Higher-order exceptional point in a blue-detuned non-Hermitian cavity optomechanical system

Higher-order exceptional points (EPs) in non-Hermitian systems have attracted great interest due to their advantages sensitive enhancement and distinct topological features. However, realization of such EPs is still challenged because more fine-tuning parameters generically required quantum systems, compared the second-order EP (EP2). Here, we propose a three-mode optomechanical system blue-sideband regime for predicting third-order (EP3). By deriving pseudo-Hermitian condition proposed system, one cavity with loss other gain must be required. Then show EP3 or EP2 can observed when mechanical resonator (MR) neutral, gain. For neutral MR, find both two degenerate non-degenerate EP3s predicted by tuning parameter space, while four EP2s derivate from EP3s, which distinguished previous study red-detuned system. (loss) only enhanced coupling strength. Our proposal provides potential way predict higher-order multiple multimode squeezing around using blue-detuned systems.