Inthe seventh and final lesson, we gave a few details on QND measurements of microwave trapped fields, and concluded the lecture with a few perspectives. We saw (lesson 6) that measuring a sequence of m atoms passing one by one through a cavity C, all subjected to the same phase shift per photon Φ0, progressively reduces the field to a Fock state |n>. The number m increases as nm2, wherenm is the upper bound of n. We described the principle of a variant of this experiment, successively using atoms subjected to phase shifts Φ0 = π , π/2, π/4..., which can determine n with only m~log2nm atoms.
We then turned our attention to the first intermediate state of the field, between the initial coherent state and the final Fock state. The feedback action of the QND measurement produces, after detection of the first atom, a superposition of field states with 2 different classical phases. When Φ0 = π, the components of this "Schrödinger cat " have opposite amplitudes and contain, depending on the final state of the atom, only an even or odd number of photons. By injecting a coherent homodyne field into C and continuing to measure the parity of n in a QND fashion with the following atoms, we reconstruct the Wigner function of these "cats" and study their decoherence in real time. We presented the principle of these experiments, which were described in greater detail in the seminar by I. Dotsenko's seminar which followed the lecture. Finally, we concluded the lesson with a description of a Zeno effect experiment on a repeatedly measured field and a brief presentation of the non-locality studies we plan to carry out, as an extension of these experiments, with two cavities.
