The phonon effect of polaron and qubit in spherical shell quantum dot

Abstract

The influence of phonon on the properties of polaron and qubit in spherical shell quantum dot is studied by solving accurately the time-independent Schrödinger equation, Lee-Low-Pines unitary transformation and variation methods. The numerical results indicate that phonon effect leads to a lower energy of ground (or excited) state of polaron than electronic energy of ground (or excited) state and the increased oscillating period of a qubit, and the phonon effect becomes more obvious with outer radius increasing when inner radius is const. The numerical results also show that the phonon effect cannot influence the amplitude of probability density distribution of electrons in quantum bit, and that the probability density distribution of electrons is dependent on co-ordinate and time and its amplitude is maximal in centre spherical surface and but zero in boundary surface. The probability density of electrons at each position oscillates periodically with time.