Depuis l’avènement de la mécanique quantique, l’étude des interactions lumière-matière à l’échelle quantique s’est énormément développée en tant que domaine de recherche. Par exemple, grâce à des prédictions théoriques surprenantes, des interactions d’une force sans précédant ont été démontrées entre de la matière et des radiations terahertz et microonde. Ces résultats correspondent à un régime dit de couplage ultrafort, atteint lorsque l’énergie d’interaction devient comparable aux énergies propres de la lumière et de la matière lorsque celles-ci n’interagissent pas. Dans ce régime, des propriétés intrigantes peuvent subsister telles que la présence de photons même lors qu’aucune énergie n’est fournie au système. Cependant, ces photons ne peuvent, a priori, être émis du système vers l’extérieur de manière à pouvoir être mesurés et par conséquent démontrer ces propriétés.Dans cette thèse, nous avons étudié ces propriétés intrigantes et proposé plusieurs moyens permettant d’y accéder expérimentalement. Nous nous sommes appuyés sur plusieurs plate-formes physiques qui sont de bon candidats pour ces études, et pour chacun de ces systèmes nous avons mis au point un modèle mettant en évidence ces propriétés d’une manière ou d’une autre. De cette façon, nous avons exploré le lien entre le régime de couplage ultrafort et la génération d’états non-classiques de la lumière. En outre, dans une étude plus ouverte nous avons montré que les interactions lumière- matière dans l’une de ces plate-formes peuvent être utilisés pour concevoir des protocols de communication quantique. En plus de montrer un intérêt fondamental, nos résultats s’inscrivent dans une optique de développement d’applications pour les technologies quantiques en utilisant différents systèmes expérimentaux disponibles actuellement / Since the advent of quantum mechanics, the study of light-matter interactions at thequantum level has been greatly developed as a research field. For instance, surprisingtheoretical predictions gave rise to experiments with unprecedented interactionstrengths between matter, and terahertz and microwave radiations. These results correspondto the so-called ultrastrong coupling regime, that is reached when the interactionenergy becomes comparable to the typical energies of the light and matter when they arenot interacting. In this regime, intriguing properties can be found such as the presenceof photons even when no energy is given to the system. However, these photons cannot,a priori, be emitted from the system to the outside world in order to be measured andtherefore demonstrate these properties. In this thesis, we studied these intriguing properties and proposed several means toaccess them experimentally. We relied on several physical platforms which are goodcandidates for such studies, and for each one of these systems we devised a model thatcan evidence these properties one way or another. By doing so, we explored the linkbetween the ultrastrong coupling regime and the generation of nonclassical states oflight. Additionally, as an outlook we showed that the light-matter interactions in oneof these platforms could be used to design quantum communication protocols. On topof showing fundamental interest, our results fit in the line of developing applications forquantum technologies using different experimentally available systems.

We investigate two different coupling schemes between a nano-scale mechanical resonator and one-electron atoms. In these schemes, classical electromagnetic radiation mediates a mutual communication between the mechanical resonator and the atoms. In the process it generates atomic coherences, quantum superpositions of excited electronic levels of the atoms. An atomic coherence is highly responsive to subtle variations in the relative frequencies of the levels participating in such superposition state. By exposing the atoms to electromagnetic radiation modulated by the motion of the mechanical resonator, we show how the response of an atomic coherence can, under appropriate conditions, be used to affect on demand the dynamical state of the mechanical resonator. The first scheme realizes a long range interface between a mechanical resonator and an ensemble of three-level atoms. Here, mechanically modulated electromagnetic radiation comes from a laser beam reflected off an oscillating mirror, the mechanical resonator. This light beam drives the transition between an excited level and a hyperfine sublevel of the atoms with a certain detuning. A weaker light beam resonantly couples to the transition between the excited level and another hyperfine sublevel. On full resonance, the atoms evolve into a stationary coherence of the above (non-absorbing) hyperfine sublevels only. The atoms then become transparent to the weaker light beam, in a phenomenon called electromagnetically induced transparency. Off resonance, we find that this transparency is modulated at the mirror frequency with some phase shift, which allows the weaker beam to cause resonant backaction onto the moving mirror. The strength of this backaction is enhanced near atomic resonances and its character can be switched between amplification or damping of mirror vibrations by adjusting the detuning. In contrast, the second scheme accomplishes a closer range interface between a torsion pendulum and guided two level Rydberg atoms. Attaching a point electric dipole to the torsion pendulum allows electromagnetic coupling to two Rydberg levels of a passing atom. This coupling modifies the eigenfrequencies of the Rydberg levels such that they become dependent on the phonon number of the torsion pendulum. Via Ramsey interferometry, we may readout this effect and thus measure the phonon number. We show that, by subjecting several atoms, one by one, to a Ramsey measurement, a quantum non-demolition detection of the phonon number is feasible. Likewise, we show coherent oscillator displacements possible, by driving the atoms with external fields while they interact with the torsion pendulum. We propose a protocol to reconstruct the quantum state of motion of the torsion pendulum, combining these two techniques, Ramsey measurements and oscillator displacements. Our interfaces between a mechanical resonator and atoms provide alternative routes for the control of the state of motion, ultimately quantum mechanical, of a mechanical resonator, in which the latter is not restricted to be part of a cavity. We will thus ease quantum dynamical manipulations of mechanical resonators of sub micron scales, for which an efficient design of cavity opto- and electro-mechanical systems is hard.