Fig. 3: Observing the spin subsystem equilibration.

a Measured initial Gaussian distributions (orange bars in the left two panels) \(P(x)\) with corresponding \({\Delta}_x = 0.9\) and \({\Delta}_x = 0.5\) in the lattice space, and the associated distributions (solid orange lines in the right two panels) \({{{\mathcal{P}}}}(k)\) with corresponding \({\Delta}_k = 0.56\) and \({\Delta}_k = 1.0\) in momentum space. The gray bars and solid gray lines represent the theoretical simulations, and the gray regions denote the width (\(2\delta k = 2\sqrt {2\ln 2} {\Delta}_k\)) of the distributions. b Fidelity \({{{\mathcal{F}}}}(\bar \rho _t|\rho _{{{{\mathrm{DE}}}}})\) (yellow and green symbols) between the measured time-averaged coin state and diagonal ensemble prediction at each time step starting from the prepared two-bath states coupling to the coin state \(\left| { \downarrow _y} \right\rangle\). The lines (solid yellow and dashed green) give the theoretical simulations. c Bloch sphere representations of the initial coin states (gray points), ten-step-averaged coin states (black points), and diagonal ensemble predictions (pointed by the orange arrows). All the error bars represent the statistical errors estimated by applying the Monte Carlo simulations