## 3 Examples: Comparison of Our Model with a Set of Multilevel Structures
effectively coupled to the system, so Equation (20), which is obtained from treating the probe field as perturbation to the system is not suitable for this area. Alternatively from the point of view of atomic physics, Equation (20) describes optical response of the stable atomic media, which means we measure the optical response some time after the atom-field interaction. In this case the only coupling field frequency that need to be considered is the on-resonance one, so what survives through Equation (20) is the probe field satisfying \(|\Delta_{p}|\sim 0\). We can also look at the \(n=5\) case of Equation (21), which we call five-leg type, and the ladder type (or \(\Xi\) type), which although is different from the \(\Lambda\) type, still shares the same expression of probe susceptibility under the assumption of on-resonance strong field coupling (\(\Delta_{2}=0\)) [3]. The difference between the ladder type and \(\Lambda\) type in parameter setting is that \(\gamma_{I2}\
eq 0\) for ladder type. We set \(\gamma_{I2}=0.2\), \(\Omega_{4}=1\), \(\Omega_{5}=1\), \(\Delta_{4}=0\), \(\Delta_{5}=0\) and all the other parameters the same as in Figure 2 and get the results of comparison in Figure 3. As can be seen from the plot, the probe susceptibility curves of five-leg and ladder configurations do not coincide with our model now, because they are not typical EIT configurations any more. Equation (21) shows that a five-leg configuration under our parameter setting is equivalent to a \(\Lambda\) type configuration with doubled Rabi frequency. Also, for the ladder type configuration, the existence of nonzero decay rate \(\gamma_{I2}\) brings atypical EIT observation. When \(|\Delta_{p}|\) deviates from zero, the existence of a weak probe field can be ignored, and the measurement of probe susceptibility between energy levels \(|k\rangle\) and \(|l\rangle\) is equivalently performed on the system with only all the strong coupling fields existing. The entire EIT curve can therefore be looked on as the combination of two parts: the profile determined by the presence of strong coupling fields, and the steep change imposed on the central area of \(|\Delta_{p}|=0\) by the weak probe field. The latter has been described by Equation (20), then how do we figure out the shape of the former? In addition, why there is a minus sign needed when Equation (20) is used to describe the central area of EIT phenomena? We may not be able to answer these questions in the most general cases; however, when the polarization of all the applied fields are of the same direction, these two questions can be answered together. Here is the imaginary operation that we perform. Suppose all the applied fields are of the same polarization direction \(\xi\), and all the strong coupling fields from Equation (10) are of the similar magnitude \(E_{c}\), i.e. \(|\mathbf{E}_{c(nm)}|\sim E_{c}\), then we know there is also \(|\mathbf{E}_{probe}|\ll E_{c}\) for the weak probe field. We now apply a set of adjusting electric fields \(\mathbf{E}_{adjust(nm)}(t)=-\mathbf{E}_{c(nm)}(t)\), where \(\mathbf{E}_{c(nm)}(t)=\mathbf{E}_{c}(\omega_{f(nm)})e^{-i\omega_{f(nm)}t}\) as defined in Equation (11), coupled to the corresponding energy levels \(|n\rangle\) and \(|m\rangle\), can also be approximately written as \(E_{c}\xi e^{-i\omega_{f(nm)}t}\). We then have  
\[\mathbf{E}_{adjust(nm)}(t)=-E_{c}\xi e^{-i\omega_{f(nm)}t}. \tag{22}\]  
For the probe field coupling energy levels \(|k\rangle\) and \(|l\rangle\), we apply  
\[\mathbf{E}_{adjust(probe)}(t) = -E_{c}\xi e^{-i\omega_{f(kl)}t} \tag{23}\] \[= -\frac{\mathbf{E}_{probe}(\omega_{f(kl)})}{|\mathbf{E}_{probe}( \omega_{f(kl)})|}E_{c}e^{-i\omega_{f(kl)}t}\]  
which is in reverse direction of \(\mathbf{E}_{probe}(t)\), but with a much larger amplitude \(E_{c}\).