It has been suggested that both quantum superpositions and nonlinear interactions are important resources for quantum metrology. However, to date the different roles that these two resources play in the precision enhancement are not well understood. Here, we experimentally demonstrate a Heisenberg-scaling metrology to measure the parameter governing the nonlinear coupling between two different optical modes. The intense mode with n (more than 10^6 in our work) photons manifests its effect through the nonlinear interaction strength which is proportional to its average photon-number. The superposition state of the weak mode, which contains only a single photon, is responsible for both the linear Hamiltonian and the scaling of the measurement precision. By properly preparing the initial state of single photon and making projective photon-counting measurement, the extracted classical Fisher information (FI) can saturate the quantum FI embedded in the combined state after coupling, which is ~ n^2 and leads to a practical precision ~ 1.2/n. Free from the utilization of entanglement, our work paves a way to realize Heisenberg-scaling precision when only a linear Hamiltonian is involved.
@article{arxiv.1808.02683,
title = {Achieving Heisenberg-scaling precision with projective measurement on single photons},
author = {Geng Chen and Lijian Zhang and Wen-Hao Zhang and Xing-Xiang Peng and Liang Xu and Zhao-Di Liu and Xiao-Ye Xu and Jian-Shun Tang and Yong-Nan Sun and De-Yong He and Jin-Shi Xu and Zong-Quan Zhou and Chuan-Feng Li and Guang-Can Guo},
journal= {arXiv preprint arXiv:1808.02683},
year = {2018}
}