  We extend the non-Markovian quantum state diffusion (QSD) equation to open
quantum systems which exhibit multi-channel coupling to a harmonic oscillator
reservoir. Open quantum systems which have multi-channel reservoir coupling are
those in which canonical transformation of reservoir modes cannot reduce the
number of reservoir operators appearing in the interaction Hamiltonian to one.
We show that the non-Markovian QSD equation for multi-channel reservoir
coupling can, in some cases, lead to an exact master equation which we derive.
We then derive the exact master equation for the three-level system in a
vee-type configuration which has multi-channel reservoir coupling and give the
analytical solution. Finally, we examine the evolution of the three-level
vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations
numerically.
