With the unique advantage of great isolation from the thermal environment, levitated optomechanics has emerged as a powerful platform for various fields of physics including microscopic thermodynamics, precision measurements, and quantum mechanics. Experiments with optically levitated micro- and nanoparticles have already obtained remarkable feats of zeptonewton force sensing and ground-state cooling. The novel system has also been proposed to assess various theories including the objective collapse models and macroscopic quantum mechanics. <br><div><br></div><div>This thesis reports experimental results on a levitated Cavendish torsion balance, a GHz nanomechanical rotor, and a torque sensor with unprecedented sensitivity realized with optically levitated nanoparticles in a vacuum environment. The system at room temperature achieves a sensitivity of (4.2±1.2)×10−27Nm/ √ Hz surpassing the sensitivity of most advanced nanofabricated torque sensors at cryogenic environments. Calculations suggest potential detection of Casimir torque and vacuum friction under realistic conditions. Moreover, the nanoparticles are driven into ultrafast rotations exceeding 5 GHz, which achieves the fastest humanmade nanomechanical rotor. Such fast rotations allow studies on the ultimate tensile strength of the nanoparticles as well. <br></div><div><br></div><div>Subsequently, the electron spin control of nitrogen vacancies (NV) in optically trapped diamond naoparticles is demonstrated in low vacuum. The configuration is analogous to trapped atoms and ions which serve as a quantum system with internal states. The effect of the air pressure, surrounding gas, and laser power on the electron spin resonance (ESR) are studied, and the temperature of the diamond is also measured with the ESR. The levitated nanodiamonds will provide the means to implement a hybrid spin-optomechanical system.<br></div>

Covariant density functional theory (CDFT) is one of the modern theoretical tools for describing the nuclear structure physics of finite nuclei. Its performance is defined by underlying covariant energy density functionals (CEDFs). In this dissertation and within the framework of the CDFT, different physical properties of the ground and the excited states of rotating and non-rotating nuclei have been investigated. A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref.\ \cite{TMR.09}. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in the neutron subsystem. However, the situation is less certain in the proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to the uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. Although the present investigation is based on the NL5(E) covariant energy density functional (CEDF), its general conclusions are expected to be valid also for other CEDFs built at the Hartree level. It is shown for the first time that rotational bands which are proton unbound at zero or low spins can be transformed into proton bound ones at high spin by collective rotation of nuclear systems. This is due to strong Coriolis interaction, which acts on high-$N$ or strongly mixed M orbitals and drives the highest in energy occupied single-particle states of nucleonic configurations into the negative energy domain. Proton emission from such proton bound rotational states is suppressed by the disappearance of static pairing correlations at high spins of interest. These physical mechanisms lead to a substantial extension of the nuclear landscape beyond the spin zero proton drip line. In addition, a new phenomenon of the formation of giant proton halos in rotating nuclei emerges: it is triggered by the occupation of strongly mixed M intruder orbitals. Possible experimental fingerprints of the transition from particle bound to particle unbound part of rotational bands are discussed and compared for proton and neutron rich nuclei near and beyond respective drip lines.

Cette thèse présente les résultats d'observations d'étoiles en rotation rapide menées sur le spectro-interféromètre AMBER du VLTI dans ses modes haute et moyenne résolutions spectrales. Les mesures effectuées sont les visibilités estimées sur trois bases simultanées, les phases différentielles en fonction de la longueur d'onde et des phases de clôtures avec, pour certaines nuits une bonne couverture du plan (u,v). Les données utilisées sont issues de plusieurs campagnes d'observation. Ces dernières étaient fortement dégradées par les défauts optiques d'AMBER, et affectés par des bruits classiques d'interférométrie optique à longue base en IR: défauts du détecteur, bruit de lecture, instabilités du suiveur de franges, ...etc. Leur analyse a nécessité la mise au point d'outils numériques de réduction spécifiques pour atteindre les précisions nécessaires à l'interprétation de mesures interférométriques. Pour interpréter ces mesures j'ai développé un modèle semi-analytique chromatique d'étoile en rotation rapide qui m'a permis d'estimer, à partir des phases différentielles; le degré d'aplatissement, le rayon équatorial, la vitesse de rotation, l'angle d'inclinaison, l'angle position de l'axe de rotation de l'étoile sur le ciel, la distribution de la température effective locale et de la gravité à la surface de l'étoile dans le cadre du théorème de von Zeipel. Les résultats concernant 4 étoiles massives de types spectraux B, A et F m'ont permis de les caractériser pour les mécanismes évoqués ci-dessus et d'ouvrir ainsi la perspective d'études plus systématiques d'objets similaires en étendant ultérieurement ces études à la relation photosphère-enveloppe circumstellaire. / This thesis presents the results of rapidly rotating stars observations conducted on the AMBER spectro-interferometer VLTI in its high average spectral modes and resolutions. The measurements are estimated on three simultaneous visibility bases, differential phases depending on the wavelength and closure phases, with good coverage of the (u, v) plane for some nights. The data used are from several observation campaigns. These were highly degraded by the optical defects of AMBER, and assigned by standard optical interferometry long base IR noises: defects of the detector, reading noise, fringes follower instabilities, ... etc. Their analysis required the development of digital reduction of specific tools to achieve the necessary details to the interpretation of interferometric measurements. In interpreting these measures I developed a chromatic semi-analytical model of rapidly rotating star that allowed me to estimate, from the differential phases; the degree of flattening, the equatorial radius, speed of rotation, angle of inclination, the position angle of the star rotation axis in the sky, the local distribution of the actual temperature and the gravity to the surface of the star within the von Zeipel theorem. The results for four massive stars of spectral type B, A and F have allowed me to characterize the mechanisms discussed above and thus open framework for more systematic studies of similar objects subsequently extending these studies to the relationship photosphere circumstellar envelope.