  The non-Markovian dynamics of a three-level quantum system coupled to a
bosonic environment is a difficult problem due to the lack of an exact dynamic
equation such as a master equation. We present for the first time an exact
quantum trajectory approach to a dissipative three-level model. We have
established a convolutionless stochastic Schr\"{o}dinger equation called
time-local quantum state diffusion (QSD) equation without any approximations,
in particular, without Markov approximation. Our exact time-local QSD equation
opens a new avenue for exploring quantum dynamics for a higher dimensional
quantum system coupled to a non-Markovian environment.
