Atoms with exaggerated properties

The first lesson was an introduction to the physics of Rydberg atoms, atomic species in which an electron is carried in a highly excited state, giving them "exaggerated" properties very different from those of ordinary atoms. These states are manifested by the existence of a series of absorption and emission lines whose wavelengths (and frequencies) are defined by the formula that the Swedish physicist Rydberg empirically established at the end of the 19th century - hence the name given to these states. They are characterized, among other parameters, by a principal quantum number n, which appears in Rydberg's formula and identifies the atom's level of energetic excitation. The size of these atoms, measuring the dimensions of the excited electron's orbit or the extension of its wave function, increases as the square of the principal quantum number and becomes of the order of a thousand to ten thousand times that of an atom in its ground state for n of the order of 50 to 100, which goes a long way towards explaining the exaggerated properties of these atoms.

The lesson began with a brief historical account recalling that these states played an important role in the reflections that led Niels Bohr in 1913 to establish his famous model of the atom, the precursor of the description given by modern quantum physics. Rydberg atoms then made their appearance in physics in the 1930s with the study of the shift in atomic lines of the Rydberg series when atoms are excited in the presence of rare gas atoms (argon, xenon or helium). Fermi and his collaborators studied this problem in the 1930s, both experimentally and theoretically, and interpreted the displacement of the lines by the effect of collisions of the excited electron of Rydberg atoms, described by its quasi-free particle wave function, on noble gas atoms entering the Rydberg orbit. In this study, Fermi introduced for the first time the notion ofscattering length, which was later to play an important role in theory, in nuclear physics and then in cold-gas atomic physics. Rydberg atoms first appeared in astrophysics in the 1960s, when they were detected in the millimeter-wave spectrum emitted by interstellar gas from the recombination of ions and electrons. The transient excitation of Rydberg atoms with principal quantum numbers in the hundreds was observed. But it wasn't until the 1970s that the experimental study of these atoms could really begin in the laboratory, with the advent of frequency-tunable lasers, essential for preparing them efficiently and selectively in an atomic jet.

The lecture recalled the role these atoms then played in the study of the coupling of atoms with radiation, and how their very strong interaction with microwaves led to the development in the 1980s, 1990s and 2000s of cavity electrodynamics, a subject that had been the focus of several lectures in previous years. This historical review concluded with the revival of the study of Rydberg atoms in the early 2000s, with theoretical proposals to exploit their very strong mutual dipole-dipole interactions, either to perform quantum logic operations between atoms considered as qubits, or to study the quantum behavior of ensembles of atoms sharing one or more Rydberg excitations. These proposals were soon followed by experiments demonstrating the possibilities offered by these atoms in quantum information in particular. The possibility of manipulating gases of ultra-cold atoms, in which the atoms' external degrees of freedom - position and velocity - are well controlled, has greatly facilitated these experiments, which were impossible to carry out in previous years. It is to the description of these experiments that the bulk of this year's lecture is devoted.

After this general historical introduction, the lesson recalled the principle of realizing quantum gates between atoms. For this, a controlled interaction between two atoms can be achieved, either through their coupling with phonons (the case of quantum information with trapped ions), or through their interaction with photons in a cavity (the case of cavity electrodynamics). The physics of Rydberg atoms provides another method. The two atoms, each carrying a qubit encoded in a two-state subspace of the fundamental level of each atom, interact directly and at great distance through their dipole-dipole interaction when excited by a laser in a Rydberg state. This excitation leads to the phenomenon of Rydberg blocking: once one atom is excited, the laser cannot excite a second one in its vicinity, as the frequency of this second excitation is displaced by the interaction between atoms by an amount greater than the width of the excitation (proportional to the amplitude of the laser field, or its Rabi frequency). It is the conditional nature of the excitation of a "target" atom in the presence of a "control" atom, depending on whether or not the control is excited, that enables the quantum gate mechanism to be implemented. The lesson presented the principle of such a gate, without going into the details of its realization. It then showed how Rydberg blocking could be used on a set of Rydberg atoms to achieve collective entanglement of these atoms. The orders of magnitude of these effects were presented, explaining why it is generally necessary to carry out these experiments with quasi-stationary atoms, strongly cooled by lasers.

After this general qualitative presentation of the effects that will be described in greater detail in subsequent lectures, the rest of the first lesson recalled in greater depth the main properties of isolated Rydberg atoms, giving a semi-classical description following the Bohr and Sommerfeld models, then a fully quantum analysis, recalling the form of the electronic wave functions of Rydberg atoms, first in the case of hydrogen, then in that of alkali atoms, which are those generally used in experiments. The dynamic symmetry of the hydrogen atom (corresponding to the conservation of the Runge-Lenz vector) means that semi-classical electron orbitals are closed and quantum states of a given energy are highly degenerate. In alkali atoms, this symmetry is broken, orbits are opened and the degeneracy of states with different angular momentum corresponding to the same principal quantum number is lifted. These effects are due to the perturbative effect of the non-point ionic core of alkali Rydberg atoms, and occur especially for low angular momentum states where the excited electron has a high probability of entering the core. These perturbative effects are described by a parameter, the quantum defect, which depends essentially on the angular momentum of the excited electron, and very little on its principal quantum number. Despite the correction provided by the quantum defect, the properties of alkali Rydberg states are very close to those of the corresponding hydrogen states, and a hydrogen model is generally sufficient to explain qualitatively the properties of Rydberg atoms, with a few notable exceptions that are mentioned in the following lessons.