Giant magneto-optical rotation in a Rydberg atomic gas via symmetry-breaking wave mixing

The nonlinear magneto-optical rotation effect is central to precision measurements of weak magnetic fields and optical quantum information processing. In conventional single-beam excitation systems, the propagation of the nonlinear signal is restricted by an energy-symmetry-induced propagation blockade. This blockade originates from the symmetrical evolution of the orthogonal circularly polarized components of the probe field, which prevents spatial accumulation of the nonlinear polarization. We propose introducing a far-detuned, counterpropagating wave-mixing (WM) field into an ultracold five-level Rydberg atomic gas to actively break the excitation symmetry. Theoretically, the far-detuned WM field is treated as a steady-state dressing field. Through adiabatic elimination, the conventional third-order wave-mixing process is effectively reduced and incorporated into the first-order linear background of the system. Combined with the reduced density-matrix expansion method, this approach goes beyond both the mean-field and ground-state approximations, allowing for a self-consistent solution of the many-body dynamics that include nonlocal cascaded integrals governed by long-range van der Waals interactions. Our analytical derivations and numerical calculations demonstrate that this symmetry-breaking mechanism breaks the propagation blockade, enabling efficient utilization of the nonlocal Rydberg Kerr effect. As a result, the third-order nonlinear rotation angle is enhanced by a factor exceeding 24, offering a highly efficient mechanism for ultrasensitive atomic magnetometry and all-optical quantum information processing.