Summary
The third lesson described the ENS experiments on controlled entanglement between atoms and photons, the demonstration of quantum gates and the illustration of complementarity in an atomic interferometer. These experiments, carried out in the 1990s and early 2000s, were performed with circular Rydberg atoms with a principal quantum number of the order of 50, whose physical properties and methods of preparation and manipulation were first recalled. As their name suggests, these atoms have a circular electron orbit, corresponding to a maximum angular momentum in the direction perpendicular to the plane of the orbit. Their advantages for cavity electrodynamics experiments are manifold: they have a very long lifetime, a very large electric dipole associated with the transition between neighboring Rydberg levels, which couples them very strongly to millimeter radiation. They are easy to ionize in an electric field of the order of a hundred volts per cm. Finally, their electrical polarizability is enormous, making transitions between levels tunable over a MHz range by the Stark effect in a field of the order of one volt per cm. All these properties can be demonstrated by the simple classical calculations described in this lesson.
The method used to prepare these states exploits optical transitions excited in successive steps by three lasers, followed by radio-frequency transitions performed in an electric field that lifts the degeneracy of angular momentum levels increasing in the multiplicity of Rydberg states by the Stark effect. The transition to the circular levels takes place by adiabatic passage along the scale of Stark levels thus created, with very high efficiency. A classical microwave pulse then coherently mixes two neighboring circular levels, creating a superposition of states whose wave function is a packet rotating around the atom's core at the frequency of the transition between these levels. This wave packet is reminiscent of a planet revolving around the sun, or the hand of a clock turning on its dial. The latter image will be used in the next lesson to describe the non-destructive photon detection method using these atoms.
