Nonlinear coherence in three-level systems and SU(3) symmetries

Abstract

The problem of nonlinear coherence in three-level systems exposed to two monochromatic radiation fields is treated using the unitary symmetries of SU(3). The Hamiltonian and the initial density operator are brought by a series of unitary transformations into a form in which the problem is reduced to a nutation between the two levels connected by the two-photon transition, i.e., to a time-dependent unitary rotation within the proper SU(2) subgroup. The net effect of the two modes in which the photons can combine in the nonlinear transition is shown to vanish gradually as the three levels approach an equidistant pattern. This certifies that two-photon processes can occur in systems which obey SU(3) symmetry, but not in those which obey the symmetry of SU(2). Four independent constants of motion are identified for the process of two-photon nutation in three-level systems.