Giant second-order cross nonlinearities via direct perturbation to the dark state in coherent population trapping

Abstract

We study the nonlinearities due to direct perturbation to the dark state in coherent population trapping (CPT). To extract the susceptibilities of the CPT atoms with respect to probe fields, we treat the CPT dressing fields as control parameters and redefine susceptibilities with respect to the probe fields alone. With such a redefinition, we reveal that a CPT-based system displays an ultralarge, resonantly enhanced second-order cross susceptibility ${\ensuremath{\chi}}^{(2)}$ together with vanishing linear absorption. Physically, this effect is based on the CPT dark-state shift, which is traced to the six-photon parametric processes for all involved fields (including the dressing and probe fields). Because of the lack of the direct perturbation, this effect is absent in the electromagnetically induced transparency (EIT)-based system, in which only resonantly enhanced third-order (Kerr) susceptibility ${\ensuremath{\chi}}^{(3)}$ is obtainable but much weaker than the second-order one. The second-order nonlinearity, because of its stronger effect, can be more sensitive for quantum nonlinear optics at low light levels than the third-order nonlinearity.