Soliton Properties In Both BEC And Quantum Dot EIT Media

Solitons,which are from the balance of between the dispersion effect and the nonlinear effect of the system,have been extensively studied in some fields of physics,such as Bose-Einstein condensates(BECs),nonlinear lattice,fluid mechanics,electromagnetically induced transparent(EIT)media and so on.In recent years,the studies on the soliton properties of BECs in shallow optical lattice potential have been perfected increasingly,however the studies on the soliton properties of BECs in deep optical lattice potential are starting.Just in 2020,O(?)dziejewski's group reports that BECs localized in the deep optical lattice potential can show some novel quantum local phenomena.Inspired by this,we study the soliton properties of BECs in a deep optical lattice potential.In addition,EIT is regarded as an ideal carrier for the optical solitons propagation,because it possesses strong nonlinear effect under the condition of the low light excitation.Early studies on EIT media focused on ultracold atomic systems.However,it is difficult to measure and control accurately such a rare gas at very low temperature.This seriously hinders its practical application.With the development of the semiconductor technology,it is found that the quantum dot EIT medium has the energy level structure similar to the super-cold atom,and can also construct the multi-quantum dot array beneficial to practical application by "artificial clipping".Therefore,semiconductor quantum dot EIT medium is considered as an ideal carrier for optical soliton propagation.In this thesis,we first study the soliton local properties of BECs in a deep optical lattice potential.Taking this opportunity,the retention,storage and retrieval of optical solitons in semiconductor quantum dot EIT media are then studied.The main innovation points of this thesis are the following.1)By developing quasi-discrete multiple-scale method combined with tight-binding approximation,a novel quadratic Riccati differential equation is first derived for the soliton dynamics of the condensed bosons trapped in the optical lattices.So far,there is no exact solution to the quadratic Riccati differential equation.Therefore,the trial solutions of the Riccati equation have been analytically explored for the BECs with various scattering length in the deep optical lattice potential.It is found that for the positive scattering length condensates trapped in the shallow optical lattice potential,there exists the bright-gap solitons which is in qualitative agreement with the experimental observation in the system.For the deeper lattice potential,it is found that some novel intrinsically localized modes of symmetrical envelope,topological(kink)envelope and anti-kink envelope solitons can be observed within the band gap in the system,of which the amplitude increases with the increasing lattice spacing and(or)depth.In the case of the negative scattering length condensates trapped in the optical lattice,the band gap brings out intrinsically localized grey or black soliton.This well provides experimental protocols to realize transformation between the grey and black solitons by reducing light intensity of the laser beams forming optical lattice.2)In the EIT medium model of asymmetric double quantum dot molecules,the tunneling coupling effect between semiconductor quantum dots is considered.The nonlinear enveloping equation is derived analytically by means of the density matrix method combined with the multiple scales method.The results show that optical solitons with very low propagation velocity can be generated in the system,and the propagation velocity of optical solitons can be controlled by the coupling strength.In addition,the storage and retrieval of slow optical solitons are studied by controlling the tunneling coupling strength between double quantum dots by switching off and on the gate electric field.It is shown that the optical soliton signals can be stored and retrieved in double quantum dot EIT medium with high fidelity.The results have potential application value for optical and quantum information storage.3)We first propose an asymmetric linear triple quantum dot molecule model.And then,the linear and nonlinear dynamical properties of the double neighboring dot-dot tunneling coupling are analytically studied by using an amplitude variable approach combined with multi-scale method.It is shown that double transparency windows are formed by the double tunneling coupling.The dark or bright optical solitons are then obtained,of which both the types and the propagating velocity can be controlled by the two tunneling coupling strengths.Interestingly,the propagating velocity of the solitons can approach to zero at certain tunneling coupling strengths,the motionless optical solitons appearing there.The results indicate potential applications of the semiconductor quantum devices for optical soliton storage.