Switching time of optical memory devices composed of photonic crystals with an impurity three-level atom

We calculate the switching time of an optical memory device composed of three-dimensional photonic crystals with an impurity three-level atom, that is, a photonic memory device. We determine the switching time to be a function of the overshoot and the time constant of a decaying oscillation of the upper level population of the impurity atom. The analytical solutions for the overshoot and the time constant are given by using the Euler approach. Using these functions, we calculate the switching time for the Rabi frequency and the transition frequency of the impurity atom. Our results show that the switching time is improved by changing the transition frequency from inside the photonic band gap to outside it and/or by increasing the Rabi frequency, where the transition frequency and the Rabi frequency can be controlled by a small power field. We determine suitable ranges of these frequencies for realizing a high-speed photonic memory device, which are important for atomic-scale optical systems such as high-density integrated optical circuits and quantum computers.