  Control of the dynamics of an open quantum system is crucial in quantum
information processing. Basically there are two ways: one is the control on the
system and the other is tuning the bath parameters. In this paper, we use the
latter to analyze the non-Markovian dynamics of the open system. The model is
that the system is immersed in non-Markovian squeezed baths. For the dynamics,
a non-Markovian master eqation is obtained using the quantum state diffusion
(QSD) equation technique for the weak system-bath couplings. We use the
adiabatic evolution or quantum state transmission as examples to analyze the
effects of the bath parameters: non-Markovianity $\gamma$, the squeezed
direction $\theta$ and squeezed strength $r$. For the adiabatic or state
transmission fidelity, the calculation results show that they both can be
enhanced by a smaller $\gamma$ or bigger $p$-quadrature. Interestingly, when
$0<\theta<\pi/2$, the squeezed quadrature is determined by the combination of
$r$ and $\theta$, and by numerical simulation we find that the fidelity peak
occurs at $r=1-2\theta/\pi$. The fidelities increase with increasing $r$ when
$r\in (0,1-2\theta/\pi]$. When $\theta\ge\pi/2$, lower fidelities are obtained
due to the squeezed bath. Our results show that the dynamics of the open
systems can be effectively controlled by reservoir enginerring.
