Investigations On Nonlinear Propagation Properties Of Ultraslow Light In Cold Atomic Media

The invention of lasers leads to the naissance of nonlinear optics which has greatly extended the research region of conventional optics in the past half century. The novel nonlinear phenomena presented by interaction between light and matter are the main subjects of nonlinear optics.As we know, the nonlinearity of a conventional optical medium is very weak when working far from resonant regime, or there is a very large optical absorption when working near resonant regime where nonlinear effect is strong. Thus people are used to consider that it was difficult to enhance nonlinearity without suffering serious absorption.The proposal of electromagnetically induced transparency (EIT) solves the above difficulty. Due to the quantum interference induced by a coupling laser field, the absorption of a probe laser field can be largely suppressed even it is tuned to a strong one-photon resonance. The wave propagation in an optical medium under EIT configuration displays many striking features such as a significant reduction of the group velocity of the probe field which can be used to optical buffers and storage of the probe pulse. A great enhancement of Kerr nonlinearity in EIT media is beneficial to certain nonlinear processes under weak driving conditions. A great enhancement of cross-Kerr nonlinearity in EIT media can be use to construct effective all-optical quantum phase gates which supports quantum information and computation.Although absorption is suppressed, the dispersion effect in such media is still very strong and hence the wave shape of the probe pulse will suffer a serious deformation during the propagation which is harmful to the information transmission. How to balance the dispersion with nonlinearity to get a distortion free propagation of the probe wave packet is a main subject of the present dissertation. In this dissertation, we have adopted a strange perturbation method, i. e. the multiple-scale method, to investigate the nonlinear properties of the wave propagation in cold atomic media under EIT configurations. Our work includes the following aspects:1. We have investigated the influence of high order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a four-state atomic system under EIT configuration. We have derived a high-order nonlinear Schrodinger equation and showed that for short pulse duration these high-order effects may be significant and therefore must be treated from a nonperturbative viewpoint. The exact soliton solutions of the high-order nonlinear Schrodinger equation have been given which may travel with an extremely slow velocity. We have also carried out numerical simulations on the stability and interaction of these high-order ultraslow optical solitons.2. We have studied the formation and propagation of stable (2+1)-D spatial optical solitons in a resonant three-level atomic system. We have obtained a NLS equation with a saturation nonlinearity, which governs the dynamics of the envelope of the probe field and support stable (2+1)-D spatial optical solitons. We have demonstrated that the spatial optical soliton in such a system can be generated by using an extremely weak probe-light intensity. We have also made a detailed numerical study on the interaction between two (2+1)-D spatial optical solitons. The controllability of the spatial optical soliton has also been studied by manipulating the coupling laser field.3. We have proposed a scheme to create temporal vector optical solitons in a coherent five-level atomic system. Such solitons can have ultraslow propagating velocity and may be produced with extremely low input power. We have demonstrated both analytically and numerically that it is easy to realize Manakov temporal vector optical solitons by actively manipulating the dispersion and nonlinear effects of the system. The system proposed can be also used to realize a complete control over the polarization of the probe field.4. We have investigated the three-way entanglement and three-qubit phase gates based on a coherent six-level atomic system. From the density matrix equations, we have shown that the completely cross fifth-order optical susceptibilities are greatly enhanced with other susceptibilities being simultaneously suppressed in our system. Based on such important feature we have demonstrated that the system can produceefficient three-way entanglement and implement a robust three-qubit quantum phase gate which can be further transferred to a Toffoli gate.The nonlinear optical properties of the EIT media have attracted more and more attentions in recent years. The investigations on nonlinear propagation properties of ultraslow light in EIT media not only make sense in exploring the nonlinear optical properties of the EIT media, but also have a potential application in modern optical information processing and transmission at a low light level.