Temporal Order in Periodically Driven Spins in Star-Shaped Clusters

We experimentally study the response of star-shaped clusters of initially unentangled N = 4, 10, and 37 nuclear spin-1/2 moments to an inexact pi-pulse sequence and show that an king coupling between the center and the satellite spins results in robust period-2 magnetization oscillations. The period is stable against bath effects, but the amplitude decays with a timescale that depends on the inexactness of the pulse. Simulations reveal a semiclassical picture in which the rigidity of the period is due to a randomizing effect of the Larmor precession under the magnetization of surrounding spins. The timescales with stable periodicity increase with net initial magnetization, even in the presence of perturbations, indicating a robust temporal ordered phase for large systems with finite magnetization per spin.