  We analyse the problem of a two-level atom interacting with a time-dependent
dissipative environment modelled by a bath of reservoir modes. In the model of
this paper the principal features of the reservoir structure remain constant in
time, but the microscopic structure does not. In the context of an atom in a
leaky cavity this corresponds to a fixed cavity and a time-dependent external
bath. In this situation we show that by chirping the reservoir modes
sufficiently fast it is possible to inhibit, or dramatically enhance the decay
of the atomic system, even though the gross reservoir structure is fixed. Thus
it is possible to extract energy from a cavity-atom system faster than the
empty cavity rate. Similar, but less dramatic effects are possible for moderate
chirps where partial trapping of atomic population is also possible.
