Coherent control of whispering-gallery-mode optomechanical microresonators and perfect transparency

Cavity-optomechanics has emerged as a new interdisciplinary research field, which studies the interaction between light field and mechanical systems of micro-and nanoscale. It is a promising avenue to solid-state quantum optics and has potential applications in high sensitivity measurement of weak force, tiny displacement and mass, and quantum information science. As a solid-state system of quantum optics, it has many interesting coherent phenomena, such as optomechanically induced transparency (OMIT), which is the optomechanical analog of the well-known phenomenon of electromagnetically induced transparency (EIT). However, due to diversity in structure, OMIT systems must have many new phenomena which do not exist in ordinary EIT systems. On the other hand, whispering-gallery-mode (WGM) microresonators have been investigated extensively. WGM microresonators have a wide range of applications due to their high quality factors and microscale mode volumes. WGM microresonators can also be used for OMIT systems, which have been investigated extensively. In this paper, we study the coherent control of an double-cavity optomechanical system which is composed of two WGM microresonators. We assume that the two WGM microcavties are driven by two strong control fields and two weak probe fields, and, one of the two cavities can create a macroscopic mechanical breathing mode under the action of a radiation pressure force. We also assume that the two WGM microcavties are directly coupled by an evanescent field. We theoretically study the quantum coherent control of electromagnetically induced transparency in this system, and find that in contrast with ordinary EIT systems, there are many new properties in this OMIT system, for example if two control fields with appropriate amplitudes and detunings are used to drive the system, the probe field, which is input to one of the two cavities, will be completely output from the other cavity, i.e., the perfect transparency of the quantum coherence phenomenon can occur in this system. We also find that the electromagnetically induced transparency can be realized and controlled in this optomechanical system by adjusting the relative intensity and the relative phase between the two input probe fields, and the width and depth of the EIT window are sensitive to the relative intensity of the two control fields, which may be used for switching between fast and slow light. These results indicate important progress toward signal amplification, light storage, fast light, and slow light in quantum information processes. Considering the fact that WGM microresonators are the frontier research subjects ranging from biosensing, nonlinear optics, and laser physics, to fundamental physics such as cavity quantum electrodynamics, we believe that the results in this paper have a wide range of applications.