  We report Ramsey spectroscopy on the clock states of individual Cs impurities
immersed in an ultracold Rb bath. We record both the interaction-driven phase
evolution and the decay of fringe contrast of the Ramsey interference signal to
obtain information about bath density or temperature nondestructively. The
Ramsey fringe is modified by a differential shift of the collisional energy
when the two Cs states superposed interact with the Rb bath. This differential
shift is directly affected by the mean gas density and the details of the Rb-Cs
interspecies scattering length, affecting the phase evolution and the contrast
of the Ramsey signal. Additionally, we enhance the temperature dependence of
the phase shift preparing the system close to a low-magnetic-field Feshbach
resonance where the $s$-wave scattering length is significantly affected by the
collisional (kinetic) energy. Analyzing coherent phase evolution and decay of
the Ramsey fringe contrast, we probe the Rb cloud's density and temperature.
Our results point at using individual impurity atoms as nondestructive quantum
probes in complex quantum systems.
