  In this paper we present a comprehensive analysis of the coherence phenomenon
of two coupled dissipative oscillators. The action of a classical driving field
on one of the oscillators is also analyzed. Master equations are derived for
both regimes of weakly and strongly interacting oscillators from which
interesting results arise concerning the coherence properties of the joint and
the reduced system states. The strong coupling regime is required to achieve a
large frequency shift of the oscillator normal modes, making it possible to
explore the whole profile of the spectral density of the reservoirs. We show
how the decoherence process may be controlled by shifting the normal mode
frequencies to regions of small spectral density of the reservoirs. Different
spectral densities of the reservoirs are considered and their effects on the
decoherence process are analyzed. For oscillators with different damping rates,
we show that the worse-quality system is improved and vice-versa, a result
which could be useful for quantum state protection. State recurrence and swap
dynamics are analyzed as well as their roles in delaying the decoherence
process.
