  Dynamical quantum phase transitions (DQPTs) extend the concept of phase
transitions and thus universality to the non-equilibrium regime. In this
letter, we investigate DQPTs in a string of ions simulating interacting
transverse-field Ising models. We observe non-equilibrium dynamics induced by a
quantum quench and show for strings of up to 10 ions the direct detection of
DQPTs by measuring a quantity that becomes non-analytic in time in the
thermodynamic limit. Moreover, we provide a link between DQPTs and the dynamics
of other relevant quantities such as the magnetization, and we establish a
connection between DQPTs and entanglement production.
