We discuss the physical problem of a molecule interacting with an electromagnetic field pulse and model the problem using a time-dependent perturbation of the Born-Oppenheimer approximation to the Schrodinger equation. Using previous results that develop asymptotic series solutions in the Born-Oppenheimer parameter ε, we derive a formal Dyson series expansion in the perturbation parameter μ, which is proportional to the electromagnetic field strength. We then prove that this series is asymptotically accurate in both parameters, provided that the Hamiltonian for the electrons has purely discrete spectrum. Under more general hypotheses, we show that the series is accurate to first order in μ, and that it is accurate to one higher order if we place conditions on the abruptness of the EM pulse. We also show how this series development provides a justification for the Franck-Condon factors in the case of a diatomic molecule. / Ph. D.

Achieving the quantum control of ever more complex systems has been a driving force of atomic, molecular, and optical physics. This goal has materialized in the harnessing of systems with increasingly rich structures and interactions: the more sophisticated the system, the more faceted and fascinating its application to fields as varied as quantum simulation, quantum information, many body physics, metrology, and quantum chemistry. One of the current frontiers of quantum control is ultracold dipolar molecules. They present rich internal structures and long-range, anisotropic dipole-dipole interactions which promise to revolutionize AMO physics, for example by realizing realistic Hamiltonians in quantum simulation, by providing a new platform for quantum information, and by achieving a novel kind of quantum liquid. Despite its promises, the full quantum control of dipolar molecules has been over a decade in the making. The difficulties in either directly laser cooling molecules or in collisionally stabilizing their bulk samples have been major roadblocks that have hampered the development of this quantum system. The realization of a Bose-Einstein condensate of dipolar molecules has been a particularly elusive milestone. In this thesis, I report on the first observation of this quantum state of matter. The work that brought us to this achievement parallels the historical evolution of AMO physics in the last thirty years. To reach a BEC of molecules, we initially constructed a dual species experiment capable of realizing the simultaneous Bose-Einstein condensation of atomic sodium (Na) and cesium (Cs). Individual BECs of sodium and cesium were first reported in 1995 and 2003 respectively, while our experiment was the first instance of their concurrent condensation. The study of the Na-Cs interatomic scattering properties in an homogeneous magnetic field showed us the path to the Feshbach association of loosely-bound sodium-cesium (NaCs) molecules, a technique first demonstrated in 2006 for heteronuclear molecules but never attempted on our species. Following the Feschbach association, we determined a novel pathway to the molecular electronic, vibrational and rotational ground state using STIRAP. From this point, we found ourselves at the forefront of the field: bulk samples of bosonic molecules such as NaCs had neither been stabilized against collisional losses nor evaporatively cooled. At first, we successfully applied a single-frequency microwave shielding approach to decrease in-bulk losses by a factor of 200 and reach lifetimes on the order of 2 s, allowing us to measure high elastic scattering rates and characterize their dipolar anisotropy. Moreover, we demonstrated the first evaporative cooling of a bosonic molecular gas by increasing its phase-spacedensity by a factor of 20 and reaching a temperature of 36(5) nK. Since this proved insufficient to achieve Bose-Einstein condensation due to unexpected three-body losses, we introduced an enhanced microwave shielding technique, double microwave shielding. This further decreased loss rates enabling efficient evaporative cooling of our sample to a long-lived Bose-Einstein condensate of dipolar molecules. This new double microwave shielding technique also allows the tunability of the strength of dipole-dipole interaction, establishing ultracold bosonic dipolar molecules as a new quantum liquid for the exploration of many body physics. In addition to the experimental work on dipolar NaCs, we have theoretically explored the field of direct molecular laser cooling. Our aim was twofold: we aimed to expand the category of molecules that can be laser cooled and to simplify the identification of laser cycling schemes. For the former goal, we lifted the widespread assumption that only molecules with diagonal Franck-Condon factors could be laser cooled. For the latter, we decided to employ publicly available repositories of molecular transitions. A second consequence of the use of these databases is that they contain data on molecules of interest to other scientific fields, further establishing direct laser cooling as a technique that could be of interest beyond AMO physics. Our work was successful in that we identified laser cycling schemes for C₂ and OH+. To simplify the determination of laser cycling schemes, we developed a graph-based algorithm form their identification starting from spectroscopic data.

Les dernières évolutions technologiques en matière de laser ont permis l'observation de nouveaux phénomènes hautement non-linéaires lors de l'interaction de ces sources brèves et intenses avec la matière. Du point de vue moléculaire, ces processus, tels que l'affaiblissement de la liaison ou la génération d'harmonique, sont consécutifs à la création au sein de l'ion d'un paquet d'onde vibrationnel après ionisation par effet tunnel de la molécule neutre. Il est généralement admis dans nombre d'articles que cette transition électronique conduit à une distribution des états de vibration conforme à celle prédite par l'approximation de Condon. Afin de vérifier la validité de cette assertion, nous avons mis en place un dispositif expérimental original permettant une mesure fiable de l'excitation vibrationnelle de H2+ après ionisation de la molécule neutre par un champ laser intense. Les résultats obtenus contredisent fortement le postulat selon lequel la transition aurait lieu préférentiellement à la séparation internucléaire d'équilibre (approximation de Condon) et remettent en cause les interprétations des expériences de dynamique moléculaire précédentes. En faisant varier la longueur d'onde, nous avons également mis en évidence les processus dominants et l'importance de la structure électronique au sein des différents domaines d'ionisation. Ces mesures ouvrent des perspectives intéressantes quant à la mise en place d'expériences de dynamique moléculaire utilisant un faisceau d'ions moléculaires d'excitation vibrationnelle connue. / The continuing development of femtosecond laser technology allows the study of new, highly non-linear phenomena in laser-molecule interaction. Most scientists agree that the first step of all these processes is the creation of an elctronic wavepacket in the continuum by tunnelling ionisation of the neutral molecule. As a rule, most publications were also unanimous about the vibrational population created in the ion, asumed to be properly described by the classical Condon approximation. Thanks to a unique setup we were able to measure in an unambiguous way the vibrational distribution created by intense-laser-field ionisation. Our study shows a discrepancy between our results and the one predicted by the Condon approximation. Other wavelength-dependent measurements reveal the dominant processes for the different ionisation regimes. These results open new experimental perspectives for the study of the molecular dynamics.

Cette thèse consiste en une étude de jonctions tunnels à Quantum Dot (QD) unique. Le second chapitre présentera une introduction aux concepts fondamentaux nécessaires à la description d’une telle jonction. Dans le troisième chapitre, je décrirais les méthodes de fabrications et de mesures. Dans le quatrième chapitre, je décrirais une étude par spectroscopie tunnel de QDs PbS. Trois signatures distinctes du couplage électron-phonon sont observées dans le spectre tunnel. Dans le régime de « remplissage de couches », la dégénérescence d’ordre 8 des états est levée par les interactions de Coulomb et permet l’observation des sous-bandes de phonons résultant de l’émission de phonons optiques. A faible tension, une bande interdite (gap) est observée dans le spectre, laquelle ne peut être fermée avec la tension de grille, ce qui est une signature caractéristique du blocage de France-Condon. A partir de ces données, un facteur de Huang-Rhys de l’ordre de S~1.7-2.5 est obtenu. Finalement, dans le régime de « shell-tunneling », les phonons optiques apparaissent dans le spectre tunnel inélastique d2I/dV2. Dans le cinquième chapitre, je présente une étude du spectre tunnel de QDs HgSe. En appliquant une tension de grille, différents niveaux d’occupation du QD peuvent être atteints. La valeur de la bande interdite change avec le niveau d’occupation. Une valeur de 0.9 eV est observée pour l’inter-bande (QD vide), une valeur de 0.2 eV est observée pour l’intra-bande (QD occupé par 2 e). Sous illumination, un photocourant peut être mesuré en utilisant une technique de démodulation. De cette mesure, une durée de vide τ ~ 65 μs est extraite pour la paire électron-trou photo-générée. / My PhD work consists in a study of single Quantum Dot (QD) tunnel junctions. Following the introduction chapter, the second chapter will present the fundamental concepts needed to describe a single QD junction, such as quantum confinement and Coulomb blockade. In the third chapter, I will describe the sample fabrication methods and the measurement setups. In the fourth chapter, I will describe a tunneling spectroscopy study of single PbS QDs. Three distinct signatures of strong electron-phonon coupling are observed in the Electron Tunneling Spectrum (ETS) of these QDs. In the shell-filling regime, the 8 times degeneracy of the electronic levels is lifted by the Coulomb interactions and allows the observation of phonon sub-bands that result from the emission of optical phonons. At low bias, a gap is observed in the spectrum that cannot be closed with the gate voltage, which is a distinguishing feature of the Franck-Condon blockade. From the data, a Huang-Rhys factor in the range S~ 1.7 - 2.5 is obtained. Finally, in the shell tunneling regime, the optical phonons appear in the inelastic ETS d2I/dV2. In the fifth chapter, I present a tunnel spectroscopy study of single HgSe QDs. Upon tuning the gate voltage, different occupation levels of the QD can be reached. The gap observed in the ETS changes with the occupation level. A large inter-band gap, 0.9~eV, is observed for the empty QDs, and an intra-band gap 0.2~eV is observed for the doubly occupied QD. Upon illuminating the QD, a photocurrent can be measured using an especially designed demodulation technique. From this measurement, the lifetime τ ~65 μs is extracted for the photogenerated electron-hole in the QD.

The aim of this work is to investigate projection operator method of deriva- tion of equations of motion for reduced density matrix and apply it to a model open quantum system. We gradually pass from quantum mechanical model of a molecule with one vibrational degree of freedom to an example of open quantum system relevant in the theory of nonlinear spectroscopy. In the thesis we present results of numerical simulations of the time evolution of the open quantum system performed with a program written for this purpose. We are specially concerned with simulations of the solution of the time-convolutionless generalized master equation up to the a second order of the perturbation expan- sion, and we show that under certain conditions it provides an exact solution of the problem. The text also contains derivation of the recurrence relations for the Franck-Condon factors for the most general case of two quantum harmonic oscillators in one space dimension, i. e. transformation matrix between two bases of the L2 (R) space determined by the solutions of the time-independent Schrödinger equation appropriate for these oscillators. 1

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Lanthanum (La)-promoted hydrocarbon activation reactions were carried out in a laser vaporization metal cluster beam source. Reaction products were identified by time-of-flight mass spectrometry, and the approximate ionization thresholds of La-hydrocarbon complexes were located with photoionization efficiency spectroscopy. The accurate ionization energies and vibrational frequencies of the La complexes were measured using mass analyzed threshold ionization (MATI) spectroscopy. Their molecular structures and electronic states were investigated by combing the MATI spectroscopic measurements with quantum chemical and Franck-Condon factor calculations. In this dissertation, La-mediated C-H and C-C bond activation reactions were investigated for several small alkynes (acetylene, propyne) and alkenes (propene, 1,3-butadiene, 1-butene). The C-H bond activation was observed for both alkynes and alkenes and the C-C bond activation for alkenes. The metal-hydrocarbon intermediates formed by the C-H or C-C bond cleavage reacted further with one or more parent hydrocarbon molecules to produce larger species by C-C bond coupling reactions. Structural isomers of the intermediates and products were identified within an energy range of several kilocalories per mole. Reaction pathways for the intermediate and product formations were studied by theoretical calculations. The ground electron configuration of La atom is 4d16s2.Upon the hydrocarbon coordination, La atom is excited to a 4d26s1 configuration to facilitate the formation of two La-C bonds. After the metal-hydrocarbon complex formation, only one electron is left in the 6s orbital of the metal center. Therefore, the most stable electronic state of the La complexes studied in this work is in a doublet spin state. Ionization of the doublet state yields a preferred singlet ion state. Although La is in the formal oxidation state of +2, the ionization energies of the metal-complexes are significantly lower than that of the free atom. This observation suggests that the concept of the formal oxidation state widely used in chemistry textbooks is not useful in predicting the change of the ionization energy of a metal atom upon ligation. Moreover, ionization has a very small effect on the geometry of the hydrocarbon fragment in each complex but significantly reduces the La-C distances as a result of an additional charge interaction.

Dans cette thèse, les domaines diamagnétiques appelés « domaines de Condon » sont étudiés. L'origine de ces domaines est la quantification des états d'énergie des électrons soumis à un champ magnétique en niveaux de Landau conduisant à l'effet de Haas-van Alphen (dHvA). Pour la première fois, la structure magnétique des domaines de Condon est détectée à la surface d'un échantillon en argent à l'aide d'une sonde locale de l'aimantation. Pour ce faire, un réseau contenant cinq microsondes de Hall ayant une résolution spatiale d'une dizaine de micromètres et une résolution magnétique de 1e-4 est utilisé. La période de la structure des domaines et l'épaisseur des parois sont estimées. L'hystérèse est observée dans l'effet dHvA en présence de domaines de Condon. La boucle d'hystérèse est détectée par les sondes de Hall DC et par des mesures standard de susceptibilité AC. La détection de l'hystérèse par la technique AC offre une méthode très sensible avec laquelle les diagrammes de phase des domaines de Condon sont déterminés pour un échantillon d'argent et pour un échantillon de béryllium.

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