Measurement of Small Photon Numbers in Circuit QED Resonators.

Off-resonant interaction of fluctuating photons in a resonator with a qubit increases the qubit dephasing rate. We use this effect to measure a small average number of intracavity photons that are coherently or thermally driven. For spectral resolution, we do this by subjecting the qubit to a Carr-Purcell-Meiboom-Gill sequence and record the qubit dephasing rate for various periods between qubit π pulses.