Efficient ensemble randomization by tuning chaos in a nonlinear spin-1 system

We present an efficient scheme to randomize a spin-state ensemble in a nonlinear spin-1 system by tuning chaos with an external periodic drive. Without modulation, the system exhibits a mixed phase space featuring regular islands embedded in a chaotic sea, where global mixing is inhibited by energy conservation. Using numerical simulations, we demonstrate that weak modulation of a linear Zeeman field not only facilitates transport between different energy shells but also drives ensembles toward a Haar-random distribution over spin states. Under optimized conditions, complete randomization is achieved on a timescale set by the inverse nonlinear interaction energy. In the overdriven regime, randomization is unexpectedly suppressed at specific modulation amplitudes, accompanied by the formation of sticky regions in phase space. We attribute this behavior to the dynamical cancellation of the leading low-order harmonic component of the periodic drive. These results illustrate how time-periodic driving can be used to engineer chaotic systems and achieve controllable randomization in nonlinear spin systems.