超冷原子动量光晶格中的非线性拓扑泵浦

Nonlinear topological pumping in momentum space lattice of ultracold atoms

在拓扑系统中,探索相互作用引起的新奇的拓扑泵浦现象日益受到人们的关注,其中包括由相互作用诱导的非线性拓扑泵浦.本文提出可以利用超冷原子动量光晶格系统,有效地模拟一维非线性的非对角Aubry-André-Harper(AAH)模型,研究非线性拓扑泵浦的实验方案.首先,通过数值方法计算了一维非对角AAH模型的非线性能带结构随相互作用强度的变化,得到了非线性系统的孤子态解.然后,分析了不同相互作用强度下孤子态的拓扑输运,发现其质心的移动距离具有量子化的输运特征,由所占据能带的陈数决定,并讨论了非线性拓扑泵浦对相互作用符号的依赖性.同时还计算了在不同相互作用强度下,系统最低能带和最高能带对应陈数的分布.最后,基于^(7)Li原子的动量光晶格实验系统,提出了一个非线性拓扑泵浦方案.本文构造了一种近似于孤子态分布的初始态并演示了其动力学演化过程,并分析了绝热演化条件对泵浦过程的影响.结果表明,在动量晶格系统中演示非线性拓扑泵浦具有可行性.本文的工作为在超冷原子系统中研究非线性拓扑泵浦提供了一个可行的途径,有助于进一步探测非线性引起的拓扑相变和边界效应.

Topological pumping enables the quantized transport of matter waves through an adiabatic evolution of the system,which plays an essential role in the applications of transferring quantum states and exploring the topological properties in higher-dimensional quantum systems.Recently,exploring the interplay between novel topological pumping and interactions has attracted growing attention in topological systems,such as nonlinear topological pumping induced by interactions.So far,the experimental realizations of the nonlinear topological pumps have been realized only in the optical waveguide systems with Kerr nonlinearity.It is still necessary to further explore the phenomenon in different systems.Here,we present an experimental proposal for realizing the nonlinear topological pumping via a one-dimensional(1D)off-diagonal Aubry-André-Harper(AAH)model with mean-field interactions in the momentum space lattice of ultracold atoms.In particular,we develop a numerical method for calculating the energy band of the nonlinear systems.With numerical calculations,we first solve the nonlinear energy band structure and soliton solution of the 1D nonlinear off-diagonal AAH model in the region of weak interaction strengths.The result shows that the lowest or the highest energy band is modulated in the nonlinear system of g>0 or g<0,respectively.The eigenstates of the associated energy bands have the features of the soliton solutions.We then show that the topological pumping of solitons exhibits quantized transport characteristics.Moreover,we numerically calculate the Chern number associated with the lowest and highest energy bands at different interaction strengths.The result shows that the quantized transport of solitons is determined by the Chern number of the associated energy band of the system from which solitons emanate.Finally,we propose a nonlinear topological pumping scheme based on a momentum lattice experimental system with^(7)Li atoms.We can prepare the initial state,which is approximately the distribution of the soliton state of the lowest energy band,and calculate the dynamical evolution of this initial state in the case of U>0.Also,we analyze the influence of adiabatic evolution conditions on the pumping process,demonstrating the feasibility of nonlinear topological pumping in the momentum lattice system.Our study provides a feasible route for investigating nonlinear topological pumping in ultracold atom systems,which is helpful for further exploring the topological transport in nonlinear systems,such as topological phase transitions and edge effects induced by nonlinearity.