# Dynamical phase diagram of ultracold Josephson junctions

dataset

posted on 14.01.2021, 15:05 by Klejdja Xhani, Luca Galantucci, Carlo Barenghi, Giacomo Roati, Andrea Trombettoni, Nikolaos ProukakisThe first column of the files 'imbalance_z0_....dat' gives the time which could be converted in seconds by dividing the first column by 2*pi*15Hz. The third column gives the number of particle on the left well N_L and thus the population imbalance could be found by z(t)=1-2*N_L/N where N is the total number of particles and it is equal to 6x10^4. The data from such files are used to construct Fig1(i)-(iv) and Fig2 upper subplots.

The first column of the files 'mean_imbalance_vs_v0_mu_w_4xi.dat' or 'mean_imbalance_vs_w_fixed_v0_1p17mu.dat' is the value of the barrier height V_0 scaled to the chemical potential mu or the value of the barrier width w scaled to the mean condensate coherence length xi respectively; the second column is the value of the initial imbalance z_0 and the third column is the temporal mean value of z(t) in the time interval [0, 0.4]s. These files are used to construct Fig1 main panel and Fig3.

The first column of the files 'zc_vs_v0_mu_w_4xi.dat' or 'zc_vs_w_v0_1p17mu.dat' is the value of V_0/mu for fixed w/xi=4 or the value of w/xi for fixed V0/mu=1.17, the second column is the value of the critical imbalance z_cr while the third column is the value of the initial imbalance defining the beginning of the grey area. These files are used to construct Fig1 main panel and Fig3.

The first column in the files 'relative_phase_z0_0p..dat' is the time in second while the relative phase between the left and right well is extracted by the difference between the third and the second column. In all such files except for 'relative_phase_z0_0p17_v0_0p8mu_y_0p44lx.dat' the relative phase is calculated along the x-axes for y=z=0. These files are used to construct Fig2 lower subplots.

The file 'zc_vs_v0_mu_vs_w_xi.dat' has three columns: the first one is the barrier width w/xi, the second one is V0/mu and the third column is the critical imbalance z_cr. This file is used to construct Fig4(a). The file 'v0_diss_vs_w_xi.dat' and 'V0_ST_vs_w_xi.dat' has the data for the orange and blue line in Fig4.

The file 'den_center_vs_v0_mu_vs_w_xi.dat' has the values of the density at the trap center in units of lx^(-3), where lx=7.5x10^(-6)m, with and without the barrier which is the third column while the first column is w/xi and the second one is V0/mu. This file contains the data of Fig4(b) where is shown the density at the trap center scaled to the corresponding value in the absence of the barrier. From such values of the density the coherence length is found and it is scaled to its corresponding mean value; such scaled quantity is shown in Fig4(c).

The first column of the files 'semiaxes_position_z0_0p19_v0...dat' and 'semiaxes_position_z0_zc_v0...dat' is the time in ms, the second column is the semiaxes along the z-direction of the elliptic vortex ring, the third column is the semiaxes along the y-direction while the fourth column is the position of the vortex ring along the x-axes. These files are used for building figure 5.

The files 'compressible_incompressible_kinetic_energy_z0_zc_v0_...dat' has as first column the time in arbitrary units which is converted in ms by multiplying the first column with 0.1/(30*pi); the second column is the value of the incompressible kinetic energy while the third column is the value of the compressible kinetic energy in units of hnu_x/N.

Such data are used for building fig 6(a) for z0=z_cr.

The files 'max_incompressible_kinetic_energy_vs_v0_..dat'

contains the data for fig.6(b) where the first column is the value of V0/mu and the second column is the maximum value of the incompressible kinetic energy in units of hnu_x/N for z0=zcr (the file 'max_incompressible_kinetic_energy_vs_v0_z0_zc.dat') and for z0=0.19 (the file 'max_incompressible_kinetic_energy_vs_v0_z0_0p19.dat').

The files 'DEkc_at_zc.dat' and 'DEkc_at_z0_19.dat' contains the data for the compressible energy dissipation (called in the paper epsilon_c) as a function of v0/mu for the two cases considered of z0=z_cr and z0=0.19. The first column shows the value of v0/mu while the second column shows the value of epsilon_c. The files 'epsilon_i_vs_v0_mu_at_z0_zc.dat' and 'epsilon_i_vs_v0_mu_at_z0_0p19.dat' contains the value of the incompressible kinetic energy of the first vortex ring at the position x_VR around -1lx (second column) as a function of v0/mu (first column). These data are used for building fig7.

The first column of the files 'denx_15ms_43ms_..dat' is the time in ms, the second column is the x-axes value and the third column is the value of the density along the x-axes minus the equilibrium density. Such files are used for constructing the carpet plots in fig 8.

The files 'den_3d_v0_0p6mu_...vtk.gz' and 'den_3d_v0_0p8mu_...vtk.gz' contain the .vtk files where it is saved the x, y an z-axes and the corresponding value of the condensate density at certain time. These files are used for building the 3D density plots of fig9(a) by using ParaView application.

The first column of the files 'mean_imbalance_vs_v0_mu_w_4xi_spherical_trap.dat' is the value of the barrier height V_0/mu; the second column is the value of the initial imbalance z_0 and the third column is the temporal mean value of z(t) in the time interval [0, 0.4]s. These files together with the file 'zc_vs_v0_mu_w_4xi_spherical_trap.dat' are used to construct Fig10 of the main text for the spherical trap. The first column of the file 'zc_vs_v0_mu_w_4xi_spherical_trap.dat' is v0/mu; the second column is the value of the initial imbalance defining the beginning of the grey area while the third column is the value of the critical imbalance z_cr.