Evolutionary algorithms and their application to optimal control studies

Abstract

Coherent control of a physical or chemical process can be achieved by using phase and amplitude modulated femtosecond laser pulses. A self-learning loop, which connects a femtosecond pulse shaper, an optimization algorithm, and an experimental feedback signal, can automatically steer the interaction between system and electric field and allows control even without any knowledge of the Hamiltonian. The dependability of such a loop is essential to the significance of the optimization results, assigning the optimization algorithm an important role within these learning loops. In this paper, an evolutionary strategy is presented in detail that has successfully been applied to femtosecond pulse shaping in optimal control experiments. A general introduction to evolutionary algorithms is given and the specific adaptation for femtosecond pulse shaping is described. The stability and effectiveness of the algorithm is investigated both in experiments and simulations with an emphasis on the influence of steering parameters of the algorithm, number of configurations in search space, and noise. The algorithm optimizes a set of variables parametrizing the electric field. This particular mapping greatly facilitates the dissection of the optimization goal which is demonstrated by three possible parametrizations and associated applications: polynomial phase functions and adaptive femtosecond pulse compression, periodic phase functions and control of nonlinear photon transitions, multiple pulse structures and control of molecular dynamics.