Giant third-order polarization rotation via wave-mixing-induced symmetry breaking in a Rydberg-EIT medium
We investigate how wave-mixing (WM)-induced symmetry breaking leads to giant third-order polarization rotation of a weak probe field in a Rydberg electromagnetically induced transparency (EIT) medium. A far-detuned counterpropagating WM field is adiabatically eliminated and retained solely as a Raman dressing of the lower Zeeman manifold. In this reduced description, the weak static magnetic field defines the two circular propagation channels, while the WM-induced Raman coherence breaks the symmetry between these channels, without acting as a gain channel or an independent nonlinear source. The weak-probe response is calculated using a reduced density-matrix expansion for van der Waals (vdW) correlations and self-consistent Maxwell-Bloch propagation, with the nonlinear rotation extracted by subtracting the linear propagation background. Including WM dressing increases the extracted third-order rotation from 1.06 degrees to 25.70 degrees, an enhancement of more than 24 times, for the parameters considered. The response is nonmonotonic in WM strength and can even reverse sign, revealing that the WM field controls the propagation channels through symmetry breaking rather than merely amplifying the probe. Eigenchannel diagnostics further indicate that this giant rotation requires coherent excitation of both WM-dressed propagation channels, which in turn depends on three factors: Raman-induced asymmetry, the EIT-supported Rydberg pathway, and vdW nonlocality. These results demonstrate a symmetry-breaking-controlled mechanism for Rydberg magneto-optics, with applications to weak-light polarimetry and all-optical polarization control.