Temporal Order in Periodically Driven Spins in small NMR spin Clusters*

We present the results of experimental studies on the magnetization response of star-shaped clusters of initially unentangled N=4, 10, and 37 nuclear spin-1/2 moments when subjected to inexact pi-pulse sequences. We find that an Ising coupling between the center and the satellite spins results in robust period-2 magnetization oscillations. On the other hand, control experiments (using alternate Isotopes ) without the Ising coupling do not show a robust time period. The period is stable against bath effects, but the amplitude decays with a timescale that depends on the inexactness of the pulse. Numerical simulations of the system reveal a simple semiclassical picture in which the rigidity of the period is due to a randomizing effect from the Larmor precession due to the magnetization of the surrounding spins. The timescale with stable periodicity increases with the net initial magnetization, even in the presence of perturbations and absence of disorder, indicating a robust temporal ordered phase for large systems with finite magnetization per spin. We also present results of numerical simulations of the system with simple model couplings to a bath.
Ref: Phys. Rev. Lett. 120, 180602 (2018)