Studies On The Formation Of Ultraslow Solitons In Single Molecular Magnets

Since first observed as a water wave for more than one hundred and seventy years ago, soli-tons have been one of the most active and important research interests in a variety of science fields.As one of nonlinear phenomena, the propagation of solitons which belongs to the category of non-linear physics permeates the nature. Solitons which have the properties of a particle are employedto describe a class of fascinating shape-preserving propagation phenomena of wave packets orpulses in dispersive nonlinear media. Under certain conditions, a perfect balance between thenonlinear and dispersive effects can lead to wave packets maintaining their shapes not only dur-ing propagation but also during mutual collisions. Because of crucial and potential application inmany fields, solitons in nonlinear medium have attracted a great deal of attention. In recent years,the existence of solitions is proved through theory and experiment in so many branches of physicsand states of matters such as optical fiber, Bose-Einstein condense, semiconductor quantum dots,cold atoms media and plasma. In this thesis, we mainly make use of a semiclassical theory tostudy the formation of ultraslow solitons in single molecular magnets. The main content is asfollows:Basing on a semiclassical theory, we have analyzed the formation of ultraslow dark andbright solitons via four-wave mixing (FWM) in a crystal of molecular magnets in the presenceof a uniform dc magnetic field. The single molecular magnet can be treated as a quantumfour-level system, which interacts with two strong continuous wave pump electromagnetic fieldsand a weak pulsed probe electromagnetic field, and a pulsed FWM electromagnetic field can begenerated effectively. By solving the Maxwell-Schro¨dinger equations under the slowly varyingenvelope approximations and rotating-wave approximation, we find that there exist two modesdescribing the propagation of the probe and FWM electromagnetic fields in the crystal mediumof molecular magnets. Moreover, two modes'absorption coefficients are so much differentfrom each other in certain parameter regime that one mode decays very sharp quickly and evenvanishes after a very short propagation distance. Under the properly approximate conditions weeventually attain the standard nonlinear Schro¨dinger equations (NLSE) of the probe and FWMfields with the reasonable and realistic set of parameters. And the standard NLSE have solutionsof describing dark and bright solitons. Then we demonstrate that both the probe and FWM fieldscan evolve into dark and bright solitons with the same shape and the same ultraslow group velocity.