Extended Data Fig. 5: Modeled interaction and measured correlations.
From: Continuous symmetry breaking in a trapped-ion spin chain
a, Numerically calculated spin-spin interaction based on Eq. (4) and a simple model of the trapping potential for the three experimental configurations, assuming a harmonic trap for the radial coordinates and a combination of quadratic and quartic potentials for the axial direction. The filled circles indicate the numerically calculated values with no free parameters. The solid lines are fits to the numerical results with a profile of \(J(l)=\bar{J}{e}^{-{\beta }^{{\prime} }(l-1)}{l}^{-{\alpha }^{{\prime} }}\). The fitted parameters are \({\alpha }^{{\prime} }=0.44,\,{\beta }^{{\prime} }=0.19\) for the first configuration (purple), \({\alpha }^{{\prime} }=1,\,{\beta }^{{\prime} }=0.19\) for the second configuration (black), and \({\alpha }^{{\prime} }=3.4,\,{\beta }^{{\prime} }=0\) for the third configuration (blue). Open squares are the experimental data in two out of the three experimental configurations, where the bars represent the spread of measured values of all pairs at a specific spacing l, namely one standard error of the mean. b, Measured spin correlation for the first (left) and the third (right) configuration for the state prepared at the end of the ramp. c, Comparison between the spatially averaged correlations CN(l) for N = 23 as a function of inter-spin distance l for the long-range (purple) and the short-range (blue) configurations.
