Fig. 1: Principle and schematics of weak-measurement-based correlation spectroscopy.

The σ⁺ and σ⁻ circular components of a linearly polarized laser beam form electromagnetically induced transparency (EIT) with the atoms under a three-level Λ configuration. The transmission spectra of σ⁺ and σ⁻ overlap when the two-photon-detuning Δ = 0, but split when Δ ≠ 0. The offset spectra give opposite transmission slopes for σ⁺ and σ⁻ near δ = 0, which are responsible for the out-of-phase FM–AM conversion and the anti-correlation. The converted intensity modulations correspond to a small oscillation of the Stokes vector of light on the Poincaré sphere, and the oscillation amplitude is proportional to Δ. By post-selecting the frequency components of the two transmitted EIT fields intensities, an anomalous effective amplification of the polarization oscillation can be achieved, giving rise to a reduction in the correlation resonance linewidth. Here, δ is the averaged one-photon detuning of the two circular light fields, and Δ is the two-photon detuning due to Zeeman splitting of the atomic ground states caused by the total magnetic field B along the light propagation direction.