Investigation of rotation rate sensitivity in a quantum optomechanical gyroscope with two coupled cavities

In this paper, we have demonstrated the design of a quantum optomechanical gyroscope consisting of a combination of a Michelson interferometer with a quantum optomechanical cavity coupled to a simple Fabry–Perot cavity, all on a rotating table. The optomechanical cavity contains one moving mirror with the freedom of movement in the directions of the cavity axis ( x direction) and perpendicular to it ( y direction). The movement of the mirror in the y direction is sinusoidal with the frequency of natural vibrations of the mirror in the x direction, which is created by a micro-piezoelectric. Despite the movement of the mirror in the y direction and the rotation of the entire gyroscope around the z axis, the virtual Coriolis force is applied to the mirror in the x direction. This leads to a new sinusoidal force in addition to thermal fluctuations and radiation pressure force on the mirror along the cavity length. Also, the presence of a simple Fabry–Perot cavity and its coupling with the optomechanical cavity helps us to control the amount of energy entering the optomechanical cavity and consequently the radiation pressure inside it. By controlling radiation pressure and optimizing parameters, we increase the gyroscope’s sensitivity by over 57% at T =0K and nearly 50% at T =300K. At the end of this article, we determine the values of two key gyroscope parameters—angular random walk (ARW) and bias stability (BS)—by analyzing Allan deviation diagrams at four temperatures: T =0K,1mK,10K,and300K. Remarkably, at the low accessible temperature of T =1mK, cooling the optomechanical cavity results in substantial enhancements: ARW increases by up to two orders of magnitude, and the BS by up to one order of magnitude, when compared to existing optical gyroscopes.