extracting ionization amplitudes from the solution of the timedependent Schrödinger equation (TDSE) describing a system in a time-dependent external field.The method is a hybrid of two earlier developed methods, the time-dependent surface flux (t-SURFF) method and the method using the propagated wavepacket as the source term in a timeindependent driven Schrödinger equation with the field-free Hamiltonian. It is demonstrated that the method combines the advantages of the parent ones and allows the extraction of ionization amplitudes by solving the TDSE within a small spatial domain (with the boundary conditions provided by exterior complex scaling) and a time interval, not exceeding the external field pulse duration.
After a brief overview of attosecond pulse measurement techniques, we consider the time delay of electron detachment from a Coulomb center in the process of ionization. It is shown that the attosecond streaking, mostly used in time delay measurements, can be formally described by placing a virtual detector of the arrival time delay at a certain distance from the center of the system. This approach allows derivation of a simple formula for Coulomb-laser coupling that perfectly agrees with the results of numerical solution of the time-dependent Schrödinger equation.
IntroductionIn 2012 a special issue of Journal of Physics B [1] was devoted to a remarkable event in the history of modern optics and atomic physics-the 10th anniversary of experimental generation of attosecond pulses [2,3]. As summarized in [1], since the appearance of attosecond light sources the attosecond science has become an active research field. Detailed studies of ultrafast phenomena in atoms and molecules have been performed, especially in the time domain. Direct measurements of ultrafast characteristic times in atoms and molecules, e.g., Auger decay time and autoionization lifetime, have been carried out. The molecular tomography method allowed the reconstruction of molecular orbital wave function. Ultrafast phenomena in condensed matter and in nanostructures have been also studied.This chapter is devoted to quantum mechanics of electrons ejected in the course of photoionization of atoms by attosecond light pulses rather than to attosecond optics itself. The motivation is that the attosecond pulse measurement actually means monitoring the motion of the ejected electrons with super-high temporal resolution. An exhaustive quantum mechanical picture is necessary to extract the light pulse duration, amplitude and shape from the measurements performed with the ionization electrons. On the other hand, if this picture is known, attosecond pulses become a powerful tool for tracing the real-time electron dynamics in atoms and molecules.
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