Spin-orbit interaction beyond diagonalization

Abstract

A new approach explains the nature of a coherent state as a macroscopic collection of in-phase precession states. The latter are the most general solution to the problem of describing a system under spin-orbit interaction. The precession states owe their name to a periodic exchange of part of their sublevel populations which is the quantum-mechanical equivalent of the classical precession. Due to an unbalanced exchange of population the precession states cannot be stationary fine-structure eigenstates. But if the initial sublevel populations are proportional to the Clebsch-Gordan coefficients, the exchange becomes balanced thus independent of time and unobservable, turning the general precession state into a stationary fine-structure eigenstate.

What is quantum interference in atoms?

“…These assumptions rely on the notion that atoms do exist primarily in totally quantized states. Recently [2], [3] we have explained that all dynamical aspects can be accounted for by a time-dependent and simultaneous treatment of the spin-orbit and electric-dipole interactions. This provides the general basis for our new theory.…”

“…The previous letter [3] has established the equations of motion for the amplitudes in general terms but then focused on the spin-orbit dynamics in the excited electronic state. The present one is devoted to looking into how these dynamics affect the probabilities for spontaneous electric-dipole transitions between precession states of any kind.…”

“…( 2) of ref. [3] had only to be solved for the homogeneous case, here the amplitudes of the excited state, eq. ( 5) of ref.…”

“…( 5) of ref. [3], have to be inserted into the right-hand side of the inhomogeneous differential equation of second order, eq. (2) of ref.…”

“…(2) of ref. [3]. The solution provides the amplitudes for the spin-orbit interacting sublevels in the lower precession state,…”