Optimal entanglement generation in optomechanical systems via Krotov control of covariance matrix dynamics

We investigate the optimal control of a continuous variable system, focusing on entanglement generation in an optomechanical system without utilizing Fock basis cutoffs. Using the Krotov algorithm to optimize the dynamics of the covariance matrix, we illustrate how to design a control objective function to manipulate the dynamics of the system to generate a desirable target state. We show that entanglement between the macroscopic mechanical mirror and the quantum optical cavity can be reliably generated through imposing the control on the detuning of the external laser field. It has been shown that the control may still be achieved when imposing spectral constraints on the external field to restrict it to low-frequency components. In addition, we systematically study the effects of quantum control on non-Markovian open system dynamics. We observe that memory effects can play a beneficial role in mitigating detrimental impacts of environmental noises. Specifically, the generated entanglement shows a reduced decay rate in the presence of these memory effects.