Absolute rotation detection by Coriolis force measurement using optomechanics

Abstract

In this article, we present an application of the optomechanical cavities for absolute rotation detection. Two optomechanical cavities, one in each arm, are placed in a Michelson interferometer. The interferometer is placed on a rotating table and is moved with a uniform velocity ofȳ with respect to the rotating table. The Coriolis force acting on the interferometer changes the length of the optomechanical cavity in one arm, while the length of the optomechanical cavity in the other arm is not changed. The phase shift corresponding to the change in the optomechanical cavity length is measured at the interferometer output to estimate the angular velocity of the absolute rotation. An analytic expression for the minimum detectable rotation rate corresponding to the standard quantum limit of measurable Coriolis force in the interferometer is derived. Squeezing technique is discussed to improve the rotation detection sensitivity by a factor of g w m m at 0 K temperature, where g m and w m are the damping rate and angular frequency of the mechanical oscillator. The temperature dependence of the rotation detection sensitivity is studied.

Gyroscope with two-dimensional optomechanical mirror

“…We propose an application of two-dimensional optomechanical oscillator as a gyroscope to detect absolute rotation. We showed that the two-dimensional optomechanical gyroscope's sensitivity is better than onedimensional optomechanical gyroscope [15] by a factor of g w m m . Using the parameters from [36], the sensitivity of the gyroscope is estimated as 7×10 −15 rad s -1 -/ Hz 1 2 at 0 K temperature.…”

“…At I l =I o , we get the best sensitivity which corresponds to the lowest point in the Purple curve. Minimizing equation ( (20) is in the same order of magnitude as the sensitivity achieved in the squeezed-vacuum gyroscope [15]. In the squeezed-vacuum gyroscope, squeezed vacuum field is injected in to two optomechanical cavities to suppress the shot noise and back-action noise and thus improving the sensitivity of the gyroscope.…”

“…As a consequence, without using squeezed vacuum field, the gyroscope in the present work is able to attain the similar sensitivity as that in the squeezed-vacuum gyroscope. It is important to note that the contributions from shot noise, back-action noise and mirror noise are almost equal in equation (20), hence the sensitivity given in equation (20) can not be improved significantly by suppressing shot noise and back-action noise, at optimal input laser intensity, by using the squeezed light technique described in [15]. Equation (20) implies that the sensitivity can be improved by decreasing w m .…”

“…When the table starts to rotate with angular velocity q , then fictitious forces begin to act on the optomechanical mirror. In presence of the fictitious forces, equation (1) is given as [15] w g c c c q q q = ---…”

“…Estimating centrifugal force requires additional procedures to locate the axis of rotation [14]. Hence, Coriolis force [15] measurement is more suitable for absolute rotation detection. In this work, we propose an optomechanical gyroscope by detecting the Coriolis force which is modulated at the natural frequency of the optomechanical oscillator.…”