# Rotation sensing in two coupled whispering-gallery-mode resonators with loss and gain

## TL;DR

This paper proposes a theoretical scheme for rotation sensing using two coupled whispering-gallery-mode resonators with loss and gain, exploiting the Sagnac effect to detect angular velocity.

## Contribution

It introduces a novel quantum gyroscope design based on coupled resonators with active gain and passive loss, sensitive to rotation-induced frequency shifts.

## Key findings

- Eigenfrequencies are sensitive to the Sagnac-Fizeau shift.
- Steady-state photon number correlates with rotation speed.
- Output field fluctuations can be used for rotation detection.

## Abstract

We theoretically propose a scheme to realize rotation sensing based on two coupled whispering-gallery-mode resonators with loss and gain. We consider that the active resonator with gain is rotated while the passive one with loss is stationary. The rotation will induce Sagnac effect and we show that the eigenfrequencies of the supermodes are sensitive to the Sagnac-Fizeau shift. Therefore, we can measure the average photon number in the steady state or the fluctuation spectrum of the output fields to detect the angular velocity of the rotation. We hope that our investigation will be useful in the design of quantum gyroscope based on spinning resonators.