Quantum information of optical magnetometry: Semiclassical Cramer-Rao bound violation and Heisenberg scaling

TL;DR

This paper investigates the quantum limits of optical magnetometry, revealing conditions under which the classical bounds are violated and demonstrating Heisenberg scaling due to measurement-induced quantum correlations, suggesting a new paradigm in quantum sensing.

Contribution

It compares semiclassical and collective spin models, showing the semiclassical model's violation of the Cramer-Rao bound and the collective model's Heisenberg scaling, advancing understanding of quantum limits in magnetometry.

Findings

Semiclassical model violates the quantum Cramer-Rao bound under certain conditions.

Collective spin model respects the Cramer-Rao bound and predicts Heisenberg scaling.

Heisenberg scaling arises from measurement-induced quantum correlations in stationary states.

Abstract

Optical magnetometers use the rotation of linearly polarized laser light induced by the Faraday effect for high precision magnetic field measurements. Here, we carry out an in-depth quantum information investigation, deploying two distinct models: The first, semiclassical model can violate the quantum Cramer-Rao bound by several orders of magnitude for weak dissipation and large atom numbers, invalidating the semiclassical approach in this parameter regime. The second model, describing the atoms as a collective spin, respects the Cramer-Rao bound for all parameters. Interestingly, the collective model also predicts Heisenberg scaling for the quantum Fisher information. The comparison of both models shows that Heisenberg scaling is a result of measurement-induced quantum correlation in an otherwise non-interacting quantum system. As the Heisenberg scaling appears in a stationary state of a macroscopic quantum system, it can be thus viewed as a new paradigm in quantum sensing. Intriguingly, the comparison of both models with experimental data can constitute a test for the foundations of quantum mechanics in a macroscopic ensemble of atoms.