Optimal pump-dump control: phase-locked versus phase-unlocked schemes Original Research Article

We report a unified theoretical framework for the study of the pump-dump control with either a single coherent field or a pair of phase-unlocked 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 relations between the pump-dump control kernels in the phase-locked (i.e. the single coherent field) and the phase-unlocked control schemes in the strong response regime. These strong field control kernels can further be linearized in the case of pure state control in the weak pump-dump 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 either the phase-locked or the phase-unlocked control scheme can be identified. The common key quantity in both of the control schemes is a Hilbert-space pump-dump control response function, B(τ,τ′), which shares a great amount of information mutually with the optical resonant Raman spectroscopies. Numerical examples of pump-dump controlling I2 vibration onto an eigenstate and onto a minimum uncertainty wave packet in the ground electronic X state are presented to further elucidate the control mechanisms in the phase-locked and phase-unlocked schemes in the weak response regime.