Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics

State-of-the-art quantum simulators permit local temporal control of interactions and midcircuitreadout. These capabilities open the way towards the exploration of intriguing nonequilibriumphenomena. We illustrate this with a kinetically constrained many-body quantum system thathas a natural implementation on Rydberg quantum simulators. The evolution proceeds in discretetime and is generated by repeatedly entangling the system with an auxiliary environment that ismonitored and reset after each time-step. Despite featuring an uncorrelated infinite-temperatureaverage stationary state, the dynamics displays coexistence of fast and slow space-time regionsin stochastic realizations of the system state. The time-record of measurement outcomes on theenvironment serves as natural probe for such dynamical heterogeneity, which we characterize usingtools from large deviation theory. Our work establishes the large deviation framework for discrete time open quantum many-body systems as a means to characterize complex dynamics and collectivephenomena in quantum processors and simulators