Investigation of the Goos-Hänchen shift in an optomechanical cavity via quantum control

Abstract

We propose a scheme to study the topic of manipulating the Goos-H\anchen (GH) shift of the reflected beam in an optomechanical cavity (OMC). Our system consists of two mirrors where one is fixed and the other is movable and a two-level atom is trapped inside the OMC. The fixed mirror is partially reflecting, whereas the movable mirror is perfectly reflecting. We theoretically investigated the behavior of the GH shift in the reflected beam when a Gaussian beam is an incident on the OMC. We find that GH shifts can be greatly enhanced in positive or negative directions via manipulating the quantum parameters such as optomechanical strength ${g}_{\text{mc}}$ and atom-cavity strength ${g}_{\text{ac}}$ under the influence of beam width of a Gaussian beam. Besides, we study the GH shift in the case of the partially coherent light beam as an incident probe field. Giant negative GH shift is achieved for an incident partially coherent beam in the presence of ${g}_{\text{mc}}, {g}_{\text{ac}}$, a measure of global coherence and beam width of a partially coherent beam. The proposed model provides feasibility in practical experiments for studying the behavior of the GH shift.