QND counting of N photons : progressive field projection

The sixth lesson showed how the dispersive QND measurement method of 0 or 1 photon can be generalized to counting a number of photons greater than 1. We recalled that measuring a single quantum of light requires that the phase shift _Φ0 induced by a photon on the atomic dipole is worth π. Each atom, described as a spin, then exits the device pointing along one of two opposite directions, indicating that C contains 0 or 1 photon. The setting _Φ0 = π is suitable for measuring the parity of the number n of quanta, assimilable to n if the field, being very small, has a negligible probability of containing more than one photon. For larger fields, QND counting is still possible by modifying _Φ0. The value of n can no longer be obtained from a single 'spin', but must be extracted from a set of atoms. By detecting the 'spins' of this ensemble one by one, we observe the progressive evolution of the field towards a Fock state, the so-called collapse of its wave function. Repeating the measurement as successive sets of atoms pass through C reveals the staircase-like cascade of photon numbers into the vacuum, due to field relaxation. After a few reminders and general remarks, we analyzed this ideal light measurement procedure by applying it to a small coherent field.