  The photon creation and annihilation operators are cornerstones of the
quantum description of the electromagnetic field. They signify the isomorphism
of the optical Hilbert space to that of the harmonic oscillator and the bosonic
nature of photons. We perform complete experimental characterization (quantum
process tomography) of these operators. By measuring their effect on coherent
states, we obtain their process tensor in the Fock basis, which explicitly
shows the "raising" and "lowering" properties of these operators with respect
to photon number states. This is the first experimental demonstration of
complete tomography of non-deterministic quantum processes.
