Kibble-Zurek dynamics in a trapped ultracold Bose gas

<div>Readme for 10.25405/data.ncl.12604721</div><div> </div><div>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 <u>i-kang.liu1@newcastle.ac.uk</u>.</div><div> </div><div><br></div><div>p.s. The plotting code, “shadedErrorBarG”, is adopted from the code “shadedErrorBar” written by Rob Campbell, <a href="https://www.mathworks.com/matlabcentral/fileexchange/26311-raacampbell-shadederrorbar">https://www.mathworks.com/matlabcentral/fileexchange/26311-raacampbell-shadederrorbar</a>, with some minor modifications for this work and is attached for the uses of the appended plotting scirpts.</div><div><br></div><div>===========================================================================</div><div> </div><div>* File Name: eqbm_data.mat</div><div>This 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.m</div><div>For Fig. 2 (a):</div><div> “TovTc” is T/T_c,0 where T_c,0 is the condensate transition temperature for ideal Bose gas;</div><div> “dTovTc” is the deviation of T/T_c,0 due to the particle number deviation in the c-field simulation and is very small.</div><div> “TovTc_expt” is the T/T_c,0 from experimental measurement;</div><div> “f0” and “f0_expt” are the condensate fractions of simulation and experiment respectively. </div><div> “dfc” is the deviation of condensate fraction from simulation;</div><div> “mu” and “T” are the temperature change from -tau_Q to tau_Q for the background colour.</div><div>For Fig. 9:</div><div> “CbPO” and “Cb” are the Binder cumulants computed according to Eq. (A2) and (A1) respectively;</div><div> “m_order” is the order parameter ;</div><div> “lcoh” and “dlcoh” are the correlation length and it confidential upper/lower bound from the fit;</div><div> “ldB” is the thermal de Broglie wavelength computed by the temperature, “T”.</div><div><br></div><div>===========================================================================</div><div><br></div><div>* File Name: dync_tauQ.mat</div><div> “tauQ” are the quench durations considered in this work.</div><div><br></div><div>* File Name: fig_2_b_and_c.mat</div><div>Contains the information for Fig. 2 (b) and (c). For Fig. 2 (b).</div><div> “time_tc” are the time in t-t_c in ms for tau_Q=150 ms.</div><div> “time_tc_eqbm” is the time axis for equilibrium data in t-t_c. </div><div> “lcoh” and “dlcoh” are the correlation length and its standard deviation for tau_Q=150 ms.</div><div> “lcoh_eqbm” and “dlcoh_eqbm” are the correlation length and its confidential bound for equilibrium data.</div><div> “DeltaLcoh” and “dDeltaLcoh” are value of Eq. (15) and its errorbar.</div><div>For Fig. 2(c):</div><div> “t” is an 1 x 5 array with the time information;</div><div> “x”, “y” and “z” are the spatial axes;</div><div> “uPOt” contains 5 PO mode for the snapshots listed in “t”;</div><div> “aho” is the length unit in meter.</div><div>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.</div><div> % ----- MATLAB PLOTTING SCRIPT ----</div><div> jj = 1, % number of snapshot from Fig. 2 (c) i to v.</div><div> u = reshape(uPOt(jj,:),[length(y) length(x) length(z)]);</div><div> [X,Y,Z] = meshgrid(x,y,z);</div><div> figure,</div><div> [faces,verts] = isosurface(X*aho*1e6,Y*aho*1e6,Z*aho*1e6,abs(u).^2,1000);</div><div> patch('Vertices', verts, 'Faces', faces,'FaceColor','g','edgecolor', 'none','FaceAlpha',0.2);</div><div> [faces,verts] = isosurface(X*aho*1e6,Y*aho*1e6,Z*aho*1e6,abs(u).^2,50);</div><div> patch('Vertices', verts, 'Faces', faces,'FaceColor','y','edgecolor', 'none','FaceAlpha',0.125);</div><div> view(3); axis xy equal;</div><div> camlight head; lighting phong;</div><div> xlim([-1 1] * 125);</div><div> title(['t-t_c=' num2str(t(jj)-tc_factor*150) ' ms'])</div><div> % The values, 1000 and 50, correspond to the green and yellow isosurface in the plots</div><div><br></div><div>===========================================================================</div><div><br></div><div>* File Name: dync_main.mat</div><div>This 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.</div><div>The plots can be reproduced by fig_4_5.m, fig_6.m, fig_8.m and fig_11.m.</div><div> “aho” the length unit</div><div> “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;</div><div> “kxp” the k_x axis for the plot in dimensionless unit (a_ho*k_x) for Fig. 5;</div><div> “nkx” and “dnkx”: Cell arrays for the momentum occupation along k_x axis ”nkx” with its standard deviation “dnkx” for Fig. 5;</div><div> “xp” the x axis for the plot in the unit of “aho”.</div><div> “den_x” and “dden_x”: Cell arrays for the spatial density along x axis with the standard deviations in dimensionless unit for Fig. 6.</div><div> “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.</div><div> “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.</div><div> “kxp”: The momentum axis in dimesionless unit, a_ho * k_x.</div><div> “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”;</div><div> “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”;</div><div> “den_cen” and “dden_cen” are the central densities and their standard deviations for different quench duraitons for Fig. 6 and Fig. 8 (a).</div><div> “i_target” the time snapshot index for Fig. 11 (c) and (d).</div><div> “cmap_nonscale” is the colormap for the left column of Fig. 5;</div><div> “cmap_k” is the colourmap for the right column of Fig. 5;</div><div> “cmap_fig_11_a” is the colormap for Fig. 11 (a);</div><div> “cmap_fig_11_b” is the colormap for Fig. 11 (b).</div><div><br></div><div>===========================================================================</div><div><br></div><div>* File Name: dync_lcoh.mat</div><div>Contains the information for Fig. 7 and Fig. 10 (b) for the use of fig_7_10.m.</div><div> “lcoh” and “dlcoh” for the dynamical correlation lengths with their standard deviations for different quench durations.</div><div> “time_tc” are the time axis in t-t_c in ms.</div><div><br></div><div><br></div><div><br><br></div>