this limit.

We find that the drive-dependent QBS shows striking quantum signatures. In the classical limit of high temperatures, it is always real and positive (like the purely thermal contribution) [@SI]. However, as temperature is lowered and quantum fluctuations become more important, this quantity can have a negative real part, and even a non-zero imaginary part. These purely quantum features become more pronounced as the magnitude of the drive detuning $\delta$ is increased. The real and imaginary parts of $S_{\mathrm{dr} }   [ {\omega}_{1},{\omega}_{2}  ]$ are plotted for zero temperature in Figs. \[fig:S2\_10\](b) and \[fig:S2\_10\](c) for a large drive detuning ($\delta / \gamma =10$).

We start by discussing the surprising negativity of the real part of the zero-temperature QBS. Negativity in the zero-frequency limit was already discussed in [@Clerk2011; @Clerk2016]. These works showed that this negativity is a purely quantum effect, and that moreover, for large detunings the magnitude of the third cumulant is so great that the fluctuations cannot be described by a positive-definite quasiprobability distribution. Our results show how this striking non-classicality also manifests itself in the [*non-zero*]{} frequency fluctuations. It also demonstrates that this quantum correction has a non-trivial frequency dependence. We find that the quantum bispectrum $ 