Simultaneous observation of super-Heisenberg scaling and spin squeezing in a nonlinear measurement of atomic spins

Techniques for making quantum-limited nonlinear measurements have attracted a great deal of recent attention because they allow a measurement sensitivity that improves as the number of measuring particles (e.g. photons) increases faster than an equivalent linear measurement. This super-Heisenberg scaling was recently demonstrated in a proof-of-principle experiment [1], in which a measurement Hamiltonian of the form studied in Ref. [2] was carefully engineered by exploiting nonlinearities in a Faraday rotation based measurement of atomic spins. However, despite the improved scaling, the absolute measurement sensitivity in this experiment remained significantly worse than a linear Faraday rotation measurement due to the weak atom-light coupling strength of the nonlinear Faraday rotation, and effect of higher-order nonlinearities at large photon number. This leaves open the question of whether it is possible to make a nonlinear measurement that both benefits from the improved scaling, and competes in absolute sensitivity with linear techniques.