Gap Solitons In An Electromagnetically Induced Transparency System

In the past decades, considerable theoretical and experimental research activities have focused on the study of optical solitons due to their important applications in optical information processing and transmission. Up to now, most optical solitons are produced in passive optical media such as glass-based optical fibers, in which far-off resonance excitation schemes are generally employed in order to avoid unmanageable optical attenuation and distortion. However, due to the lack of distinctive energy levels, the nonlinear effect in such passive optical media is very weak, and hence a very high light intensity is required to form a soliton. In addition, the lack of distinctive energy levels and transition selection rules also makes an active control of such optical soliton difficult.In recent years, due to the discovery of electromagnetically induced transparency (EIT), weak-light nonlinear optics in a coherent media has attracted many research attention and interests. The basic theory of EIT is using quantum coherence between atom states induced by a strong control light to eliminate the absorption of a weak probe light. EIT can significantly change the dispersion relation of the media and hence a magnificent reduction of group velocity of the probe light can be obtained. Based on these interesting features, in recent works it has been shown that a new type of optical soliton, called ultraslow optical soliton (or USOS), can form in a resonant multi-level media. And they can propagate in the media at velocity several magnitudes lower than they propagate in vacuum. Such study has opened a new research direction on nonlinear optical pulses formation and propagation in coherent multi-level media.If we replace the continuous control wave in EIT with a standing wave, the linear dispersion relation of the probe light will be changed from a single line to a series of photonic band gap, and these gaps can be easily manipulated. Recently, many theoretical and experimental works have been done in this area and many interesting results have been found. It is widely expected that a further exploration in this direction may offer new tools of photonic state manipulation and quantum information processing at low-light level.Different from the previous studies, in this work we consider when the control light has formed a standing wave that how the probe light propagates with weak nonlinearity. Based on a A-type three-level atomic scheme we present an optical gap soliton generation technique in a resonant media via EIT. We shall demonstrate that by modulating the parameters of the system, the oscillating frequency of the gap solitons found by us is within the forbidden gap of frequency spectrum of the probe field, and the incident light intensity needed here is very low. Further more, the physical property of such gap solitons can be easily manipulated in a controllable way. Because of their robust nature, gap solitons may become promising candidates of well-characterized, distortion-free optical pulses and hence have potential technological applications in optical information processing and telecommunication engineering.The paper is arranged as follows. The first chapter gives a simple description of soliton and electromagnetically induced transparency, and the basic concepts related. In Chapter II we give the basic theory about EIT system and solitons formed in it. In Chapter III we present our study about gap solitons formed in a A-type three-level atomic system under EIT condition, including both small and large gap solitons. The last chapter gives a summary of our main results.