Half-integer vs. integer effects in quantum synchronization of spin systems

We study the quantum synchronization of a single spin driven by an external semiclassical signal for numbers larger than S=1, smallest system to host self-sustained oscillator. The occurrence interference-based blockade is found be qualitatively different integer vs. half-integer number xmlns:mml="http://www.w3.org/1998/Math/MathML">S. explain this phenomenon as interplay between and structure limit cycle in generation coherence system. Moreover, we show that same dissipative limit-cycle stabilization mechanism leads very levels However, choosing appropriate each number, comparable can achieved both systems.