Applying a periodic Hamiltonian to a system of particles allows us to study out-of-equilibrium matter, like the prethermal discrete time crystal (PDTC). One can define a time-independent Hamiltonian that describes the dynamics of the driven system not continuously, but in a stroboscopic manner. This implies energy conservation during the validity window of this approximation. In this work, we realized a PDTC by applying such a periodic drive to a collection of 25 trapped ions, and characterized the prethermal time window where faster driving slows down the thermalization process towards higher entropy. The effective prethermal Hamiltonian description during that time is a long-range Ising model of spin-spin interactions, featuring a temperature-induced phase transition. Taking advantage of the ion trap system’s tunability, we were able to prepare both regimes above and below the critical temperature.
