On the induced metric of a photon qubit for different points of action in Bloch sphere

Abstract

Abstract Travelling with harmonical actions about the referential line, the moment the photon qubit emits form the atom as a packet, not only embedded by the envelopes of quadratic nature overlap but also by the non-quadratic overlap effect as well in concurrent. This paper followed on by the subsistence of both ways of overlapping, focuses mainly on the induced metric of photon qubit, which concluded to be in 3-sphere by the local parameterization so called as Hopf coordinates. The protruded photon qubit in the induced Riemannian metric, for different points of the Bloch sphere, are in a manner that the stereographic projection of volume enveloped in 3-sphere determines the circular geometry in 2-sphere with the cross-sectional function in perpendicular to the continuum line of travel.