Optimal decoherence control in non-Markovian open dissipative quantum systems

Abstract

We investigate the optimal control problem for a non-Markovian open, dissipative quantum system. Optimal control using the Pontryagin maximum principle is specifically derived. The influences of ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions: ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\omega}}_{c}$, ${\ensuremath{\omega}}_{0}\ensuremath{\approx}{\ensuremath{\omega}}_{c}$, or ${\ensuremath{\omega}}_{0}⪢{\ensuremath{\omega}}_{c}$, where ${\ensuremath{\omega}}_{0}$ is the characteristic frequency of the quantum system of interest, and ${\ensuremath{\omega}}_{c}$ the cutoff frequency of the ohmic reservoir. The optimal control process shows its remarkable influences on the decoherence dynamics. The temperature is a key factor in the decoherence dynamics. We analyze the optimal decoherence control in high temperature, intermediate temperature, and low temperature reservoirs, respectively. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compare the non-Markovian optimal decoherence control with the Markovian one and find that with non-Markovian the engineered artificial reservoirs are better than with the Markovian approximation in controlling the open, dissipative quantum system's decoherence.