Dark states are eigenstates or steady-states of a system that are decoupled
from the radiation. Their use, along with associated techniques such as
Stimulated Raman Adiabatic Passage, has extended from atomic physics where it
is an essential cooling mechanism, to more recent versions in condensed phase
where it can increase the coherence times of qubits. These states are often
discussed in the context of unitary evolution and found with elegant methods
exploiting symmetries, or via the Bruce-Shore transformation. However, the link
with dissipative systems is not always transparent, and distinctions between
classes of CPT are not always clear. We present a detailed overview of the
arguments to find stationary dark states in dissipative systems, and examine
their dependence on the Hamiltonian parameters, their multiplicity and purity.
We find a class of dark states that depends not only on the detunings of the
lasers but also on their relative intensities. We illustrate the criteria with
the more complex physical system of the hyperfine transitions of 87Rb and
show how a knowledge of the dark state manifold can inform the preparation of
pure states.Comment: additional example
