Semiclassical analysis of long-wavelength multiphoton processes: The Rydberg atom

Abstract

We study the problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons. An exact, nonperturbative approach is applied to the standard vector potential coupling Hamiltonian for a three-dimensional hydrogenlike atom in a microwave field treated semiclassically. Multiphoton probability exchange is calculated in both the velocity and the length gauges, by applying the Goeppert-Mayer gauge transformation. The expansion of the time-dependent solution in terms of Floquet states delineates the mechanism of multiphoton transitions. A detailed analysis of the Floquet states and quasienergies as functions of the field parameters allows us to describe the relation between avoided quasienergy crossings and multiphoton probability exchange. We formulate analytical expressions for the variation of quasienergies and Floquet states with respect to the field parameters, and demonstrate that avoided quasienergy crossings are accompanied by dramatic changes in the Floquet states. Analysis of the Floquet states, for small values of the field strength, yields selection rules for the avoided quasienergy crossings. In the case of strong fields, the simultaneous choice of frequency and strength of the field producing an avoided crossing results in improved ionization probability.

Rashba spin–orbit interaction effect on multiphoton optical transitions in a quantum dot

“…We diagonalize this matrix to obtain dressed eigenfunctions and eigenvalues. When these eigenvalues are plotted as a function of frequency (not shown here), we observe crossing and anticrossings as reported previously by Shirley , Fox and Vela‐Arevalo , and Milfeld and Wyatt . Further, the minimum separation between the branches of two quasienergies is connected with the width of the resonance peak and the location of the minimum separation determines the resonance position for the transition probability between the two states.…”

Non-perturbative multiphoton excitation studies in an excitonic coupled quantum well system using high-intensity THz laser fields

“…The shifts of the quasienergies against the unperturbed energy eigenvalues as the driving amplitude increases are generally known as ac-Stark shifts, the effect that has been observed in various atomic and heterostructure systems. [40,41] In Fig. 5, we show the variation of transition probabilities with the laser field intensity for different barriers widths while keeping well-widths constant at 8 nm.…”

Inversion in a four-terminal superconducting device on the quartet line. II. Quantum dot and Floquet theory

“…We note that avoided crossings in Floquet spectra appeared previously in the literature (see, for instance, Refs. [69][70][71][72]).…”