This paper presents a cavity-assisted coherent feedback scheme to cool a mechanical resonator to the ground-state in a weak optomechanical coupling setup. Based on the theory of sideband cooling, resolved sideband regime is a mandatory condition for the ground-state cooling (GSC) in optomechanical systems. Assisted cooling and feedback cooling methods have been proposed and shown to be beneficial for cooling in unresolved sideband cases. In this paper, a cooling method is proposed by combining both approaches. In the proposed method, a coherent feedback loop is added to a cavity-assisted optomechanical system to enhance the cooling performance. The proposed feedback aims to reach the mechanical ground-state in the USR. Rate equations of the mechanical resonator are derived, and then, by applying Fermi's golden rule and analyzing the fluctuation spectrum of the optical force, optimal conditions for cooling are obtained. Results show that applying coherent feedback, improves the cooling performance of the system significantly and it is possible to achieve GSC in unresolved sideband regime (USR). Moreover, it is shown that the proposed method is capable of cooling the mechanical resonator to much lower energy levels than it is achievable in cavity assisted method.
