Super-Heisenberg Scaling in a Triple-Point Criticality

We investigate quantum-enhanced metrology in a triple point criticality and discover that quantum criticality does not always enhance measurement precision. We have developed suitable adiabatic evolution protocols to effectively restrain excitations, which could accelerate the adiabatic evolutions and lead to an exponential super-Heisenberg scaling. This scaling behavior is quite valuable in practical parameter estimating experiments with limited coherence time. Dissipation can strengthen the super-Heisenberg scaling until decoherence increases to dominate in the dissipative dynamics. Additionally, measurement precisions beyond Heisenberg scaling can be experimentally achieved in the trapped ion system. Our findings strongly indicate that criticality-enhanced metrology can indeed significantly enhance measurement precisions to a super-Heisenberg scaling when combining a triple point and beneficial parameter modulations, which will be conducive to the exploration of other super-Heisenberg scaling and their applications.