Jacobian Exceptional Point Sensing

Exceptional points (EPs), singularities in the spectrum of a non-Hermitian linear Hamiltonian, were predicted and claimed to enhance sensing. However, several theoretical works demonstrated that EPs do not, in general, enhance sensing when the effects of noise are taken into account. Here we introduce a sensing strategy that, like EP sensing, exploits a spectral singularity. However, the singularity we exploit is not in the energy spectrum. It is in the spectrum of fluctuations around a fixed point, which corresponds to the eigenvalues of the system’s Jacobian. Our approach, which we call Jacobian exceptional point (JEP) sensing, has practical and performance advantages over those of EP sensors. While EP sensing in linear systems usually requires two or more modes, JEP sensing can be implemented using a single nonlinear mode. Furthermore, fluctuations are essential for JEP sensing. We analyze the performance of our JEP sensor embodied in a laser-driven single-mode Kerr resonator under the influence of quantum, thermal, and external noise. We find that the square-root scaling of the signal with perturbation can be clearly detected in the presence of all three noise sources. The sensing precision is even enhanced by an optimum amount of thermal noise, but it is ultimately limited by external noise interfering with the incoming cavity field. Our work sets the theoretical foundation for implementing JEP sensing in photonics, where many of the applications targeted by EP sensing can be addressed.