Process tomography of field damping and measurement of Fock state   lifetimes by quantum non-demolition photon counting in a cavity
  The relaxation of a quantum field stored in a high-$Q$ superconducting cavity is monitored by non-resonant Rydberg atoms. The field, subjected to repetitive quantum non-demolition (QND) 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 ($0\leq n \leq 7$) are found to increase linearly with $n$. The results are in excellent agreement with theory including a small thermal contribution. 
M. Brune, J. Bernu, C. Guerlin, S. Deleglise, C. Sayrin, S. Gleyzes,   S. Kuhr, I. Dotsenko, J. M. Raimond and S. Haroche