Optomechanically induced absorption in parity-time-symmetric optomechanical systems

Abstract

We explore the optomechanically induced absorption (OMIA) in a parity-time- ($\mathcal{PT}$-) symmetric optomechanical system (OMS). By numerically calculating the Lyapunov exponents, we find out the stability border of the $\mathcal{PT}$-symmetric OMS. The results show that in the $\mathcal{PT}$-symmetric phase the system can be either stable or unstable depending on the coupling constant and the decay rate. In the $\mathcal{PT}$-symmetric broken phase the system can have a stable state only for small gain rates. By calculating the transmission rate of the probe field, we find that there is an inverted optomechanically induced transparency (OMIT) at $\ensuremath{\delta}=\ensuremath{-}{\ensuremath{\omega}}_{M}$ and an OMIA at $\ensuremath{\delta}={\ensuremath{\omega}}_{M}$ for the $\mathcal{PT}$-symmetric optomechanical system. At each side of $\ensuremath{\delta}=\ensuremath{-}{\ensuremath{\omega}}_{M}$ there is an absorption window due to the resonance absorption of the two generated supermodes. Comparing with the case of optomechanics coupled to a passive cavity, we find that the active cavity can enhance the resonance absorption. The absorption rate at $\ensuremath{\delta}={\ensuremath{\omega}}_{M}$ increases as the coupling strength between the two cavities increases. Our work provides us with a promising platform for controlling light propagation and light manipulation in terms of $\mathcal{PT}$ symmetry, which might have potential applications in quantum information processing and quantum optical devices.