# 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

__i-kang.liu1@newcastle.ac.uk__.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.

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* File Name: eqbm_data.mat

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

For 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”.

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* File Name: dync_tauQ.mat

“tauQ” are the quench durations considered in this work.

* File Name: fig_2_b_and_c.mat

Contains 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

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* File Name: dync_main.mat

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.

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).

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* File Name: dync_lcoh.mat

Contains 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.

## Funding

#### NAQUAS: Non-equilibrium dynamics in Atomic systems for QUAntum Simulation

Engineering and Physical Sciences Research Council

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