  Synchronization occurs ubiquitously in nature. The van der Pol oscillator has
been a favorite model to investigate synchronization. Here we study the
oscillator in the deep quantum regime, where nonclassical effects dominate the
dynamics. Our results show: (i) squeezed driving loses its effect, (ii) noise
boosts synchronization, (iii) synchronization is bounded, and (iv) the
limit-cycle is insensitive to strong driving. We propose a synchronization
measure and analytically calculate it. These results reflect intrinsic
differences between synchronization in the quantum and deep quantum regimes.
