Study Of Left-handedness And Kerr Nonlinearity In Multi-level Atomic System

The left-handed metamaterial (LHM) is a kind of artificial composite structureor composite material with negative permittivity and negative permeabilitysimultaneously and it has some unique properties that natural materials do not have.In recent years, LHM has become one of the hot academic topics worldwide due toits potential application in the negative refraction, subwavelength imaging,invisibility cloak, optical information processing, quantum information and so on.People have realized the negative permittivity and permeability in the microwavefrequency band for the first time by using metal subwavelength resonance structureunit. With the deepening of the research, it is found that the practical application ofthis kind of left-handed materials has been seriously limited by the inherent ohmiclosses, microwave frequency response characteristics and anisotropic properties ofthe metal microstructures. However, another method based on atomic coherence andquantum interference theory to realize left-handedness in coherent atomic gas, whichis named photonic resonant media, has attracted people’s interests due to its opticalfrequency response, low loss and other advantages. This thesis will focus on how torealize dual-band or multi-band left-handedness, negative refraction with lowabsorption in the multi-level atomic systemand Kerr nonlinear effect in thisleft-handed atomic system. Specific work content is as follows:We study the left-handed effect of-type three-level atomic system withadjusting applied field. Firstly, we analyzethe effect of the phase of external field onthe permittivity andpermeability, it can find that they are sensitive to the change ofthe coupling field phase, since the coupling field phase is added to make magneticresponse enhanced, the atomic system can achieve larger negative permeability, andit presents low absorption in the left-handed frequency range; we adopt bichromaticcoupling field instead of monochromatic coupling field driven three-level atomicsystem, the results show that the permittivity and permeability can obtain negativevalues in the same frequency range with adjusting Rabi frequency and frequencydifference of the bichromatic coupling field, atomic system can realize multi-band orsingle-band left-handed effect.We study the effect of the electromagnetically induced transparency(EIT) onquasi--four-level atomic system. Firstly, we analyze the effect of EIT with doublewindows, Rabi frequency of the strong coupling and control fields on thepermittivity and permeability, the results show that the permittivity and permeabilitycan obtain negative values when the control field Rabi frequency is much smaller than the strong coupling field Rabi frequency, the atomic system can realizedual-band left-handed material, it also can be found that the atomic system showsnegative refraction with low absorption in one left-handed frequency band and itshows active medium in another left-handed frequency band; then we adjust thecontrol and probe fields to interact with a common level, we find that it cansimultaneously obtain negative permittivity and negative permeability in twofrequency bands, the atomic system can realize dual-band left-handed effect withlow absorption even zero absorption.We study the left-handed effect of V type four-level atomic system influencedby external field detuning frequency. We discuss the resonance or off-resonancedetuning frequency of the strong coupling and control fields on the permittivity andpermeability of this atomic system,it can be found that the atomic system canachieve single-band left-handed effect with resonant detuning frequency of thecoupling and control fields anddual-band left-handed effect with off-resonancedetuning frequency of the coupling and control fields; we analyzethe permittivityand permeability with different atomic density, we find that low or high atomicdensity will inhibit the atomic system to obtain negative permittivity andpermeability, it can realize left-handed effect with zero absorption.We study the Kerr nonlinearity of left-handed-type three-level atomicsystem and V-type four-level atomic system. We analyze the effect of the couplingfield phase and bichromatic coupling field on Kerr nonlinearity in three-level atomicsystem, the results show that Kerr nonlinearity is enhanced, moreover,theleft-handed atomic system can occur focusing effect or defocusing effect; then wediscuss the effect of detuning frequency of the control field and strong coupling fieldon Kerr nonlinearity, it shows that Kerr nonlinearity is enhanced in this left-handedatomic system, focusing effect or defocusing effect can be taken place in left-handedfrequency range.