Matrix solution of pseudospin equations for three-level systems

The dynamics of a three-level system is investigated within the rotating-wave approximation using the generalized pseudospin formalism of Hioe and Eberly [Phys. Rev. Lett. 47, 838 (1981)]. The Cayley-Hamilton theorem is used to obtain a matrix solution to the problem valid for arbitrary initial conditions. The pseudospin equations are phenomenologically extended to include relaxation effects, and solutions are also presented in this case. The von Neumann entropy of the system is introduced as a dynamic variable and is used to study the system's irreversible approach to equilibrium when it is subjected to relaxation effects. An oscillatory behavior of the entropy is noted, and its origin is elucidated