  We propose a new scheme for ultra-sensitive laser gyroscopes that utilizes
the physics of exceptional points. By exploiting the properties of such
non-Hermitian degeneracies, we show that the rotation-induced frequency
splitting becomes proportional to the square root of the gyration speed- thus
enhancing the sensitivity to low angular rotations by orders of magnitudes. In
addition, at its maximum sensitivity limit, the measurable spectral splitting
is independent of the radius of the rings involved. Our work paves the way
towards a new class of ultra-sensitive miniature ring laser gyroscopes on chip.
