Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope

Exceptional points are singularities of open systems, and among their many remarkable properties, they provide a way to enhance the responsivity of sensors. Here we show that the improved responsivity of a laser gyroscope caused by operation near an exceptional point is precisely compensated by increasing laser noise. The noise, of fundamental origin, is enhanced because the laser mode spectrum loses the oft-assumed property of orthogonality. This occurs as system eigenvectors coalesce near the exceptional point and a bi-orthogonal analysis confirms experimental observations. While the results do not preclude other possible advantages of the exceptional-point-enhanced responsivity, they do show that the fundamental sensitivity limit of the gyroscope is not improved through this form of operation. Besides being important to the physics of microcavities and non-Hermitian photonics, these results help clarify fundamental sensitivity limits in a specific class of exceptional-point sensor.