Keldysh photoionization theory: through the barriers

Abstract

The Keldysh photoionization theory is a conceptual cornerstone and a universal framework for the description of a broad class of fundamental effects in light–matter interaction. Here, we provide an overview of the Keldysh theory as a significant milestone in the development of modern optical physics and offer a historical perspective on the fundamental role of this theory, from the early pioneering work on quantum tunneling to the latest breakthroughs in laser optics, attosecond technologies, and ultrafast optics of high-intensity laser pulses.

Tunneling time in attosecond experiment for hydrogen atom

“…Usually the tunneling process in the attosecond experiments is explained by a simple picture, like the one shown in figure 1 for the He-atom. It is based on the strong field approximation (SFA) or Keldysh-Faisal-Reiss approximation [21,24,25]; for introductory reviews see [9,26,27]. This simple picture is very useful in explaining the experiment, although it is strictly true only in the length gauge (see [23,28,29].)…”

“…The advent of attophysics opens new perspectives in the study of time resolved phenomena in atomic and molecular physics [1][2][3][4], the tunneling process and the tunneling time (T-time) in atoms and molecules [5][6][7][8][9]. Attosecond science (asec=10 −18 s) concerns primarily electronic motion and energy transport on atomic scales and is of fundamental interest to the physics in general.…”

“…For more details we refer to the tutorials [19,20] (and the above mentioned.) A key quantity is the Keldysh parameter [9,21],…”

Tunneling Time in Attosecond Experiments and Time Operator in Quantum Mechanics

“…The tunneling process in the attosecond experiment can be visualized by a simple picture, as shown in Figure 1. This picture is related to the strong field approximation (SFA) or the Keldysh-Faisal-Reiss approximation [19,22,23]; for introductory reviews, see [24][25][26]. The main idea of the SFA is that the tunneled electron escapes the barrier at the exit point x e,+ (see Figure 1), with zero kinetic energy.…”

“…For Z e f f = 1.6875, respectively 1.375, we obtain the values v gp (d W ) < 4Ze e f f = 6.75, respectively 5.5. Using the experimental data at one point (see Equation (24)), Bauer extracted a value (2 × ξ/(v gb /c) 2 ) = ξ × 608.44 (compare Equation (22) or v C gp = (d C /τ)| F=0.069 = (13 au)/(40 as) = (13/1.66) au = 7.86 au, which was used as a fixed (independent of F) mean value in Equation 24independent of the barrier width. It is sightly larger than our values 6.75(5.5), which is caused by the use of the classical barrier width d C = I p /F = d W + 2x e,− (compare Equations (12) and (24)), and we think it is one of the reasons why Bauer needed to introduce a phenomenological parameter.…”