Dynamical Symmetries and Spectroscopy of Quantum Dots

Abstract

Hitherto we discussed the dynamical symmetries in nanoobjects which are realized in tunneling experiments in external electric and magnetic field or induced by interaction with oscillator bath of elastic deformations of the constituent atoms (molecular vibrations). Irradiation of tunneling devices with periodic electromagnetic field in optical and microwave frequency range also may activate transitions between the energy levels of nanoparticle. There is much in common between photon and phonon fields from the point of view of interaction with few electron quantum systems because being quantizes, both obey the Bose statistics without conservation of number of excitations. Excitations with a given polarization possess SO(2,1) symmetry of 1D quantum oscillator with the basis functions (2.81). There is no insistent necessity to quantize the light in the majority of applications in photon assisted transport in nanostructures. Instead interaction with light may be treated as a response of a nanostructure to periodic in time electromagnetic field. In this case the Floquet theorem is valid and one may use the quasienergy approach described in Section 2.7.