  The coherence properties of a three-level $\Lambda$-system influenced by a
Markovian environment are analyzed. A coherence vector formalism is used and a
vector form of the Lindblad equation is derived. Together with decay channels
from the upper state, open system channels acting on the subspace of the two
lower states are investigated, i.e., depolarization, dephasing, and amplitude
damping channels. We derive an analytic expression for the coherence vector and
the concomitant optical susceptibility, and analyze how the different channels
influence the optical response. This response depends non-trivially on the type
of open system interaction present, and even gain can be obtained. We also
present a geometrical visualization of the coherence vector as an aid to
understand the system response.
