The fifth lesson studied the behavior of an ensemble of atoms in the presence of excitation to a Rydberg state, and showed how the Rydberg blocking mechanism can be used to prepare collectively entangled atomic states. Radiation coupling of these states can lead to the generation of "Rydberg polaritons", states of mixed excitation of the atomic ensemble and the field. These polaritons can evolve adiabatically and reversibly between purely atomic and purely radiative states, thus opening up the possibility of quantum communication, by transferring quantum information stored in a first set of atoms to an optical field, which then transfers it into recopied information in a second atomic set.
The lesson began by analyzing the principle behind these experiments. The simple idea is that laser excitation acting on a set of N atoms contained in a spherical volume of radius less than the Rydberg blocking radius can only excite one atom, the excitation being symmetrically distributed among all the atoms in the set, forming a collectively entangled state. What's more, the Rabi frequency associated with this collective excitation is proportional to the square root of the total number N of atoms, making coupling much faster than in the case of one or two atoms. Entanglement involving an excited Rydberg atom has a lifetime limited by the spontaneous emission time of the Rydberg state. It can be copied to a set of atoms involving only fundamental states by transferring the Rydberg state to a fundamental sublevel (different from the initial atomic state) using a laser pulse. In this way, a stable collective atomic excitation is prepared in a two-level set of atoms, a so-called spin wave, in which N-1 atoms are in one state and one atom in another, this distribution being symmetrically distributed among all the atoms. The process can be repeated by then exciting a second atom in a Rydberg level, then transferring it to the ground state, achieving a symmetrical excitation where N-2 atoms are in one level and 2 in the other, and so on. The superposition of these states can constitute the general state of a collective qubit coupled much more strongly to the field than a monoatomic qubit, and the coupling of two collective qubits can lead to the realization of quantum gates faster than those coupling monoatomic qubits.
