  Quantum-enhanced measurements represent the path towards the best measurement
precision allowed by the laws of quantum mechanics. Known protocols usually
rely on the preparation of entangled states and promise high or even optimal
precision, but fall short in real-word applications because of the difficulty
to generate entangled states and to protect them against decoherence. Here, we
refrain from the preparation of entangled states but supplement the integrable
parameter-encoding dynamics by non-linear kicks driving the system in the
dynamical regime of quantum chaos. We show that large improvements in
measurement precision are possible by modeling a spin-exchange relaxation-free
alkali-vapor magnetometer where the non-linear kicks are realized by exploiting
the ac Stark effect.
