  Random tunneling two-level systems (TLSs) in dielectrics have been of
interest recently because they adversely affect the performance of
superconducting qubits. The coupling of TLSs to qubits has allowed individual
TLS characterization, which has previously been limited to TLSs within (thin)
Josephson tunneling barriers made from aluminum oxide. Here we report on the
measurement of an individual TLS within the capacitor of a lumped-element LC
microwave resonator, which forms a cavity quantum electrodynamics (CQED) system
and allows for individual TLS characterization in a different structure and
material than demonstrated with qubits. Due to the reduced volume of the
dielectric (80 $\mu$m$^{3}$), even with a moderate dielectric thickness (250
nm), we achieve the strong coupling regime as evidenced by the vacuum Rabi
splitting observed in the cavity spectrum. A TLS with a coherence time of 3.2
$\mu$s was observed in a film of silicon nitride as analyzed with a
Jaynes-Cummings spectral model, which is larger than seen from superconducting
qubits. As the drive power is increased, we observe an unusual but explicable
set of continuous and discrete crossovers from the vacuum Rabi split
transitions to the Glauber (coherent) state.
