Interferometric measurements form the basis of the most sensitive instruments, including gravitational wave detectors, atomic clocks, and optical magnetometers. The quantum theory of linear interferometers has been studied in detail, and quantum enhancements such as spin squeezing have been demonstrated in demanding, real-world applications. On the other hand, nonlinear interferometers, a class of devices that includes both optical magnetometers and Bose-Einstein condensates, have only recently begun to be understood at the quantum level. We demonstrate an ultrasensitive, nondestructive nonlinear measurement of atomic spin that achieves state-of-the-art sensitivity and, moreover, surpasses the best possible linear measurement of the same spin component.

A key feature of nonlinear interferometers is their so-called super-Heisenberg scaling, in which the sensitivity improves with particle number faster than even the best quantum-enhanced linear measurement. Better scaling suggests a fundamentally better approach, guaranteed to surpass linear interferometry for sufficient particle number. This suggestion has been the subject of much recent debate and, to date, is unconfirmed by experiment. We nondestructively measure the spin alignment of 6 × 10 5 laser-cooled Rb 87 atoms in an optical dipole trap using 2- μ s -long pulses of light. We show how the atomic spin-alignment component scales with photon number, in agreement with covariance-matrix theory. Our nonlinear measurements become more sensitive than linear measurements when the photon number increases above 3 × 10 7 , confirming the theoretical prediction that improved scaling should lead to greater sensitivity. We furthermore reproduce spin squeezing (i.e., better metrological sensitivity), which would not be induced for linear measurements given our experimental parameters.

The ability of nonlinear measurements to detect spin alignment is an improvement over previous analyses, which could only infer spin orientation. Furthermore, we expect that nonlinear measurements will contribute to the detection and preparation of exotic quantum phases in ensembles of ultracold atoms.