High Dimensional Solitons In Coherent Atomic Media

The invention of laser promote the progress of nonlinear optics. Many kinds of nonlinear optical phenomenon can be produced via the interaction between the high power laser and media. According to the interaction between optical field and media, the media can be divided into two types:the passive optical media and the active optical media. The characteristic of passive optical media is there is not energy exchange between light and media. When the frequency of the probe field is far from the resonantly frequency of media, the nonlinear susceptibility decrease sharply with its order increasing. So, to obtain strong nonlinearity, we usually need to use a laser with very high light intensity. The characteristic of active optical media is there is energy exchange between light and media. These physical quantities of the optical media are the function of light intensity. If the frequency of probe pulse is close to the resonantly frequency of media, a strong nonlinearity can be obtained by the weak light in this media, but at the same time a very large optical absorption can not be avoided. So, many nonlinear optical phenomenon are usually studied by the interaction between the passive optical media and the laser with very high light intensity.In recent years, such a paradigm had been changed after the finding of elec-tromagnetically induced transparency (EIT), which could get strong nonlinear optical susceptibility under the weak light condition. EIT is a quantum interfer-ence effect induced by an applied control laser field, by which the absorption of probe field can be largely suppressed. EIT can be used not only for suppressing optical absorption, acquiring ultraslow group velocity and enhancing Kerr non-linearity, but also for producing spatial optical solitons, spatiotemporal optical solitons and so on. However, it is difficult to produce stable high-dimensional optical solitons and vortex in Kerr type system via the EIT medium.In this dissertation, we propose a scheme to generate stable high-dimensional optical solitons in a N-type four-level EIT system. Firstly, we derive the Maxwell-Bloch equation of system; Then we use the multiple-scales method developed in resonant nonlinear optics to reduce the equation:Finally we obtain many kinds of high-dimensional optical solitons and discuss their stabilities by using the Newton methods, the Newton conjugate gradient method, the squared operator iteration method, the Fourier collocation method, and so on. The following contents are included:1. The N-type four-level EIT model is derived. Much attention has been paid to the stable high-dimensional weak-light ultraslow optical solitons in the three-level EIT system. But in the Kerr type nonlinear system, the stable high-dimensional optical solitons are hardly produced. So we extend the three-level system to four-level one. For increasing the fourth level and corresponding field can form a trapping potential under certain conditions, it is possible to produce a stable high-dimensional optical solitons. Then we derive the Maxwell-Bloch equa-tions by the quantum optical theory, and use multiple-scales method developed in resonant nonlinear optics to reduce these equations into a (3+1)-dimensional Ginzburg-Landau equation. Because of many adjustable parameters in our sys-tem, such as the decay, the beam waist, the light intensity of control field, the atomic density and so on, many kinds of models can be realized.2. High-dimensional spatial optical solitons in N-type four-level EIT are studied. Until now, in EIT system, the stable high-dimensional spatial optical solitons are found via saturable nonlinearity and cubic-quintic nonlinearity, but these solitons possess narrow existence region and poor stability. As far as we know, there is no report on such study with Kerr nonlinear system in the litera-ture up to now. By taking the wide pulse width, the (3+1)-D Ginzburg-Landau equation can be reduced into (2+1)-D nonlinear Schrodinger equation with an external potential. Finally we not only obtain many kinds of spatial optical soli-tons, but also discuss their stabilities by the numerical method, and find many solitons being stable.3. Stable (3+1)-dimensional spatiotemporal optical solitons in N-type four-level EIT are studied. Up to now, most (3+1)-dimensional spatiotemporal optical solitons are produced in passive optical media and high light intensity are needed. In EIT medium, there is no relevant report up to now. We study the (3+1)-D Ginzburg-Landau equation directly by the numerical method and find many kinds of stable spatiotemporal optical solitons by adjusting the parameter of system. These stable spatiotemporal optical solitons have many novel features, such as low generation power (submicro-watt), ultraslow group velocity (Vg/c～10-5) and so on. It is the first time that these stable3-dimensional spatiotemporal solitons are found in EIT system.All these results presented at above are useful not only for understanding the nonlinear properties of coherent atomic systems, but also for guiding exper-imental findings of high dimensional optical solitons with very low generation power, and offering the new plan of quantum control in atomic and molecular system.