Are there traps in quantum control landscapes?

Abstract

There has been great interest in recent years in quantum control landscapes. Given an objective $J$ that depends on a control field $\varepsilon$ the dynamical landscape is defined by the properties of the Hessian $\delta^2 J/\delta\varepsilon^2$ at the critical points $\delta J/\delta\varepsilon=0$. 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.