OPTIMAL PUMP-DUMP CONTROL - PHASE-LOCKED VERSUS PHASE-UNLOCKED SCHEMES

We report a unified theoretical framework for the study of the pump-du mp control with either a single coherent field or a pair of phase-unlo cked coherent fields in both the strong and weak response regimes, and in terms of both the Liouville-space density matrix dynamics and the Hilbert-space wave function evolution. Shown are also the close relati ons between the pump-dump control kernels in the phase-locked (i.e. th e single coherent field) and the phase-unlocked control schemes in the strong response regime. These strong field control kernels can furthe r be linearized in the case of pure state control in the weak pump-dum p response regime. In this case, the optimal control theory reduces to the eigen problem of a certain specially constructed Hermitian matrix , from which even the globally optimal pump-dump control fields in eit her the phase-locked or the phase-unlocked control scheme can be ident ified. The common key quantity in both of the control schemes is a Hil bert-space pump-dump control response function, B(tau,tau'), which sha res a great amount of information mutually with the optical resonant R aman spectroscopies. Numerical examples of pump-dump controlling I, vi bration onto an eigenstate and onto a minimum uncertainty wave packet in the ground electronic X state are presented to further elucidate th e control mechanisms in the phase-locked and phase-unlocked schemes in the weak response regime. (C) 1998 Elsevier Science B.V. All rights r eserved.