光场中超冷原子气体的局域化特性研究
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摘要
超冷原子气体及其玻色-爱因斯坦凝聚(BEC)是当前物理学领域热点问题之一,尤其是利用光场驱动的Feshbach共振技术对凝聚体进行操控,为研究非线性系统的局域化特性提供了一个理想的媒质。超冷原子气体的局域态包括物质波孤子、安德森定域化等。本论文从描述孤子动力学特征的非线性薛定谔方程(NLSE)出发,运用拉格朗日变分法和数值方法对光场中超冷原子气体的物质波孤子、安德森定域化等局域态及凝聚体系统的耦合特性、相互作用和操纵控制等方面进行了研究。主要研究内容和取得的成果如下：
1、研究了双势阱中耦合BEC物质波亮孤子的演化规律和特性。研究结果表明,系统参数对囚禁在双势阱中的物质波孤子的演化、交换特性和自陷行为产生重要影响。原子之间的相互作用在物质波孤子的演化过程中扮演了非常重要的作用,线性耦合度的增加导致孤子的形状发生变化。随着耦合程度的变化,孤子之间的相互作随之改变,物质波孤子先后呈现出自陷、约瑟夫森振荡现象。
2、研究了在非线性空间调制下呈线性耦合的两组分BEC物质波亮孤子演化特性和相互作用。结果表明,s-波散射长度的空间变化改变了孤子的密度包络；在合适的初始条件下,可以存在稳定的孤子；孤子的演化规律取决于非线性空间调制系数的符号和数值大小,可以对凝聚体实现非线性空间管理。
3、研究了谐振势阱中同时呈线性和非线性耦合的BEC物质波亮孤子的演化特性和动力学行为。变分和数值结果一致表明,在一定条件下,耦合凝聚体存在稳定的孤子和自发振荡行为,并与外加囚禁势、非线性空间调制系数、原子的数目以及藕合系数相关。非线性空间调制对耦合凝聚体孤子和自发振荡产生重要影响,耦合物质波亮孤子的演化规律依赖于非线性空间调制系数的符号和大小。
4、在准一维设置和弱无序的情况下,从NLSE出发,研究了囚禁在随机光斑电势中的BEC的安德森定域化及其膨胀特性和稳定性,并结合无序光场来研究物质波的非线性空间调制对安德森定域化的能量、形状和局域化长度的影响。结果发现,在无序存在和绝热条件下,BEC呈现出安德森定域化现象；局域态的中间区域宽度和尾部形状均受非线性空间调制影响。
The ultracold atom gas and Bose-Einstein condensation (BEC) is one of the hot issues in physics. More and more people focus on the manipulation of BEC by using Feshbach resonances driven by light field, which has provided an ideal medium for the localized characteristic of nonlinear systems. In this paper, by using Lagrange variational approach and numerical methods, we start from the nonlinear Schrodinger equation (NLSE) and study matter-wave soliton and Anderson localization in ultracold atomic gases, and do some work in coupling characteristics, the interaction and manipulation of BEC system. These works are summarized as follows:
1. The evolution characteristics of coupled BEC matter-wave bright soliton tapped the double-well potentials are investigated. The results show that the system parameters influence on the evolution, switching characteristics and self-trapping behavior of matter-wave solitons. Interactions between the atoms play an important role in the evolution of matter-wave soliton. The soliton's shape changes with the increasing of the linear coupling. Moreover, the interaction between solitons changes with the variety in the degree of coupling, and the self-trapping and Josephson oscillations appear in BEC.
2. The evolution and interactions of the linear coupling two-component BEC matter-wave bright soliton are studied in the presence of spatially modulated nonlinearity. The results show that the envelope of the soliton density changes with the spatial variation of the s-wave scattering length. The stable soliton can exist in appropriate initial conditions. The evolution of the solitons depends on the sign and value of the coefficient of the spatially modulated nonlinearity. The nonlinear space management to the condensate can be achieved.
3. The dynamic characteristics of the linear and nonlinear coupling BEC matter wave bright solitons trapped an harmonic trap are investigated. The results show that there exist stable solitons and spontaneous oscillation in the condensates under the variant conditions. The stability of the two stationary states is relative to the external trapping potential, the spatially modulated nonlineanty, the number of atoms and the coupled terms. Moreover, we also find that the spatially modulated nonlinearity influences on both the solitons and spontaneous oscillation of atoms in two linearly coupling condensates. The validity of the theoretical predictions is confirmed by the numerical simulation of the coupled equations.
4. Starting from the quasi-one-dimensional NLSE, we studied the localization of a weakly interacting BEC in a random speckle. The stability and dilatation of localized states are investigated. Meanwhile, we also studied the effects of the spatially modulated nonlinearity on the shape, energy and localization length of the density envelope. The results show that there exists Anderson localization in the presence of disorder and adiabatic condition, It was found that the nonlinear spatial modulation has influence on the central region and the tail of the localized state.
1、研究了双势阱中耦合BEC物质波亮孤子的演化规律和特性。研究结果表明,系统参数对囚禁在双势阱中的物质波孤子的演化、交换特性和自陷行为产生重要影响。原子之间的相互作用在物质波孤子的演化过程中扮演了非常重要的作用,线性耦合度的增加导致孤子的形状发生变化。随着耦合程度的变化,孤子之间的相互作随之改变,物质波孤子先后呈现出自陷、约瑟夫森振荡现象。
2、研究了在非线性空间调制下呈线性耦合的两组分BEC物质波亮孤子演化特性和相互作用。结果表明,s-波散射长度的空间变化改变了孤子的密度包络；在合适的初始条件下,可以存在稳定的孤子；孤子的演化规律取决于非线性空间调制系数的符号和数值大小,可以对凝聚体实现非线性空间管理。
3、研究了谐振势阱中同时呈线性和非线性耦合的BEC物质波亮孤子的演化特性和动力学行为。变分和数值结果一致表明,在一定条件下,耦合凝聚体存在稳定的孤子和自发振荡行为,并与外加囚禁势、非线性空间调制系数、原子的数目以及藕合系数相关。非线性空间调制对耦合凝聚体孤子和自发振荡产生重要影响,耦合物质波亮孤子的演化规律依赖于非线性空间调制系数的符号和大小。
4、在准一维设置和弱无序的情况下,从NLSE出发,研究了囚禁在随机光斑电势中的BEC的安德森定域化及其膨胀特性和稳定性,并结合无序光场来研究物质波的非线性空间调制对安德森定域化的能量、形状和局域化长度的影响。结果发现,在无序存在和绝热条件下,BEC呈现出安德森定域化现象；局域态的中间区域宽度和尾部形状均受非线性空间调制影响。
The ultracold atom gas and Bose-Einstein condensation (BEC) is one of the hot issues in physics. More and more people focus on the manipulation of BEC by using Feshbach resonances driven by light field, which has provided an ideal medium for the localized characteristic of nonlinear systems. In this paper, by using Lagrange variational approach and numerical methods, we start from the nonlinear Schrodinger equation (NLSE) and study matter-wave soliton and Anderson localization in ultracold atomic gases, and do some work in coupling characteristics, the interaction and manipulation of BEC system. These works are summarized as follows:
1. The evolution characteristics of coupled BEC matter-wave bright soliton tapped the double-well potentials are investigated. The results show that the system parameters influence on the evolution, switching characteristics and self-trapping behavior of matter-wave solitons. Interactions between the atoms play an important role in the evolution of matter-wave soliton. The soliton's shape changes with the increasing of the linear coupling. Moreover, the interaction between solitons changes with the variety in the degree of coupling, and the self-trapping and Josephson oscillations appear in BEC.
2. The evolution and interactions of the linear coupling two-component BEC matter-wave bright soliton are studied in the presence of spatially modulated nonlinearity. The results show that the envelope of the soliton density changes with the spatial variation of the s-wave scattering length. The stable soliton can exist in appropriate initial conditions. The evolution of the solitons depends on the sign and value of the coefficient of the spatially modulated nonlinearity. The nonlinear space management to the condensate can be achieved.
3. The dynamic characteristics of the linear and nonlinear coupling BEC matter wave bright solitons trapped an harmonic trap are investigated. The results show that there exist stable solitons and spontaneous oscillation in the condensates under the variant conditions. The stability of the two stationary states is relative to the external trapping potential, the spatially modulated nonlineanty, the number of atoms and the coupled terms. Moreover, we also find that the spatially modulated nonlinearity influences on both the solitons and spontaneous oscillation of atoms in two linearly coupling condensates. The validity of the theoretical predictions is confirmed by the numerical simulation of the coupled equations.
4. Starting from the quasi-one-dimensional NLSE, we studied the localization of a weakly interacting BEC in a random speckle. The stability and dilatation of localized states are investigated. Meanwhile, we also studied the effects of the spatially modulated nonlinearity on the shape, energy and localization length of the density envelope. The results show that there exists Anderson localization in the presence of disorder and adiabatic condition, It was found that the nonlinear spatial modulation has influence on the central region and the tail of the localized state.
引文
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