Topological optomechanical amplifier in synthetic PT $\mathcal{PT}$ -symmetry

We propose how to achieve synthetic PT $\mathcal{PT}$ symmetry in optomechanics without using any active medium. We find that harnessing the Stokes process in such a system can lead to the emergence of exceptional point (EP), i.e., the coalescing of both the eigenvalues and the eigenvectors of the system. By encircling the EP, both nonreciprocal optical amplification and chiral mode switching can be achieved. As a result, our synthetic PT $\mathcal{PT}$ -symmetric optomechanics works as a topological optomechanical amplifier. This provides a surprisingly simplified route to realize PT $\mathcal{PT}$ -symmetric optomechanics, indicating that a wide range of EP devices can be created and utilized for various applications such as topological optical engineering and nanomechanical processing or sensing.