An analytical model for cross-Kerr nonlinearity in a four-level N-type atomic system with Doppler broadening

We present an analytical model for cross-Kerr nonlinear coefficient in a four-level N-type atomic medium under Doppler broadening.The model is applied to87 Rb atoms to analyze the dependence of the cross-Kerr nonlinear coefficient on the external light field and the temperature of atomic vapor.The analysis shows that in the absence of electromagnetically induced transparency(EIT)the cross-Kerr nonlinear coefficient is zero,but it is significantly enhanced when the EIT is established.It means that the cross-Kerr effect can be turned on/off when the external light field is on or off.Simultaneously,the amplitude and the sign of the cross-Kerr nonlinear coefficient are easily changed according to the intensity and frequency of the external light field.The amplitude of the cross-Kerr nonlinear coefficient remarkably decreases when the temperature of atomic medium increases.The analytical model can be convenient to fit experimental observations and applied to photonic devices.

Comparative Study of Light Manipulation in Three-Level Systems Via Spontaneously Generated Coherence and Relative Phase of Laser Fields

We present a comparative study of the control of group velocity in three-level atomic systems including Λ-, Ladder-, and V-types via spontaneously generated coherence(SGC) and relative phase of laser fields.In the steady regime, expressions of group index are derived as an analytical function of controllable parameters related to SGC and relative phase.It is shown that the group velocity can be further slowed down or speeded up under SGC in which modifications of group velocity due to the SGC in Λ-and V-systems are stronger than that in Ladder-system.In particular, when interference strength of SGC p increases from 0.7 to 1.0, the light propagation is switched from superluminal to subluminal modes(for Λ-and Ladder-systems) or from subluminal to superluminal modes(for Vsystem).In the presence of relative phase, the group velocity changes between subluminal and superluminal modes with a period of 2π.In resonant region, the largest positive value of group index reaches at the relative phase φ=π while the largest negative value of group index reaches at φ= 0 and 2π for the Λ-and Ladder-systems, otherwise, for the V-system the largest positive group index occurs at φ= 0 and 2π, and the largest negative group index occurs at φ=π.