Controllability of population transfer to degenerate states: Analytical and numerical results for a four-level system

We examine, both numerically and analytically, the limits of controllability and the dynamics of population transfer in systems with degenerate target states embedded in a finite manifold of states. An analysis of the dressed eigenstates of coupled field-matter systems is combined with the theory of the controllability of invariant systems on Lie groups to show the existence of a control scheme using a pair of shaped laser pulses acting upon a four-state system with intermediate degenerate states and a diamond-shaped array of transition moments (μ₁₂,μ₂₄,μ₁₃,μ₃₄≠0,μ₁₄,μ₂₃=0). The limits of the controllability of these systems are linked to the symmetry of the transition dipole moments connecting the states. A broken symmetry of the transition dipole moments (μ₁₂/μ₂₄≠μ₁₃/μ₃₄) permits complete population transfer to one of the pair of degenerate states. Numerical simulations of the optimized population transfer to one of a pair of degenerate states in the system agree quantitatively with the analytically predicted limits of population transfer in different regimes in the joint material-field characteristics of the system. The applicability of the four-state model to selective population transfer in vibrationally mediated photodissociation experiments is discussed.