Dynamics of multilevel quantum systems and Christoffel-Legendre orthogonal polynomials
Mazurenko A.S., Savva V.A.
New orthogonal polynomial sequences: the Christoffel-Legendre ones of the first, second, and fourth degrees have been constructed with the use of the Christoffel-Uvarov formula. Some properties of the polynomials including the recurrence formulae have been investigated. It is shown that to each polynomial sequence there corresponds a certain multilevel system excited by laser radiation. The characteristics of quantum systems: energy levels, dipole moment function, frequency detunings on transitions have been found. Exact analytical solutions of the equations describing coherent dynamics of radiative excitation of these systems in a powerful laser field have been obtained. The peculiarities of the excitation dynamics have been investigated.