Effects of non-Markovian squeezed bath on the dynamics of open systems

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 $0<\theta <\pi \mathrm{/}2$, the squeezed quadrature is determined by the combination of $r$ and $\theta$, and by numerical simulation we find that the fidelity peak occurs at $r=1-2\theta \mathrm{/}\pi$. The fidelities increase with increasing $r$ when $r\in (0,1-2\theta \mathrm{/}\pi ]$. When $\theta \ge \pi \mathrm{/}2$, 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.