Phase-controlled optical Kerr effect in a microwave-driven X-type atomic system

Abstract

We theoretically investigate the first- and third-order probe response of a five-level X-type atomic system coupled by the microwave field. The analytical solutions describing the phase dependence of linear/nonlinear probe coherence are obtained by invoking the iterative perturbation method. We find that for both stationary and moving atoms, EIT and Kerr nonlinear behavior of our considered system can be manipulated by altering the relative phase ( $$\phi $$ ) of the applied e.m. fields. The appropriate choice of $$\phi $$ gives rise to colossal Kerr nonlinearity accompanied by the reduced absorption. Further, we analyzed the effect of wavelength mismatch on the linear/nonlinear optical response for three different regimes of wavelength. Our results demonstrate that out of the three wavelength mismatch regimes, maximum Kerr index is obtained when probe field’s wavelength is chosen to be larger than that of the upper two control fields, i.e., $$\lambda _p=\lambda _{c_1}>\lambda _{c_2}\approx \lambda _{c_3}$$ . Besides providing the largest Kerr effect, this scheme is easy to implement experimentally.