Semiclassical two-step model for ionization by a strong laser pulse: further developments and applications

Abstract

We review the semiclassical two-step model for strong-field ionization. The semiclassical two-step model describes quantum interference and accounts for the ionic potential beyond the semiclassical perturbation theory. We discuss formulation and implementation of this model, its further developments, as well as some of the applications. The reviewed applications of the model include strong-field holography with photoelectrons, multielectron polarization effects in ionization by an intense laser pulse, and strong-field ionization of the hydrogen molecule. Graphic Abstract

Advanced momentum sampling and Maslov phases for a precise semiclassical model of strong-field ionization

“…To resolve interference, this requires very small bins and typically in excess of a billion trajectories. Additionally, it has also been shown in [60] that these 'forward' approaches do not yield the correct sampling weight in terms of the Jacobian J s , leading to 1/|J s | instead of the correct 1/ |J s | computed by inverse approaches (see equation ( 18)).…”

Analysis of correlations in strong field ionization

“…We used the Heisenberg representation to give the definition (8). For practical calculations of the correlation function given by this expression, it is convenient to go back to the Schrödinger representation, which can be done by using the transformation equation (7) with the results: where P Ω and PΩ are the time-independent operators defined in equations ( 4) and ( 6), |Ψ(t) = Û(t, 0)|φ 0 -state vector of the system in the Schrödinger picture at the moment of time t. Using equation ( 9) we can give a more physically transparent interpretation of the correlation function C(Ω, t 2 ; Ω, t 1 ). Suppose that we have atomic system which evolves in the laser field according to the TDSE (1), so that its wave-function at t = t 1 is Ψ(r, t 1 ).…”

“…This property of the tunneling ionization regime, that electron motion after the ionization event can be pictured in * Author to whom any correspondence should be addressed. classical terms, has been successfully exploited in the semiclassical approaches based on the so-called two-step model of ionization (see [7,8] for review), in which the electron ionization event is treated quantum-mechanically and the subsequent electron motion is treated classically or semi-classically. Various approaches such as the well-known TIPIS model [5,9,10], the quantum trajectory Monte Carlo model [11], semiclassical two-step model [12] or Coulomb quantum orbit strong-field approximation [13,14] exploiting this idea, are known to produce quite accurate quantitative results [5,6,9,11,15,16].…”

“…Another possible solution is based on the observation that the ultimate reason for the difficulty in combining the quantum and classical steps in the two step model is the impossibility of assigning definite values of the coordinate and velocity to an electron in the conventional QM [7]. One can try, therefore, to bypass this problem by restoring the notion of the electron's trajectory using unconventional interpretations of QM such as the Bohmian mechanics [34,35].…”

Joint probability calculation of the lateral velocity distribution in strong field ionization process

“…The most essential features of these processes can often be understood with the help of the well-known simple man model (SMM) 6,[10][11][12][13] , which represents electron's motion after the ionization event occurs as entirely classical. This fact underlies a variety of highly efficient semi-classical approaches [12][13][14][15][16][17][18][19] , in which the electron ionization event is treated quantum-mechanically, with electron's ionization occurring near the local peaks of the electric field, and the subsequent electron motion treated classically or semi-classically. These approaches include the well-known TIPIS model 12,16,20 , the quantum trajectory Monte Carlo model (QTMC) 19 , semi-classical two-step model 21 or Coulomb quantum orbit strong-field approximation (CQSFA) 22,23 .…”