We measure the quantum fluctuations of a pumped nonlinear resonator, using a
superconducting artificial atom as an in-situ probe. The qubit excitation
spectrum gives access to the frequencyand temperature of the intracavity field
fluctuations. These are found to be in agreement with theoretical predictions;
in particular we experimentally observe the phenomenon of quantum heating.
We observe measurement-induced qubit state mixing in a transmon qubit
dispersively coupled to a planar readout cavity. Our results indicate that
dephasing noise at the qubit-readoutdetuning frequency is up-converted by
readout photons to cause spurious qubit state transitions, thus limiting the
nondemolition character of the readout. Furthermore, we use the qubit
transition rate as a tool to extract an equivalent flux noise spectral density
at f ~ 1 GHz and find agreement with values extrapolated from a $1/f^alpha$
fit to the measured flux noise spectral density below 1 Hz.