DOI: 10.17863/cam.113114
title: Research data supporting 'Parametric tuning of quantum phase transitions in ultracold reactions'

description: This dataset contains the data obtained from quantum dynamics simulations of the Tavis-Cummings model with an interaction term, which describes the magneto-association of atoms into molecules at ultracold temperatures. We refer the readers to the following publication for more details about the model and simulations: https://arxiv.org/abs/2403.09291 The code for the same was obtained from simulations of the time-dependent Schrodinger equation (TDSE) which was written mainly in Python. This code is also contained in this online repository. The code is organised in 3 parts: 'Engine/Core file' (named integrator_TC.py), 'Simulation file' (named SImfile_TC_*.py) and 'Postprocessing file' (named Postprocessing_file_TC_*.py), and is available under the folder named 'code'. The dataset is organised in terms of the figure number in the associated manuscript. Each folder (except the one named 'code') contains text files with the simulation data stored in .txt format and python files to process the data and create the respective plots. The filenames contain the parameters of the model and the simulation parameters. The model parameters are as follows: N: Total possible molecule number or total number of atom pairs (conserved by the dynamics) Starting state: Initial state of the system (‘atom’ for the case with no molecules at the start and ‘mol’ for the case with no atoms at the start). eps: Sweeping rate (fixed to 1 in all our simulations) g: Atom-molecule coupling constant r: Interaction strength The simulation parameters are as follows: dt: Integration time step (for the TDSE) tin: Starting time of the numerical simulation (in theory, it should t=-infty) tout: Ending time of the numerical simulation (in theory, it should t=+infty) Apart from these parameters, some simulation specific keywords are also included in the filenames. fig1c: Each text file in this folder contains the asymptotic molecule number distribution (ordered row-wise from n=0 to n=N) after the reaction has happened, for different values of r and g. The keyword ‘asymptotics’ specifies the same. The python file ‘Postprocessing_file_2D.py” interpolates this data on a 2D grid and plots and imageplot. fig2: Each text file in this folder again contains the asymptotic molecule number distribution (ordered row-wise from n=0 to n=N) after the reaction has happened, for different values of g at r=-g/2, r=0, r=g/2 and r=g. The python file “Postprocessing_file_IIPT.py” plots the same and compares it with analytical results predicted by Painleve theory. fig3a: Each text file in this folder again contains the asymptotic molecule number distribution (ordered row-wise from n=0 to n=N) after the reaction has happened, for different values of r in the adiabatic limit. The python file “Postprocessing_file_ad_C.py” plots the same along with a numerical fit for a Kibble-Zurek-like scaling law. fig3b: Each text file in this folder again contains the asymptotic molecule number distribution (ordered row-wise from n=0 to n=N) after the reaction has happened, for small deviations from r=0 in the adiabatic limit. The python file “Postprocessing_file_ad_NC.py” plots the same along with a linear fit, as predicted by analytical theory. fig3c: Each text file in this folder again contains the asymptotic molecule number distribution (ordered row-wise from n=0 to n=N) after the reaction has happened, for small deviations from r=0 in the nonadiabatic regime for different values of g. The python file “Postprocessing_file_nad_NC.py” plots the same along with a linear fit, as predicted by analytical theory. fig4abc: This folder contains 3 types of text files: The first type (with the keyword ‘asymptotics’) contains the asymptotic molecule number distribution as before. The second type (with the keyword ‘navg’) contains the average number of molecules (second column) as a function of time (along with first column). The third type (with the keyword ‘timedata’) contains the molecule number distribution as a function of time. All these data are for r=-3g. The python file “Postprocessing_file_TC_movie_r3g_lt.py” plots the average molecule number as a function of time and the Husimi projection at a few instances of time. The python file “Postprocessing_file_TC_Nhist.py” plots the asymptotic molecule number of distribution after the reaction and the instantaneous molecule number distribution at a few instances of time. The FORTRAN binding for obtaining the Husimi projections can be obtained by the following command: f2py3 -c --f90flags="-fopenmp" -m coh_proj husimi_projection.f90 -lgomp fig4def: Exactly the same as the folder fig4abc except that r=0. fig4g: Each text file contains the average number of molecules as a function of time. The python file “Postprocessing_file_TC_navg.py” plots the number of revivals as a function of interaction strength. fig4h: Each text file contains the average number of molecules as a function of time. The python file “Postprocessing_file_TC_Trev.py” plots the time period of revivals as a function of interaction strength.