Controlling isolated quantum particles : atoms and photons

The development of methods for controlling trapped atoms and ions, the subject of the fourth lesson, has been made possible by the precise manipulation, using lasers, of atoms' internal and external degrees of freedom. Observations of quantum trajectories and atomic quantum jumps have become routine operations. These experiments extend and generalize to atoms those carried out in the 1960s-70s on trapped single electrons, which led to extremely precise tests of quantum electrodynamics. In parallel with studies of single atoms, experiments involving the manipulation and detection of single photons have also developed, with the observation of quantum jumps in light and the preparation of non-classical field states (quantum optics and cavity quantum electrodynamics). In these experiments, the behavior of atoms and photons illustrates the fundamental principles of quantum theory (superposition of states, entanglement and decoherence). The possibility of exploiting quantum logic for communication and calculation has been a major driving force behind the development of what is known as quantum information. Quantum Condensed Matter Physics is used in experiments where atoms are replaced by artificial quantum systems (e.g. circuits containing Josephson junctions).

The first part of the lesson was devoted to trapped charged particles. After an historical review of Dehmelt's experiments on a single electron, which led to the ultra-precise measurement of the electron's "anomalous magnetic moment", the principle of the Paul trap was described, as well as the methods of manipulation and laser detection of ions (fluorescence imaging, "sideband" cooling, observation of ion quantum jumps as a method of selective detection of their internal states). The second part of the lesson was devoted to the trapping of individual neutral atoms. This trapping is achieved in microscopic wells using the dispersive optical force resulting from the action on the atomic dipole of the gradient of a non-resonant light field. This gradient is produced by strongly focusing a laser beam (optical tweezers) or by creating a standing wave with a periodicity of the order of the optical wavelength (arrays of potential wells). As with trapped ions, atoms are detected by imaging their fluorescence under resonant laser irradiation. In the presence of the detection laser, atoms are ejected from the trap through light-assisted binary collisions, leaving zero or one atom in each trap. The trap ends up empty if the initial number of atoms before resonant irradiation was even, and ends up with a single atom if this number was odd. Optical imaging thus amounts to measuring the parity of the number of atoms in the trap. The expulsion of an atom by collision, or the fall of an atom into the trap, is detected by a sudden jump in the level of the light it scatters by fluorescence. The method can be used to observe single atoms in isolated traps or in two traps placed at a controlled distance. It can also be used to create "conveyors" for atoms trapped in a one-dimensional periodic structure created by contra-propagating beams, or two- or three-dimensional "atomic crystals" in which individual atoms can be imaged and manipulated.

The third part of the lesson described methods for studying single photons in quantum optics, recalling first their generation by excitation of isolated atoms in a dilute atomic jet, then that produced by laser excitation of single colored centers (diamond NV centers, for example). Another method involves generating pairs of photons in two field modes by a non-linear process in a crystal, and using the detection of one photon in one mode to "announce" the presence of a single photon in the other mode. The detection of single photons by "anti-coincidence" of clicks recorded by two detectors after splitting the light beam on a semi-reflective plate was recalled.

The lesson then focused on the various methods of cavity electrodynamics, which have been the subject of many previous lectures given by the Chair. A distinction was made between experiments performed in optical cavities and those carried out in microwave cavities with Rydberg atoms passing through the cavity one by one. The main results of the Chair's team in the latter field were recalled (preparation and study of Schrödinger field states, study of decoherence, detection of quantum jumps in the microwave field, non-destructive QND photon counting, quantum tomography reconstruction of non-classical fields, demonstration of quantum feedback). The analogy of microwave quantum electrodynamics with "Circuit QED" experiments in which Rydberg atoms are replaced by artificial structures containing Josephson junctions was also recalled and illustrated by the description of some fine recent results in Circuit Electrodynamics.

The lesson ended with a discussion of quantum information, a rapidly expanding field that aims to exploit the manipulation of individual systems (atoms, ions, photons, artificial quantum structures) to perform quantum logic operations that will one day lead to innovations in communication or computation. We began by recalling Aspect's pioneering Bell inequality violation experiment, which dramatically demonstrated the properties of quantum entanglement and non-locality. We then described the principle of quantum logic gates, demonstrated on several systems (trapped ions, cold neutral atoms, QED Circuit), before concluding the lesson by evoking quantum simulation, which consists in bringing into interaction a set of well-controlled quantum systems in a trap or in a periodic structure whose parameters are adjustable, and studying the evolution of this system. In this way, we emulate phenomena occurring on other scales in condensed matter, which cannot be calculated using conventional computers because the space of states in which the system evolves is so large. These quantum simulation methods hold great promise for the discovery and study of as yet unknown phases of matter.