Optimal control theory is introduced for the control of quantum molecular rotational excitations induced by electric fields. Particular emphasis is given to the case where the electric field pulse is sufficiently short (∼ 1 ps) so that the sudden approximation can be made. Consequently, the time evolution of the rotational wave functions can be obtained analytically for general molecular rotations. A hyperbolic curve is shown to explicitly describe the relationship between the rotational energy and the action integral, x(T) = ∫0 TdS∈(t) dt where d is the molecular permanent dipole moment, S the direction cosine matrix, and ∈(t) the applied electric field over time [0, T]. For the case that the control cost functional has the form Q = F(x(T)) + β∫0 T∈2(t) dt, it is found that the optimal fields are constant in time. The controllability of both rotational energy and transition probability is investigated. A detailed discussion on properties of the optimal fields, as well as the initial and final rotational states, is presented. Numerical calculations are performed for the molecule CsF.
All Science Journal Classification (ASJC) codes
- Physical and Theoretical Chemistry