Fig. 1. Diagram of cold atoms with two KD pulses in harmonic oscillator potential. At the measurement time , the coherent superposition of different modes occurs. is the external field. 简谐势阱中冷原子受到两次KD脉冲的示意图　在测量时刻 , 不同模式相干叠加, 为外场

Fig. 2. In the absence of an external field ( ), the density distribution function of system varies with time. The dimensionless parameter are . The measurement time is at . Both KD pulses are represented by red arrows. The color bar on the right side of the density of states evolution diagram indicates that the value of the density distribution function changes from low (blue) to high (red). 没有外场的情况下( ), 系统态密度分布函数的演化规律　无量纲参数为 , 测量时刻在 , 两次KD脉冲都用红色箭头表示, 态密度演化图右边的彩色条表示态密度分布函数值由低(蓝色)变到高(红色)

Fig. 3. In the case of external field , the evolution of density distribution function of the system is obtained. The dimensionless parameters in this figure are the same as those in Figure 2. The red arrow are KD pulses. The measurement time is at . 在外场 的情况下, 系统态密度分布函数的演化规律　图中除 之外的其他无量纲参数与图2相同, 红色箭头为KD脉冲, 测量时刻在

Fig. 4. In the case of external field , the evolution of density distribution function of the system is obtained. The dimensionless parameters in this figure are the same as those in Figure 2. The red arrow are KD pulses. The measurement time is at . 在外场 的情况下, 系统态密度分布函数的演化规律　图中除 之外的其他无量纲参数与图2相同, 红色的箭头为KD脉冲, 测量时刻在

Fig. 5. The density distribution functions at measuring time for figure 2, 3, and 4. 图2、图3、图4中测量时刻 态密度的分布规律

Fig. 6. In the case of external field , the density distribution function of the ground state of the system. Different colors correspond to the density distribution function under different non-linear interactions. 外场 的情况下系统基态的态密度分布函数, 不同的颜色对应不同非线性相互作用下的态密度分布函数

Fig. 7. In the case of external field , the density distribution function of the ground state of the system. Different colors correspond to the density distribution function under different non-linear interactions. 在外场 的情况下系统基态的态密度分布函数, 不同的颜色对应不同非线性相互作用下的态密度分布函数

Fig. 8. In the case of , the density distribution functions at measuring time. Different colors correspond to the density distribution function under different non-linear interactions. 在 的情况下测量时刻的态密度分布函数, 不同的颜色对应不同非线性相互作用下的态密度分布函数

Fig. 9. Detailed diagram of 0 mode in Fig. 8. 图8中0模式的放大图

Fig. 10. The density distribution functions at measuring time, dimensionless parameters other than non-linear parameters are the same as those in Fig. 8. 测量时刻系统态密度的分布函数, 除了非线性参数以外的其他无量纲参数和图8相同

Fig. 11. Detailed diagram of 0 mode in Fig. 10. 图10中0模式的放大图

Fig. 12. The variation of measuring accuracy of the system with nonlinear parameters, dimensionless parameters other than non-linear parameters are the same as those in Fig. 8. 系统的测量精度随非线性参数的变化规律, 除了非线性参数以外的其他无量纲参数和图8相同