  We show that single electron tunneling devices such as the Cooper-pair box or
double quantum dot can be sensitive to the zero-point fluctuation of a single
trapping center hybridized with a Fermi sea. If the trap energy level is close
to the Fermi sea and has line-width \gamma > k_B T, its noise spectrum has an
Ohmic Johnson-Nyquist form, whereas for \gamma < k_B T the noise has a
Lorentzian form expected from the semiclassical limit. Trap levels above the
Fermi level are shown to lead to steps in the noise spectrum that can be used
to probe their energetics, allowing the identification of individual trapping
centers coupled to the device.
