  In this paper we extend current perspectives in engineering reservoirs by
producing a time-dependent master equation leading to a nonstationary
superposition equilibrium state that can be nonadiabatically controlled by the
system-reservoir parameters. Working with an ion trapped inside a nonindeal
cavity we first engineer effective Hamiltonians that couple the electronic
states of the ion with the cavity mode. Subsequently, two classes of
decoherence-free evolution of the superposition of the ground and decaying
excited levels are achieved: those with time-dependent azimuthal or polar
angle. As an application, we generalise the purpose of an earlier study [Phys.
Rev. Lett. 96, 150403 (2006)], showing how to observe the geometric phases
acquired by the protected nonstationary states even under a nonadiabatic
evolution.
