Kibble-Zurek dynamics in a trapped ultracold Bose gas

Readme for 10.25405/data.ncl.12604721 The files are in MATLAB format, and the corresponding MATLAB scripts for Fig. 2, 4 to 11 are included (named by the *.m files). If there is any question/problem, please contact [e-mail]. p.s. The plotting code, “shadedErrorBarG”, is adopted from the code “shadedErrorBar” written by Rob Campbell, https://www.mathworks.com/matlabcentral/fileexchange/26311-raacampbell-shadederrorbar, with some minor modifications for this work and is attached for the uses of the appended plotting scirpts.=========================================================================== * File Name: eqbm_data.matThis file contains the information for Fig. 2 (a) and Fig. 9. The variables are listed below. Can be easily plotted by using fig_2_a_b.m and fig_9.mFor Fig. 2 (a): “TovTc” is T/T_c,0 where T_c,0 is the condensate transition temperature for ideal Bose gas; “dTovTc” is the deviation of T/T_c,0 due to the particle number deviation in the c-field simulation and is very small. “TovTc_expt” is the T/T_c,0 from experimental measurement; “f0” and “f0_expt” are the condensate fractions of simulation and experiment respectively. “dfc” is the deviation of condensate fraction from simulation; “mu” and “T” are the temperature change from -tau_Q to tau_Q for the background colour.For Fig. 9: “CbPO” and “Cb” are the Binder cumulants computed according to Eq. (A2) and (A1) respectively; “m_order” is the order parameter ; “lcoh” and “dlcoh” are the correlation length and it confidential upper/lower bound from the fit; “ldB” is the thermal de Broglie wavelength computed by the temperature, “T”.===========================================================================* File Name: dync_tauQ.mat “tauQ” are the quench durations considered in this work.* File Name: fig_2_b_and_c.matContains the information for Fig. 2 (b) and (c). For Fig. 2 (b). “time_tc” are the time in t-t_c in ms for tau_Q=150 ms. “time_tc_eqbm” is the time axis for equilibrium data in t-t_c. “lcoh” and “dlcoh” are the correlation length and its standard deviation for tau_Q=150 ms. “lcoh_eqbm” and “dlcoh_eqbm” are the correlation length and its confidential bound for equilibrium data. “DeltaLcoh” and “dDeltaLcoh” are value of Eq. (15) and its errorbar.For Fig. 2(c): “t” is an 1 x 5 array with the time information; “x”, “y” and “z” are the spatial axes; “uPOt” contains 5 PO mode for the snapshots listed in “t”; “aho” is the length unit in meter.It can be easily plotted by the below matlab script for the isosurface plot. The purple line is the high velocity field region, please refer to Ref. [19] for detail. % ----- MATLAB PLOTTING SCRIPT ---- jj = 1, % number of snapshot from Fig. 2 (c) i to v. u = reshape(uPOt(jj,:),[length(y) length(x) length(z)]); [X,Y,Z] = meshgrid(x,y,z); figure, [faces,verts] = isosurface(X*aho*1e6,Y*aho*1e6,Z*aho*1e6,abs(u).^2,1000); patch('Vertices', verts, 'Faces', faces,'FaceColor','g','edgecolor', 'none','FaceAlpha',0.2); [faces,verts] = isosurface(X*aho*1e6,Y*aho*1e6,Z*aho*1e6,abs(u).^2,50); patch('Vertices', verts, 'Faces', faces,'FaceColor','y','edgecolor', 'none','FaceAlpha',0.125); view(3); axis xy equal; camlight head; lighting phong; xlim([-1 1] * 125); title(['t-t_c=' num2str(t(jj)-tc_factor*150) ' ms']) % The values, 1000 and 50, correspond to the green and yellow isosurface in the plots===========================================================================* File Name: dync_main.matThis file contains the most infomraiton of this work for Fig. 4, 5, 6, 8 and 11, including the momentum occupations, spatial densities and density wavefronts for 6 dynamical data. Information is saved in CELL array format, and the j-th cell correspond to the information of j-th tauQ in “dync_tauQ.mat”. The wavefronts are smoothed data after tracing the density.The plots can be reproduced by fig_4_5.m, fig_6.m, fig_8.m and fig_11.m. “aho” the length unit “nk0”, “dnk0” and “dnkl”: Cell arrays for the momentum occupation for k=0 mode “nk0” with its standard deviation, “dnk0” and the lower bound error “dnk0l” for plotting things in log scale, for Fig. 4; “kxp” the k_x axis for the plot in dimensionless unit (a_ho*k_x) for Fig. 5; “nkx” and “dnkx”: Cell arrays for the momentum occupation along k_x axis ”nkx” with its standard deviation “dnkx” for Fig. 5; “xp” the x axis for the plot in the unit of “aho”. “den_x” and “dden_x”: Cell arrays for the spatial density along x axis with the standard deviations in dimensionless unit for Fig. 6. “time_tc”: Cell arrasy for the time axis in t-t_c in ms for the momentum data. For the scale axis in the figures, please read the \hat{t} from “dync_tauQ” by evaluating \hat{t}=\sqrt{t0*tauQ} with t0 =hbar/(gamma*muf) * 1e3 with gamma=5e-4 and muf=22*hbar*w_perp=22*hbar*131.4 Hz and plot above quantities in (time_tc-1.3*that)/tauQ axis. “time_tc_den”: Cell arrasy for the time axis in t-t_c in ms for density data. For the scale axis in the figures, please read the \hat{t} from “dync_tauQ” by evaluating \hat{t}=\sqrt{t0*tauQ} with t0 =hbar/(gamma*muf) * 1e3 with gamma=5e-4 and muf=22*hbar*w_perp=22*hbar*131.4 Hz and plot above quantities in (time_tc-1.3*that)/tauQ axis. “kxp”: The momentum axis in dimesionless unit, a_ho * k_x. “den_x_front” and “t_den_x_front” are the density front and the corresponding time axis respectivley for the x direction in the unit of “aho”; “den_rho_front” and “t_den_rho_front” are the density front and the corresponding time axis respectively for the transverse direction in the unit of “aho”; “den_cen” and “dden_cen” are the central densities and their standard deviations for different quench duraitons for Fig. 6 and Fig. 8 (a). “i_target” the time snapshot index for Fig. 11 (c) and (d). “cmap_nonscale” is the colormap for the left column of Fig. 5; “cmap_k” is the colourmap for the right column of Fig. 5; “cmap_fig_11_a” is the colormap for Fig. 11 (a); “cmap_fig_11_b” is the colormap for Fig. 11 (b).===========================================================================* File Name: dync_lcoh.matContains the information for Fig. 7 and Fig. 10 (b) for the use of fig_7_10.m. “lcoh” and “dlcoh” for the dynamical correlation lengths with their standard deviations for different quench durations. “time_tc” are the time axis in t-t_c in ms.

本数据集的说明文档对应于10.25405/data.ncl.12604721。数据文件采用MATLAB格式，并包含图2、4至11相应的MATLAB脚本（以*.m文件命名）。如遇任何疑问或问题，请通过[e-mail]与我联系。附言：绘图代码“shadedErrorBarG”源自Rob Campbell编写的“shadedErrorBar”代码（https://www.mathworks.com/matlabcentral/fileexchange/26311-raacampbell-shadederrorbar），针对本研究进行了一些细微的修改，并随附用于附加绘图脚本的代码。=========================================================================== * 文件名称：eqbm_data.mat 本文件包含图2（a）和图9的信息。以下列出了变量，可通过fig_2_a_b.m和fig_9.m轻松绘制。对于图2（a）：“TovTc”代表T/Tc,0，其中Tc,0是理想玻色气体的凝聚相转变温度；“dTovTc”是由于c场模拟中粒子数偏差引起的T/Tc,0的偏差，非常小；“TovTc_expt”为实验测量的T/Tc,0；“f0”和“f0_expt”分别为模拟和实验的凝聚相分数；“dfc”为凝聚相分数的偏差；“mu”和“T”分别为从-τQ到τQ的背景颜色温度变化。对于图9：“CbPO”和“Cb”分别根据公式（A2）和（A1）计算得到的Binder累积量；“m_order”为序参量；“lcoh”和“dlcoh”为拟合得到的关联长度及其置信上限/下限；“ldB”为通过温度“T”计算得到的热德布罗意波长。=========================================================================== * 文件名称：dync_tauQ.mat “tauQ”为本研究中考虑的淬火持续时间。* 文件名称：fig_2_b_and_c.mat 包含图2（b）和（c）的信息。对于图2（b）：“time_tc”为在τQ=150 ms时t-tc的时间（以毫秒为单位）；“time_tc_eqbm”为平衡数据的t-tc时间轴；“lcoh”和“dlcoh”为τQ=150 ms时的关联长度及其标准偏差；“lcoh_eqbm”和“dlcoh_eqbm”为平衡数据的关联长度及其置信上限/下限；“DeltaLcoh”和“dDeltaLcoh”分别为公式（15）的值及其误差条。对于图2（c）：“t”是一个1x5的数组，包含时间信息；“x”、“y”和“z”分别为空间坐标轴；“uPOt”包含“t”中列出的快照的5个PO模式；“aho”为长度单位，单位为米。可以通过以下MATLAB脚本进行等值面绘图。紫色线表示高速场区域，请参阅参考文献[19]以获取详细信息。% ----- MATLAB 绘图脚本 ---- jj = 1, % 图2（c）中的快照编号i至v。u = reshape(uPOt(jj,:),[length(y) length(x) length(z)]);[X,Y,Z] = meshgrid(x,y,z);figure,[faces,verts] = isosurface(X*aho*1e6,Y*aho*1e6,Z*aho*1e6,abs(u).^2,1000);patch('Vertices', verts, 'Faces', faces,'FaceColor','g','edgecolor', 'none','FaceAlpha',0.2);[faces,verts] = isosurface(X*aho*1e6,Y*aho*1e6,Z*aho*1e6,abs(u).^2,50);patch('Vertices', verts, 'Faces', faces,'FaceColor','y','edgecolor', 'none','FaceAlpha',0.125);view(3);axis xy equal;camlight head;lighting phong;xlim([-1 1] * 125);title(['t-tc=' num2str(t(jj)-tc_factor*150) ' ms'])% 1000和50的值对应于图中绿色和黄色的等值面。* 文件名称：dync_main.mat 本文件包含本研究关于图4、5、6、8和11的大部分信息，包括6个动力学数据的动量占据、空间密度和密度波前沿。信息以单元格数组格式保存，第j个单元格对应于“dync_tauQ.mat”中第j个τQ的信息。波前沿是追踪密度后的平滑数据。可以通过fig_4_5.m、fig_6.m、fig_8.m和fig_11.m重现绘图。aho为长度单位；“nk0”、“dnk0”和“dnkl”为k=0模式的动量占据单元格数组“nk0”，及其标准偏差“dnk0”和下限误差“dnk0l”，用于图4的对数尺度绘图；“kxp”为图5中无量纲单位（a_ho*k_x）的k_x轴；“nkx”和“dnkx”为沿k_x轴的动量占据单元格数组“nkx”，及其标准偏差“dnkx”；xp为绘图的无量纲单位x轴；“den_x”和“dden_x”为沿x轴的空间密度单元格数组，其标准偏差以无量纲单位表示，用于图6。time_tc为动量数据的时间轴，在t-tc中以毫秒为单位。对于图中刻度轴的读取，请从“dync_tauQ”中评估hat{t}=sqrt{t0*tauQ}，其中t0 =hbar/(gamma*muf) * 1e3，gamma=5e-4，muf=22*hbar*w_perp=22*hbar*131.4 Hz，并在(time_tc-1.3*that)/tauQ轴上绘制上述量。time_tc_den为密度数据的时间轴，在t-tc中以毫秒为单位。对于图中刻度轴的读取，请从“dync_tauQ”中评估hat{t}=sqrt{t0*tauQ}，其中t0 =hbar/(gamma*muf) * 1e3，gamma=5e-4，muf=22*hbar*w_perp=22*hbar*131.4 Hz，并在(time_tc-1.3*that)/tauQ轴上绘制上述量。kxp为动量轴的无量纲单位，a_ho * k_x；“den_x_front”和“t_den_x_front”分别为x方向上的密度前沿及其对应的时间轴，单位为“aho”；“den_rho_front”和“t_den_rho_front”分别为横向方向上的密度前沿及其对应的时间轴，单位为“aho”；“den_cen”和“dden_cen”为不同淬火时间的中心密度及其标准偏差，用于图6和图8（a）；i_target为图11（c）和（d）的时间快照索引；“cmap_nonscale”为图5左侧列的颜色映射；“cmap_k”为图5右侧列的颜色映射；“cmap_fig_11_a”为图11（a）的颜色映射；“cmap_fig_11_b”为图11（b）的颜色映射。* 文件名称：dync_lcoh.mat 包含用于fig_7_10.m的图7和图10（b）的信息。“lcoh”和“dlcoh”为不同淬火时间的动力学关联长度及其标准偏差。“time_tc”为t-tc的时间轴，以毫秒为单位。