Controlling isolated quantum particles (4)

In its simplest form, the experiment distinguishes between 0 and 1 photon field states. This is achieved by adjusting the device so that a single photon shifts the phase of the atomic dipole by an angle π (this adjustment is made by choosing the interaction time t between the atoms and the C field and the atom-cavity frequency detuning). The dipole of the atoms leaving C then points in two opposite directions, depending on whether the cavity contains 0 or 1 photon. The Ramsey bangs corresponding to the probability of finally detecting the atoms in e or g are then shifted by half a fringe as the number of photons varies by one. Simply set the interferometer so that it has a maximum of one fringe if C contains 1 photon. When C is empty, the interferometer is at its minimum of one fringe. The majority of atoms are then detected in e if there is a photon in C, and in g if C is empty (as the fringe contrast is not perfect, there is some noise corresponding to counting errors). The measurement was carried out on the thermal field of C at a temperature of 0.8 K. The cavity contains a photon with a probability of 5%. A sequence of atoms passing through the cavity clearly shows how the number of photons jumps randomly between 0 and 1: a sequence of atoms detected predominantly in the g state (indicating that C is empty) is followed by a sequence of atoms detected in e (indicating the spontaneous appearance of a thermal photon), with the following atoms then returning predominantly to g when the photon disappears.

When the cavity contains a larger field, a single atom is no longer sufficient to measure the number of photons. We then need to extract information from the field progressively, by detecting a succession of atoms crossing C, each atom providing a bit of information (atom found in e or g). The experiment was carried out on a small coherent field, containing between 0 and 7 photons injected into the cavity by a conventional microwave source. The photons emitted by this pulsed source are diffracted at the edges of the C mirrors, and some end up trapped in the cavity. The distribution of the number of photons in C, initially flat (total absence of information), evolves as atoms are detected, until a single number of photons is fixed. The probability distribution is inferred after each atom by an argument exploiting Bayes' law. Once this number has been obtained, subsequent atoms confirm the result, until relaxation (loss of photons due to the finite quality factor of C) causes it to vary by quantum jump. These jumps are detected by the atoms and observed for the first time on light. A statistical analysis of a large number of realizations from this experiment is in perfect agreement with the predictions of quantum electrodynamics. In particular, it shows that an n-photon Fock state has a lifetime _Tc/n, where _Tc is the classical field damping time in C.

This QND photon-counting experiment can also be seen as a method of preparing well-determined photon-number Fock states from a classical coherent field initially injected into C. This preparation method is non-deterministic, as there is no way of predicting in advance which photon number will ultimately be chosen by the measurement. However, the process can be made deterministic by applyingquantum feedback to the cavity field. As the atoms detected provide information on the field, the computer coupled to the device estimates the photon distribution in real time, determines a "distance" separating this distribution in state space from that of the Fock state we are seeking to produce, and controls the injection of a corrective field into C to bring the field closer to the sought-after state.

This corrective field can be either a small classical coherent field injected into C by diffraction, or the field of a photon emitted or absorbed in C by resonant atoms sent into C between sequences of non-resonant detector atoms. To switch between resonant and non-resonant atoms, the computer controlling the experiment applies a small voltage between the mirrors of C. The experiment is run in a loop, with measurement and correction sequences alternating until the computer considers that the desired state has been obtained. A subsequent independent QND measurement confirms this result. If feedback is continued after convergence of the photon number, it detects quantum jumps when they inevitably occur and corrects their effects, effectively maintaining the field in the desired Fock state on average. States with a fixed number of photons from n = 0 to n = 7 could thus be prepared and stabilized. The lesson briefly described this quantum feedback experiment, which had already been analyzed in detail in a previous lecture (see 2010-2011 yearbook).