The potential impact of quantum computing has stimulated a worldwide effort to develop the necessary experimental and theoretical resources. In the race for the quantum computer, several candidate systems have emerged, but the ultimate system is still unclear. We study theoretically how to realize atomic Fock states both for fermionic and bosonic atoms, mainly in one-dimensional optical traps. We demonstrate a new approach of quantum computing based on ultracold fermionic atomic Fock states in optical traps. With the Pauli exclusion principle, producing fermionic atomic Fock states in optical traps is straightforward. We find that laser culling of fermionic atoms in optical traps can produce a scalable number of ultra-high fidelity qubits. We show how each qubit can be independently prepared, and how to perform the required entanglement operations and detect the qubit states with spatially resolved, single-atom detection with adiabatic trap-splitting and fluorescence imaging. On the other hand, bosonic atoms have a strong tendency to stay together. One must rely on strong repulsive interactions to produce bosonic atomic Fock states. To simulate the physical conditions of producing Fock states with ultracold bosonic atoms, we study a many-boson system with arbitrary interaction strength using the Bethe ansatz method. This approach provides a general framework, enabling the study of Fock state production over a wide range of realistic experimental parameters. / text

Ce mémoire décrit la conception, la construction et la caractérisation d'un appareil capable de piéger et refroidir des atomes fermioniques de 6Li et 40K à des températures ultrabasses. L'étude des mélanges des gazes de Fermi dégénérés ouvre la porte vers la création des nouveaux systèmes quantiques à N corps. Nous présentons une nouvelle technique de refroidissement laser capable de refroidir simultanément 6Li et 40K à des températures sub-doppler basée sur un schéma de molasses grises fonctionnant sur la transition atomique D1. Cette stratégie améliore la densité dans le espace des phases des deux espèces atomiques à 104, la valeur la plus élevée rapportée dans la littérature pour le refroidissement laser du 6Li et du40K. L'optimisation d'un dispositif capable de transporter un nuage atomique piégé magnétiquement de l'enceinte MOT à une cellule de science est décrite. Dans cette cellule on effectue du refroidissement évaporatif d'abord dans un piège magnétique quadripolaire dont le zéro du champ est interdit par un potentiel répulsif et après dans un piège optique dipolaire. Nous rapportons la production d'un gaz quantique de Fermi dégénéré de 1.1x106 atomes de 40K dans un piège dipolaire croisé avec T/TF = 0.27,ouvrant la voie à la création des superfluides de 40K en interactions fortes. / This thesis describes the design, construction and characterization of an apparat us capable of trapping and cooling fermionic atoms of 6Li and 40K to ultracold temperatures.The study of mixtures of degenerate Fermi gases opens the door for the creation of new many-body quantum systems.We present a novel laser cooling technique able to simultaneously cool 6Li and 40K to the sub-Doppler regime based on the gray molasses scheme operating on the D1 atomic transition. This strategy enhances the phase space density of both atomic species to 104, the highest value reported in the literature for laser cooled 6Li and 40K. The optimization of a device able to transport a magnetically trapped atomic cloud from the MOT chamber to a science cell is described. In this cell evaporative cooling is performed first in a plugged magnetic quadrupole trap and then in an optical dipoletrap. We report the production of a quantum degenerate Fermi gas of 1.1x106 atoms40K in a crossed dipole trap with T/TF = 0.27, paving the way for the creation of strongly interacting superfluids of 40K.

<p>    </p> <p><em>P</em>-wave Efimov physics for three equal mass fermions with different symmetries has been modeled using two-body interactions of Lennard-Jones potentials between each pair of Fermi atoms, and is predicted to modify the long range three-body interaction potential energies, but without producing a real Efimov effect. Our analysis treats the following trimer angular momenta and parities, L^Π = 0⁺,1⁺,1⁻ and 2⁻, for either three spin-up fermions (↑↑↑), or two spin-up and one spin-down fermion (↑↓↑). Our results for the long range behavior in some of those cases agree with previous work by Werner and Castin and by Blume <em>et al.</em>, namely in cases where the s-wave scattering length goes to infinity. This thesis extends those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and considers additional unitarity scenarios where the p-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized. For the equal mass fermionic trimers with two different spin components near the unitary limit are shown to possess a universal van der Waals bound or resonance state near s-wave unitarity, when p-wave interactions are included between the particles with equal spin. Our treatment uses a single-channel Lennard-Jones interaction with long range two-body van der Waals potentials. While it is well-known that there is no true Efimov effect that would produce an infinite number of bound states in the unitary limit for these fermionic systems, we demonstrate that another type of universality emerges for the symmetry L^Π = 1⁻. The universality is a remnant of Efimov physics that exists in this system at p-wave unitarity, and it leads to modified threshold and scaling laws in that limit. Application of our model to the system of three lithium atoms studied experimentally by Du, Zhang, and Thomas [Phys. Rev. Lett. <strong>102</strong>, 250402 (2009)] yields a detailed interpretation of their measured three-body recombination loss rates. </p>