Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory)

The theoretical description of the nonlinear photoionization of atoms and ions exposed to high-intensity laser radiation is underlain by the Keldysh theory proposed in 1964. The paper reviews this theory and its further development. The discussion is concerned with the energy and angular photoelectron distributions for the cases of linearly, circularly, and elliptically polarized laser radiation, with the ionization rate of atomic states exposed to a monochromatic electromagnetic wave and to ultrashort laser pulses of various shape, and with momentum and angular photoelectron spectra in these cases. The limiting cases of tunnel ($\gamma\ll 1$) and multiphoton ($\gamma\gg 1$) ionization are discussed, where c is the adiabaticity parameter, or the Keldysh parameter. The probability of above-barrier ionization is calculated for hydrogen atoms in a low-frequency laser field. The effect of a strong magnetic field on the ionization probability is discussed. The process of Lorentz ionization occurring in the motion of atoms and ions in a constant magnetic field is considered. The properties of an exactly solvable model—the ionization of an \it{s}-level bound by zero-range forces in the field of a circularly polarized electromagnetic wave—are described. In connection with this example, the Zel'dovich regularization method in the theory of quasistationary states is discussed. Results of the Keldysh theory are compared with experiment. A brief discussion is made of the relativistic ionization theory applicable when the binding energy of the atomic level is comparable with the electron rest mass (multiply charged ions) and the sub-barrier electron motion can no longer be considered to be nonrelativistic. A similar process of electron-positron pair production from a vacuum by the field of high-power optical or X-ray lasers (the Schwinger effect) is considered. The calculations invoke the method of imaginary time, which provides a convenient and physically clear way of calculating the probability of particle tunneling through time-varying barriers. Discussed in the Appendices are the properties of the asymptotic coefficients of the atomic wave function, the expansions for the Keldysh function, and the so-called ‘ADK theory’.