Quantum nondemolition measurement of the photon number in a Josephson-junction cavity

This paper proposes a quantum nondemolition measurement of the photon number in a Josephson-junction cavity. Under a current-biased Josephson junction with small capacitance, the Josephson phase fluctuates quantum-mechanically around its classical value due to the charging effect, and it couples to the photons in the junction cavity nonlinearly, which is necessary for the quantum nondemolition measurement. We show that the photon number in the junction cavity can be nondestructively measured by detecting the fluctuation of Josephson supercurrent through the junction.