Quantum Simulation Of Topological Soliton Transport In DNA

Deoxyribose nucleic acid(DNA)is a double helix structure composed of bases,pentose and phosphate,and its biological properties such as replication,transcription and translation of genetic information are closely related to its dynamic behavior.The rotation of based in the DNA double chain,the overall vibration of the molecule and the local excitation of the unit molecular groups are all nonlinear motion.Therefore,the dynamic simulation of DNA and its numerical calculation have become a hot topic of current research.Due to the very huge number of atomic and molecules in DNA and the complexity of their interactions,the dynamics simulation of DNA and its numerical calculation are very difficult.The cold atomic system in the optical lattice provides a new platform for quantum simulations due to its properties of long coherence time and highly controllable parameters.In particular,the cold atomic system in the two-legged ladder optical lattice has good similarity to the structure of the deconvoluted DNA double chain,providing an ideal platform for quantum simulations of DNA dynamics.After considering complex interactions such as long-range dipole-dipole interactions and spin-orbit coupling between atoms,this paper simulates the properties of topological solitons and their dynamics in DNA using the cold atomic system in a two-dimensional optical lattice.The specific research contents are as follows:In the first chapter,we give a brief introduction to the current status and research significance of DNA,the soliton dynamics of DNA,the quantum simulation in cold atom system and optical system.In the second chapter,we study construction and dynamics of two-dimensional(2D)anisotropic vortex-bright(VB)soliton in spinor dipolar Bose-Einstein condensates confined in a 2D optical lattice(OL),with two localized components linearly mixed by the spin-orbit coupling and long-range dipole-dipole interaction(DDI).It is found that the OL and DDI can support stable anisotropic VB soliton in the present setting for arbitrarily small value of norm N.We then present a new method via examining the mean square error of norm share of bright component to implement stability analysis.It is revealed that one can control the stability of anisotropic VB soliton only by adjusting OL depth for a fixed DDI.In addition,the dynamics of the anisotropic VB soliton was studied by applying the kick to them.The mobility of the single kicked VB soliton is Rabbi-like oscillation.However,for the collision dynamics of two kicked anisotropic VB solitons,their properties mainly depend on their initial distance and the depth of OL,and they can realize the transition from the bright component to the vortex component.In the third chapter,the topologically protected Floquet surface bound states in the continuum(BIC)and their dynamics of two-dimensional SSH model are studied.The BIC generally exist in special systems and have very strict requirements on parameters.We successfully extract the topologically protected BIC in the Floquet modulation system,and introduce different detuning forms into the system.It is shown that the introduction of different forms of detuning can affect the position and the degree of locality of the surface BIC.Subsequently,we introduce different strengths with different forms of disorder to the system,and the results show that the surface BIC under Floquet modulation maintain good robustness to disorder.In addition,it is found that surface BIC under Floquet modulation are stable to structural perturbations and can exist in a wide range of parameter spaces compared to bound states in continuous bands supported by specific potential wells.Finally,based on the edge repulsion effect of BIC,we propose to distinguish BIC from bound states out of the continuum by quantum walk.In the fourth chapter,we summarize the whole paper and give an outlook.