# Observation of an Electromagnetically Induced Grating in Cold \({}^{85}\)Rb Atoms
## 3 Results and Discussion
Since the \(5S_{1/2}(F=3)-5P_{3/2}(F^{\prime}=4)\) absorption is much more prominent, we choose this transition for the following experiment--while by locking the probe laser frequency on the transition of \(5S_{1/2}(F=3)-5P_{3/2}(F^{\prime}=4)\) and scanning the frequency of coupling laser, we obtained the absorption spectrum of probe laser in the presence of coupling laser. With the probe laser (with its frequency far from the resonance) launched into the MOT and the coupling fields blocked, we observed the corresponding Gaussian profile in the CCD, which is illustrated in Figure 3b. When we lock the coupling laser frequency on the \(5S_{1/2}(F=3)-5P_{1/2}(F^{\prime}=3)\) transition and fix the probe laser frequency near the transition of \(5S_{1/2}(F=3)-5P_{3/2}(F^{\prime}=4)\), a distinct diffraction pattern is obtained as shown in Figure 3c. Here, the powers of the coupling and probe lasers are about 16 \(\upmu\)W and 1 \(\upmu\)W, and the frequency detunings are \(\Delta_{c}=0\) and \(\Delta_{p}=10\) MHz, respectively. The density of the cold atoms in MOT is the Gaussian distribution, which is different from the randomly distribution of atomic density in a thermal vapor cell, and the cold atoms are more concentrated in the center of the MOT. In addition to being diffracted, the probe laser also has a strong absorption at the center of the cold atom ensemble. Therefore, the diffraction intensity at the corresponding position will appear relatively weak affected by the distribution of atomic density. This is significantly different from the diffraction patterns in thermal atoms. However, the observation of the diffraction pattern is more stable compared with the thermal atomic vapor case owing to the low-fluctuation of cold atom density. Figure 2: (**a**) dispersion (\(\chi^{\prime}\)) and (**b**) absorption (\(\chi^{\prime\prime}\)) as a function of the probe laser frequency detuning and coupling laser Rabi frequency. Here, \(\Delta_{c}=0\); (**c**) a hybrid grating with \(\Omega_{c}=11_{2}\), \(\Delta_{p}=1.5\Gamma_{2}\) and \(\Delta_{c}=0\). The blue curve is the transmission function \(|E_{p}(x,L)|\) and the red curve is corresponding phase \(\Phi\). In the simulation, \(\Gamma_{1}=0\) and \(\Gamma_{3}=0.95\Gamma_{2}\). According to Equation (1), some system parameters can influence the susceptibility of this system, such as the density of cold atoms, the coupling laser power, and the two-photon detuning. This means that the diffraction pattern can be controlled by these tunable parameters. In some experiments related to cold atoms, the atomic density mainly depends on the power of the lasers used in MOT configuration. We keep the initial density of cold atoms for about \(10^{10}\) cm\({}^{-3}\) throughout the experiment. The grating constant is determined by the angle of the two coupling lasers. When the angle is too small, the diffraction phenomenon is hard to be detected due to the less diffraction orders, while, when the angle is too large, the diffraction patterns become dense and less distinguishable. The crossing angel \(\theta\) of two coupling lasers is about 0.13 degree in this work, which resulted in a grating constant of 175 \(\upmu\)m and a better diffraction pattern. Figure 4a-f are a series of diffraction patterns obtained by changing the coupling laser power, and the yellow curves are the corresponding spatial intensity distributions. With a coupling laser power of 7 \(\upmu\)W, the diffraction of probe laser begins to appear. Then, the diffraction patterns gradually become distinct with the increasing power, which are shown from Figure 4b,c. The most recognizable pattern is observed when the power attains to 16.2 \(\upmu\)W as illustrated in Figure 4d. With the increase of the coupling intensity, the nonlinear enhancement of the EIT effect greatly promotes the formation of the distinct diffraction patterns [6]. Further increasing the power, the diffraction intensities of each order have a corresponding growth, but the resolution becomes worse.