We examine structural and dynamical properties of quantum resonances
associated with an avoided crossing and identify the parameter shifts where
these properties attain maximal or extreme values, first at a general level,
and then for a two-level system coupled to a harmonic oscillator, of the type
commonly found in quantum optics. Finally the results obtained are exemplified
and applied to optimize the fidelity and speed of quantum gates in trapped
ions.Comment: 4 pages, 1 figur