Rydberg blocking in mesoscopic sets of atoms

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.

These atomic spin waves can be adiabatically coupled to an optical field, resulting in a mixed atom-field "polariton" system. The atomic and field components appear in a coherent quantum superposition, the weights of the two components evolving adiabatically as the field passes over the atomic sample. In this way, the spin wave can be continuously transformed into a quantum field and vice versa, copying the probability amplitudes from one system to the other. If the field propagates in an optical fiber, this creates the conditions for a quantum communication experiment, copying the information carried by a first set of atoms onto a second, at an arbitrary distance from the first.

After these theoretical considerations, based on the analysis of articles published in the early 2000s, the lesson moved on to the description of a recent experiment, highlighting some of the effects. Collective excitation of a set of rubidium atoms has shown that the Rabi frequency of the excitation is indeed proportional to the root of the total number of atoms. The excited Rydberg state is observed using a two-photon stimulated emission process, the sum of whose frequencies is equal to that of the transition from the Rydberg to the ground state. A laser beam at one of these frequencies stimulates the emission of a photon at the complementary frequency. The photon thus emitted is sent to a semi-reflective plate, followed by two detectors in the plate's output channels. The anti-coincidence of the detections in these two channels shows that only one photon is emitted in the process, and that only one atom is excited in the set of atoms. The process of transferring this single atomic excitation to a field containing a single photon is analogous to the atom-field excitation transfer process described theoretically above.

We concluded the lesson by describing a fine experiment carried out at the Max Planck Institute for Quantum Optics in Garching, in which ensembles of Rydberg atoms are prepared from a Mott crystal of atoms in a two-dimensional optical trap lattice. The atoms can only be excited if they are at distances greater than the blocking radius, and their interaction forces them to build structures where they maximize their mutual distances in a two-dimensional circular disk geometry. We then observe the formation of "crystals" composed of either two atoms (arranged along the diameter of the disk), three atoms (arranged in an equilateral triangle inscribed in the disk), four atoms (arranged in a square) or even five atoms forming a regular pentagon. These figures are observed by starting with a regular lattice of atoms in the ground state and exciting the ensemble with lasers resonant with the transition to a Rydberg state. The atoms remaining in the ground state are then "chased" out of their wells by the radiation pressure of a resonant laser, and the excited atoms in the Rydberg state are caused to fall back to the ground state by laser-stimulated emission. Finally, the falling atoms are detected by fluorescence imaging, revealing the Rydberg atom structures transiently formed. Repeating the experiment reveals a structure whose orientation varies randomly from one run to the next. This suggests that the experiment is in fact preparing quantum crystals of Rydberg atoms, coherent superpositions of structures with different orientations, a single structure being revealed by quantum projection at the moment of measurement. The experiment measured the radial and angular correlations of the atoms in these crystals, which are in good agreement with theoretical models.