Invariance of quantum optimal control fields to experimental parameters

We consider an ensemble of closed finite-level systems described by a density matrix where the goal is to find an optimal control field to maximize the expectation value of an observable. The eigenvalues of the initial density matrix are assumed to depend on an experimental parameter (e.g., the temperature), whereas the eigenvalues of the observable may depend on an additional application-specific experimental parameter. We show that an optimal control will remain optimal for all such experimental parameters, if the relative ordering, by magnitude, of the eigenvalues of the initial density matrix as well as of the observable is unaltered regardless of the parameter values. More generally, we show like invariance of a control associated with any particular critical point on the corresponding control landscape. The invariance of control laser fields with respect to temperature is illustrated for vibrational excitation of diatomic molecules and photoassociation of atoms.