Higher-order exceptional point in a pseudo-Hermitian cavity optomechanical system

Higher-order exceptional points (EPs), resulting from non-Hermitian degeneracies, have shown greater advantages in sensitive enhancement than second-order EPs (EP2s). Therefore, seeking higher-order various quantum systems is important for information science. Here we propose a benchmark cavity optomechanical (COM) system consisting of mechanical resonator coupled to two cavities via radiation pressure predicting the third-order point (EP3). We first give pseudo-Hermitian condition COM by taking bath effects into account. Then consider gain effect, and find that without $\mathcal{PT}$ symmetry can host both EP3 EP2 symmetric asymmetric cavities. In case, only or be predicted parameter space, but transformed each other tuning coupling strength case. further case one with gain. For this also EP2. The influence parameters on them discussed. Our proposal provides potential way realize detection study physical phenomena around systems.