Cross-coupling-induced sensitivity enhancement beyond divergent exceptional points

Exceptional points (EPs) realized in electronics have been reported to be able to merge with a divergent point in a high-order parity-time ($PT$)-symmetric system, forming the so-called divergent EP (DEP), which can provide enhanced eigenvalue bifurcation. However, such divergence makes it hard for any practical circuit to operate exactly at the DEP, resulting in large device-to-device deviations, and thus significantly degrading the sensitivity of EP sensors. To this end, we propose a method to realize the DEP by introducing cross-coupling into the $PT$-symmetric circuit. We theoretically demonstrate that by manipulation of the cross-coupling strength, the DEP destruction/restoration exhibits ultrasensitivity against the variation of the coupling between gain (loss) and neutral components. This characteristic allows the system to operate beyond the DEP to achieve enhanced sensitivity with great device consistency. Our experimental measurements verify the analytical results well, showing that the cross-coupled DEP systems exhibit superior sensitivity and device consistency compared with non-cross-coupled systems. Our work may pave the way for practical implementation DEP in diverse sensing scenarios.