  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.
