We consider the optomechanically induced transparency in the double quadratically coupled optomechanical cavities within a common reservoir, in which the two cavities are driven by the coupling fields. It is shown that the probe transparency is improved by increasing the coupling field (the left coupling field) applied on the probing cavity, but the transparency position (the probe frequency of the maximal transparency) is shifted to high frequency. The coupling field (the right coupling field) applied on the other quadratically coupled cavity can lead to a low-frequency shift for the transparency position, which can be used to fix the transparency position by adjusting the right coupling field. We get the quantitative findings that the transparency position is exactly determined by the intensity difference between the two coupling fields. On the other hand, it is found that when the two coupled optomechanical cavities interact with their common reservoir, the cross decay induced by the common reservoir can improve the probe transparency and widen the transparency window. Finally, the effects of the environment's temperature on the transparency are investigated. This will be useful in cooling the membrane, squeezing and entangling the output fields.

• Received 3 September 2015
• Revised 4 February 2016

DOI:https://doi.org/10.1103/PhysRevA.93.043804