Quantum entanglement assisted via Duffing nonlinearity

We propose a scheme to enhance quantum entanglement in an optomechanical system by exploiting the so-called Duffing nonlinearity. Our model system consists of two mechanically coupled mechanical resonators, both driven by an optical field. One resonator supports Duffing nonlinearity, while the other does not.The resonators are coupled to each other via the so-called phonon hopping mechanism. The hopping rate is $\theta$-phase-dependent that induces Exceptional Points (EPs) singularities in the system. Interestingly, while the resonator with Duffing nonlinearity exhibits vanishing entanglement with light, we observe an increase in entanglement between light and the other mechanical resonator. This enhanced entanglement persists longer against thermal fluctuations compared to the one without the nonlinearity. Additionally, this entanglement features a sudden death and revival phenomenon, where the peaks happen at the multiple of $\theta =\frac{\pi }{2}$. This work opens a new avenue for exploiting nonlinear resources to generate strong quantum entanglement, paving the way for advancements in quantum information processing, quantum sensing, and quantum computing within complex systems.