Optomechanical systems are currently of great interest as they lie at the boundary between quantum and classical mechanics, promising fundamental insights as well as new technologies. The practical operation of an optomechanical system requires that it satisfy the criteria of mechanical stability. Further, for quantum applications, it is important to characterize the degree of nonclassical correlation present between the mechanical and optical subsystems. In this study, we analyze the stability and entanglement in an optomechanical system where couplings linear as well as quadratic in the mechanical displacement are present simultaneously. Such systems can be realized experimentally. Our analysis of the optomechanical system is accomplished by inspecting the equations of motion that characterize the system. By analyzing the steady state of the system, we find a stability diagram which differs dramatically from the case of pure linear coupling which has been studied earlier. Specifically, we find generally a major loss of stability and a disconnection of the stability diagram when a quadratic coupling is introduced. We derive and state analytically in this thesis the stability criteria for our more generalized system. Further, by linearizing the equations of motion, we characterize the entanglement present in the system, using the logarithmic negativity as a measure. We thereby characterize the changes in the system entanglement that result from the addition of a quadratic coupling to a linearly coupled system.

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Mishkatul Bhattacharya


TA1522 .S38 2013


RIT – Main Campus

Plan Codes