Process tomography of field damping and measurement of Fock state lifetimes by quantum nondemolition photon counting in a cavity.

The relaxation of a quantum field stored in a high-Q superconducting cavity is monitored by nonresonant Rydberg atoms. The field, subjected to repetitive quantum nondemolition photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the n photon states (0 < or = n < or = 7) are found to increase linearly with n. The results are in excellent agreement with theory including a small thermal contribution.