Fig. 1: Critical quench dynamics.

a Disorder-to-order phase transitions emerge even in the non-equilibrium setting of quench dynamics, and exhibit critical behavior at the transition. The ordered and disordered phases are shown in thick and thin lines, respectively, and the arrows indicate a quench to the critical point. While a quench from a gapped initial state (top panel) to the critical point (red circles) generically leads to effective thermal behavior, a quench from a gapless state (bottom panel), corresponding to a distinct critical point, gives rise to non-equilibrium criticality. b Ground-state phase diagram with Ising interaction along x or y direction. \({{{\mathcal{J}}}}{\gamma }^{x,y}/{B}^{z}\) is the ratio of the Kac-normalized effective interaction strength \({{{\mathcal{J}}}}{\gamma }^{x,y}\) to the transverse field strength B^z (see text). The phase boundary is shown in gray dashed lines, with red and green circles indicating the critical points where the quenches are performed. c The experimental sequence starting with all spins initialized along \({\left\vert \downarrow \right\rangle }_{z}\). The first quench is applied with interactions along the x direction, and the evolution is measured by projecting the spins along x. For the second quench, both the interaction and measurement bases are switched from x to y direction. In the double-quench experiment, the second quench is applied after evolving under the first quench, but no measurement is performed before the second quench. The curved lines illustrate the long-range interaction among all the spins where the opacity reflects interaction strengths that weaken with distance.