The Theoretical Study of Multiphoton Ionization of Atom by Multiple Laser Beams

Abstract

Multiphoton processes occur and are important for many aspects of matter-radiation interaction that include the efficient ionization of atoms and molecules, and more gen- erally atomic transition mechanism, system-environment couplings, and dissipative quantum dynamics, laser physics, optical parametric processes and interferometry. A single review can not account for all aspects such an enormously vast subject. Here we concentrate our attention on atomic transition due to presence of multiple beams in non-linear media.

The interference of the amplitudes of atomic transition from an initial state |g⟩ to the given final state |f ⟩ is one of the major consequences of the validity of quantum mechanics. In the case of radiative transitions, new possibilities for the illustration and investigation of this phenomenon are created in the simultaneous interaction of an atom with the fundamental frequency of laser.

The time dependent Schrodinger equation (TDSE) for non relativistic, semi-classical in dipole approximation, based under the framework of high order perturbation theory is solved by using Dalgarno-Lewis technique. We have evaluated multiphoton ionization of ground state hydrogen atom due to the simultaneous interaction with multiple laser beams of the same frequencies, direction of propagation but different polarization. We could able to separate the radial and angular part of transition amplitudes and obtain the analytical expression for the various multiphoton tran- sition rates as a function of polarization, phase shift, intensities and frequency of the incident photon. In this formulation we can use any number of incident beams with arbitrary polarization. Based on our analytical expression, we have shown numerical results the change in angular distribution of ejected photo- electrons by varying intensity, phase, and polarization of different beams. The results illus- trate the influence of laser frequency on angular distribution of ejected electron by varying phases and polarization on the differential ionization cross-section of the MPI.