CONTROL OF COHERENT WAVE-FUNCTIONS - A LINEARIZED MOLECULAR-DYNAMICS VIEW

In this paper, the Schrodinger equation is linearized with regard to a low-intensity controlling electric field. For such a linearized quant um dynamical system, the present work answers the issue of controllabi lity and explicitly provides the control field. Starting in a particul ar eigenstate, the resultant necessary and sufficient conditions for c ontrollability require that the system satisfy the following two crite ria: (1) the N eigenstates of the field-free Hamiltonian superimposed to form the coherent final state must be nondegenerate and (2) the ele ctric dipole transition moments from the initial state to each of the above eigenstates must be nonzero. The control field is obtained analy tically in terms of N monochromatic electric fields, each of which has a frequency corresponding to the transitions of the field-free Hamilt onian. We show that the physical properties of the control field are n ot affected by the overall phase of the coherent wave function. Using Li2 as an example, we investigate the control properties of creating s pecified coherent wave functions on the excited potential energy surfa ce A1SIGMA(u)+ by excitation from an initial state on the X1SIGMA(g)surface. The numerical results suggest that the required control field is reasonable for laboratory realization.