Achieving Heisenberg-scaling precision with projective measurement on single photons

TL;DR

This paper demonstrates a practical method to achieve Heisenberg-scaling precision in quantum metrology using single-photon superpositions and projective measurements, without relying on entanglement, by exploiting nonlinear interactions.

Contribution

It introduces an experimental approach to attain Heisenberg-scaling precision through projective measurements on single photons in nonlinear optical systems, bypassing the need for entanglement.

Findings

Achieved Heisenberg-scaling measurement precision proportional to 1/n.

Demonstrated saturation of classical Fisher information to quantum Fisher information.

Showed that nonlinear coupling with a single photon can enhance measurement precision without entanglement.

Abstract

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.