Are there Traps in Quantum Control Landscapes?

There has been great interest in recent years in quantum control landscapes. Given an objective J that depends on a control field epsilon the dynamical landscape is defined by the properties of the Hessian delta(2)J/delta epsilon(2) at the critical points delta J/delta epsilon = 0. We show that contrary to recent claims in the literature the dynamical control landscape can exhibit trapping behavior due to the existence of special critical points and illustrate this finding with an example of a 3-level Lambda system. This observation can have profound implications for both theoretical and experimental quantum control studies.