title: Theory for the optimal control of time-averaged quantities in quantum systems.
abstract: We present a variational theory for the optimal control of quantum systems with relaxation over a finite time interval. In our approach, which is a nontrivial generalization of previous formulations and which contains them as limiting cases, the optimal control field fulfills a high-order Euler-Lagrange differential equation, which guarantees the uniqueness of the solution. We solve this equation numerically and also analytically for some limiting cases. The theory is applied to two-level quantum systems with relaxation, for which we determine quantitatively how relaxation effects limit the control of the system.
authors.affiliation: Institut für Theoretische Physik der Freien Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
authors.forename: Ilia
authors.initials: I
authors.lastname: Grigorenko
authors.forename: Martin E
authors.initials: ME
authors.lastname: Garcia
authors.forename: K H
authors.initials: KH
authors.lastname: Bennemann