  Conditional dynamics due to continuous optical measurements has successfully
been applied for state reconstruction and feedback cooling in optomechanical
systems. In this article, we show that the same measurement techniques can be
used to unravel nonclassicality in optomechanical limit cycles. In contrast to
unconditional dynamics, our approach gives rise to nonclassical limit cycles
even in the sideband-unresolved regime, where the cavity decay rate exceeds the
mechanical frequency. We predict a significant reduction of the mechanical
amplitude fluctuations for realistic experimental parameters.
