Multiphoton Absorption by Polarons in a Spherical Quantum Dot
Theory of Multiphoton Absorption by Polarons
The discovery of quantum generators and fast development of quantum electronics have stimulated theoretical development and investigation of the interaction of electrons with matter as well as the electromagnetic field [2,58-60]. This is the basis of non-linear optics and spectroscopy. One of the fundamental problems in this domain is the investigation of multiphoton processes that may yield absorption or the generation of some quanta of the electromagnetic field in some elementary interaction.
The given problem is related to the theory of absorption of laser radiation by charge carriers in matter. The theory gives insights to the development of laser technology of new non-linear materials, the investigation of laser heating of plasma as well as the technology of fabrication of new mesoscopic structures. At low temperatures and in the weak-coupling regime, the optical absorption of a Frohlich polaron is due to the elementary polaron scattering process with the absorption of incoming photon and emission of a phonon.
In the works, [2,61] is examined non-linear absorption by free charge carriers due to the laser field considering the scattering probability of electrons on ionized impurities. In [62] on the basis of the classical examination of the non-linear effects is studied the kinetic equation for the electron in a strong homogenous electric field. In the work [63] is obtained the quantum mechanical correction to the scattering cross-section due to two photon processes. The investigation of the asymptotic behavior of the high-frequency conductivity (or scattering cross-section) in these works show that, for exceedingly high
3
intensities, I is described by the relation Cl 2. In the work [63], for the first time the multiphoton absorption of light by charge carriers in semiconductors is examined for a deformable scattering. The probability of the multiphoton absorption is computed by summing the perturbation series considering the interaction of charge carriers with light field. The coefficient of multiphoton light absorption can be obtained via the solution of the Schrodinger equation for the electron in a strong electromagnetic field in the first order approximation of the perturbation theory in the low-temperature limit
Here, Q. is the laser field frequency and T is the absolute temperature in the units of energy.
The new aspect of the multiphoton absorption problem involves the interaction of the strong electromagnetic radiation with nanocrystals and with longitudinal optical phonons. The dimensional quantization of the electronic energy spectrum in mesoscopic structures presents new particularities in the absorption process compared to ones in unbounded media. In quantum dots, the electronic spectrum completely quantizes due to the laser frequency dependence in the absorption coefficient with the absorption spectrum having stripes. The heights and intensities of these stripes depends on the laser intensity, dimension of the nanocrystal and the dominant absorption mechanism. So, we must develop a formula for the absorption coefficient of the multiphoton absorption in spherical quantum dots defining the peculiarity of the absorption spectrum as a function of their dimensions and interaction mechanism of the electron with the third body. This is done using the method of the density matrix in the representation of Feynman path integrals for the case of an electron. This will result in the multiphoton non-linear absorption light coefficient in the second order of interaction energy with polar optical phonons. This coefficient will be found to describe any electron interaction mechanism with phonons.
