This dataset is associated with the paper: Generation of high-winding-number superfluid circulation in Bose-Einstein condensates Kali E. Wilson, E. Carlo Samson, Zachary L. Newman, and Brian P. Anderson.  Accepted for publication in Physical Review A 2022.  https://doi.org/10.48550/arXiv.2109.12945
Figures 2,3,6 show optical depth profiles from experimental images (.tiff files). Optical depth profiles are calculated from the respective raw images (FigX.tiff).  Note each image file contains the following:
(1) image: the absorption image of the BEC.
(2) background: the background image (probe only, no BEC).
(3) dark: the dark image (probe off, no BEC) to account for any stray light or camera noise.  

The image data is processed as follows:

A = image Ð dark.
B = background Ð dark.
An optimized version of B is then obtained using the method of C. F. Ockeloen, A. F. Tauschinsky, R. J. C. Spreeuw, and S. Whitlock, ÔDetection of small atom numbers through image processingÕ. Phys. Rev. AÊ82, 061606(R) (2010). Their method creates an optimal background image based on a set of experimental background images. This accounts for small shifts in the spatial structure of the probe beam between the image and the background frames, generally due to mechanical vibration.
The transmission and optical depth associated with each pixel are then calculated by:

Transmission T = (A)/(optimized B)
Optical depth OD = -ln(T)

For residuals: Optical depth profiles are fit to a Thomas-Fermi profile (integrated over the z axis): 
F = C + A*{max[(1-(x-x0).^2/Rx^2 -(y-y0).^2/Ry^2), 1]}.^(1.5)
Here C is the offset, A the amplitude, x0 and y0 are the location of the center of the BEC in the horizontal plane, and Rx and Ry are the corresponding Thomas-Fermi radii in the x and y directions.


Figures 4,5 8-10 show BEC density and phase profiles from simulations. To reproduce these figures run the corresponding ProduceFigureX.m MATLAB file, which will load the relevant simulation (FigureX.mat) file.  ProduceFigureX.m will pull out just the time points needed for the corresponding figure, however the FigureX.mat file contains the atomic wave function sampled at regular time intervals throughout the whole spiral sequence.  

For the full simulation: each .mat file contains a vector t, which contains the timepoints in seconds from the full simulation, and a matrix mov2D_psi which is a set of 2D wavefunctions, sampled at regular intervals over the full simulation. The time between sampled wave functions is [max value of t]/[size of third dimension of mov2D_psi - 1].

Figure 7: Vortex number vs. Spiral Trajectory duration. 

The csv file Figure7_Simulation.csv contains the data for figure 7 obtained from numerical simulation of the spiral trajectory for varying trajectory duration. Trajectory durations are given in units of seconds. Column 1: trajectory duration for a spiraling potential U = u0. Column 2: number of pinned cores for a spiraling potential U = u0. Column 3: trajectory duration for a spiraling potential U = 0.75 u0. Column 4: number of pinned cores for a spiraling potential U = 0.75 u0.  

The csv file Figure7_Experiment.csv contains the data for figure 7 obtained from experiment. Column 1: trajectory duration (s). Column 2: mean number of vortex cores in the central cluster. Column 3. Standard deviation of the number of vortex cores in the central cluster. Column 4: mean total number of vortex cores. Column 5. Standard deviation of the total number of vortex cores.