Dans cette thèse, nous décrivons les premières étapes de la construction d’une expérience de condensation d’atomes de sodium. À terme, le dispositif intégrera une puce à atomes qui permettra d’étudier la dynamique hors équilibre de gaz quantiques de dimensionnalité réduite, ainsi que leur dynamique de relaxation. Le montage expérimental est constitué d’un système laser stabilisé en fréquence sur une raie de l’iode, ainsi que d’une enceinte à ultra-vide. Cette dernière comporte un four produisant un jet atomique effusif qui est décéléré dans un ralentisseur Zeeman à aimants permanents.Nous obtenons alors un flux de 2 x 108 atomes/s, ce qui nous permet de charger près de 109 atomes dans un piège magnéto-optique. Durant la caractérisation du ralentisseur Zeeman, nous avons mis en évidence un mécanisme de redistribution des populations atomiques vers l’état F = 1 en amont du ralentisseur, induit par l’interaction avec le faisceau Zeeman. Après avoir confirmé ces observations par une résolution numérique des équations de Bloch optiques, nous avons mis en place un faisceau laser avec deux composantes de fréquence permettant de préparer initialement les atomes dans le sous-niveau F = 2;mF = - 2 pour les préserver de cet effet. Enfin, nous avons conçu un dispositif de transport magnétique permettant d’acheminer les atomes depuis l’enceinte du piège magnéto-optique vers l’enceinte du condensat. Des simulations de dynamique moléculaire nous ont permis de déterminer une séquence temporelle pour le déplacement du nuage performante, autorisant un transport de 65 cm en 1 s.Mots clés : sodium, condensation de Bose-Einstein, puce à atomes, ralentisseur Zeeman, aimants permanents, transport magnétique, dynamique moléculaire. / In this thesis, we describe the early stages in setting up a new experiment which aims at producing sodium Bose-Einstein condensates. The final apparatus will integrate an atomchip, enabling us to study the non-equilibrium dynamics of low-dimensional quantum gases, as well as their relaxation dynamics. The experimental setup comprises a laser system locked to an iodine rovibronic transition, and an ultra-high vacuum chamber. The latter consists of an oven producing an effusive atomic beam, which is decelerated in a Zeeman slower made with permanent magnets.We thus obtain a flux of 2 x 108 atoms/s, allowing the efficient loading of a magneto-optical trap containing up to 109 atoms. During the slower optimization, we observed a redistribution of the atomic populations from the F = 2 state to the F = 1 state before the entrance of the Zeeman slower. This depumping mechanism, induced by the interaction of the atoms with the slowing beam, has been confirmed by the numerical resolution of the optical Bloch equations describing the system. To circumvent this effect, we now prepare the atoms before the entrance of the slower in the  F = 2 mF = - 2  magnetic substate with a two-frequency light beam. Finally, we designed a magnetic transport system to transfer the atoms from the magnetooptical trap chamber to the condensate chamber. Based on the results of molecular dynamics simulations, we found a performing temporal sequence to move the magnetic trap, and we intend to efficiently transport the atoms over 65 cm in about 1 s.

<p>In this thesis regimes of quantum degeneracy of electrons and holes in semiconductor quantum wells in a strong magnetic field are studied theoretically. The coherent pairing of electrons and holes results in the formation of Bose-Einstein condensate of magnetic excitons in a single-particle state with wave vector <b>K</b>. We show that correlation effects due to coherent excitations drastically change the properties of excitonic gas, making possible the formation of a novel metastable state of dielectric liquid phase with positive compressibility consisting of condensed magnetoexcitons with finite momentum. On the other hand, virtual transitions to excited Landau levels cause a repulsive interaction between excitons with zero momentum, and the ground state of the system in this case is a Bose condensed gas of weakly repulsive excitons. We introduce explicitly the damping rate of the exciton level and show that three different phases can be realized in a single quantum well depending on the exciton density: excitonic dielectric liquid surrounded by weakly interacting gas of condensed excitons versus metallic electron-hole liquid. In the double quantum well system the phase transition from the excitonic dielectric liquid phase to the crystalline state of electrons and holes is predicted with the increase of the interwell separation and damping rate.</p><p>We used a framework of Green's function to investigate the collective elementary excitations of the system in the presence of Bose-Einstein condensate, introducing "anomalous" two-particle Green's functions and symmetry breaking terms into the Hamiltonian. The analytical solution of secular equation was obtained in the Hartree-Fock approximation and energy spectra were calculated. The Coulomb interactions in the system results in a multiple-branch structure of the collective excitations energy spectrum. Systematic classification of the branches is proposed, and the condition of the stability of the condensed excitonic phase is discussed.</p>

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 100-103).

The Ginibre gas is a Poisson point process dened on a space of loops related to the Feynman-Kac representation of the ideal Bose gas. Here we study thermodynamic limits of dierent ensembles via Martin-Dynkin boundary technique and show, in which way innitely long loops occur. This effect is the so-called Bose-Einstein condensation.

In this thesis regimes of quantum degeneracy of electrons and holes in semiconductor quantum wells in a strong magnetic field are studied theoretically. The coherent pairing of electrons and holes results in the formation of Bose-Einstein condensate of magnetic excitons in a single-particle state with wave vector <b>K</b>. We show that correlation effects due to coherent excitations drastically change the properties of excitonic gas, making possible the formation of a novel metastable state of dielectric liquid phase with positive compressibility consisting of condensed magnetoexcitons with finite momentum. On the other hand, virtual transitions to excited Landau levels cause a repulsive interaction between excitons with zero momentum, and the ground state of the system in this case is a Bose condensed gas of weakly repulsive excitons. We introduce explicitly the damping rate of the exciton level and show that three different phases can be realized in a single quantum well depending on the exciton density: excitonic dielectric liquid surrounded by weakly interacting gas of condensed excitons versus metallic electron-hole liquid. In the double quantum well system the phase transition from the excitonic dielectric liquid phase to the crystalline state of electrons and holes is predicted with the increase of the interwell separation and damping rate. We used a framework of Green's function to investigate the collective elementary excitations of the system in the presence of Bose-Einstein condensate, introducing "anomalous" two-particle Green's functions and symmetry breaking terms into the Hamiltonian. The analytical solution of secular equation was obtained in the Hartree-Fock approximation and energy spectra were calculated. The Coulomb interactions in the system results in a multiple-branch structure of the collective excitations energy spectrum. Systematic classification of the branches is proposed, and the condition of the stability of the condensed excitonic phase is discussed.

I have been one of the main responsible for building a new laboratory for Bose-Einstein condensation with 87Rb. In particular, the experimental setup has been designed for performing experiments with Bose-Einstein condensates load into optical lattices of variable geometries. All parts essential for Bose-Einstein condensation are in place. Atoms are collected in a magneto-optical trap, transferred to another vacuum chamber, with better vacuum, and trapped in another magneto-optical trap. Atoms are successfully transferred to a dark magnetic trap, and system for diagnostics with absorption imaging has been realized. We have not yet been able to form a Bose-Einstein condensate, due to a range of technical difficulties. Equipment for alignment of optical lattices with flexible geometry has been designed, built, and tested. This tool has been proven to work as desired, and there is a great potential for a range of unique experiments with Bose-Einstein condensates in optical lattices of various geometries, including superlattices and quasi-periodic lattices. Numerical studies have been made on anisotropic optical lattices, and the existence of a transition between a 2D superfluid phase and a 1D Mott-insulating phase has been confirmed. We have shown that the transition is of Berezinskii-Kosterlitz-Thouless type. In another numerical study it has been shown that using stimulated Raman transitions is a practical method for transferring atoms between states in a double optical lattice. Thus, it will be possible to transfer populations between the lattices, with further applications in qubit read/write operations.

This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.

We demonstrate electromagnetically-induced anomalous quantum dynamics of an exciton in a photonic band gap (PBG) - quantum well (QW) hetero-structure. Within the engineered electromagnetic vacuum of the PBG material, the exciton can propagate through the QW by the emission and re-absorption of virtual photons in addition to the conventional electronic hopping mechanism. When the exciton wavevector and recombination energy coincide nearly with a photonic band edge, the exciton kinetic energy is lowered by 1-10meV through coherent radiative hopping. This capture of the exciton by the photonic band edge is accompanied by strong electromagnetic dressing in which the exciton's renormalized effective mass is 4-5 orders of magnitude smaller than in the absence of the PBG environment. This dressed exciton exhibits a long radiative lifetime characteristic of a photon-atom bound state and is robust to phonon-assisted, re-combinative decay. By inheriting properties of the PBG electromagnetic vacuum, the bound electron-hole pair becomes a stable, ultra-mobile quantum excitation. Unlike traditional exciton-polariton modes created by placing a QW in a one-dimensional optical cavity, our PBG-QW excitons exhibit strong coupling to optical modes and retain a long lifetime. This is crucial for unambiguous observation of quantum coherence effects such as Bose-Einstein condensation. We present a model for the equilibrium quantum statistics of a condensate of repulsively interacting bosons in a two-dimensional trap. Particle correlations in the ground state are treated exactly, whereas interactions with excited particles are treated in a generalized Bogoliubov mean-field theory. This leads to a fundamental physical picture for condensation of interacting bosons through an anharmonic oscillator ground state coupled to excited Bogoliubov quasiparticles in which the quantum number statistics of condensate particles emerges self-consistently. Our anharmonic oscillator model for the exciton ground state manifold goes beyond the conceptual framework of traditional Bogoliubov theory. Below the Bose-Einstein condensation temperature, our model exhibits a crossover from particle bunching to Poissonian statistics and finally antibunching as temperature is lowered or as the trapping area is decreased. When applied to Bose condensation of long-lived dressed excitons in a photonic band gap material, our model suggests that this system may serve as a novel tunable source for non-classical states of light.

We demonstrate electromagnetically-induced anomalous quantum dynamics of an exciton in a photonic band gap (PBG) - quantum well (QW) hetero-structure. Within the engineered electromagnetic vacuum of the PBG material, the exciton can propagate through the QW by the emission and re-absorption of virtual photons in addition to the conventional electronic hopping mechanism. When the exciton wavevector and recombination energy coincide nearly with a photonic band edge, the exciton kinetic energy is lowered by 1-10meV through coherent radiative hopping. This capture of the exciton by the photonic band edge is accompanied by strong electromagnetic dressing in which the exciton's renormalized effective mass is 4-5 orders of magnitude smaller than in the absence of the PBG environment. This dressed exciton exhibits a long radiative lifetime characteristic of a photon-atom bound state and is robust to phonon-assisted, re-combinative decay. By inheriting properties of the PBG electromagnetic vacuum, the bound electron-hole pair becomes a stable, ultra-mobile quantum excitation. Unlike traditional exciton-polariton modes created by placing a QW in a one-dimensional optical cavity, our PBG-QW excitons exhibit strong coupling to optical modes and retain a long lifetime. This is crucial for unambiguous observation of quantum coherence effects such as Bose-Einstein condensation. We present a model for the equilibrium quantum statistics of a condensate of repulsively interacting bosons in a two-dimensional trap. Particle correlations in the ground state are treated exactly, whereas interactions with excited particles are treated in a generalized Bogoliubov mean-field theory. This leads to a fundamental physical picture for condensation of interacting bosons through an anharmonic oscillator ground state coupled to excited Bogoliubov quasiparticles in which the quantum number statistics of condensate particles emerges self-consistently. Our anharmonic oscillator model for the exciton ground state manifold goes beyond the conceptual framework of traditional Bogoliubov theory. Below the Bose-Einstein condensation temperature, our model exhibits a crossover from particle bunching to Poissonian statistics and finally antibunching as temperature is lowered or as the trapping area is decreased. When applied to Bose condensation of long-lived dressed excitons in a photonic band gap material, our model suggests that this system may serve as a novel tunable source for non-classical states of light.

The primary study of this thesis is the experimental realization of the non-equilibrium dynamics of a quantum inverted pendulum as examined in the collective spin dynamics of a spin-1 Bose-Einstein condensate. In order to compare experimental results with the simulation past the low depletion limit, current simulation techniques needed to be extended to model atomic loss. These extensions show that traditional measurements of the system evolution (e.g. measuring the mean and standard deviation of the evolving quantity) were insufficient in capturing the quantum nature of the evolution. It became necessary to look at higher order moments and cumulants of the distributions in order to capture the quantum fluctuations. Extending the implications of the loss model further, it is possible that the system evolves in a way previously unpredicted. Spin-mixing from a hyperbolic fixed point in the phase space and low noise atom counting form the core of the experiment to measure the evolution of the distributions of the spin populations. The evolution of the system is also compared to its classical analogue, the momentum-shortened inverted pendulum. The other experimental study in this thesis is mapping the mean-field phase space. The mean-field phase space consists of different energy contours that are divided into both phase-winding trajectories and closed orbits. These two regions are divided by a separatrix whose orbit has infinite period. Coherent states can be created fairly accurately within the phase space and allowed to evolve freely. The nature of their subsequent evolution provides the shape of the phase space orbit at that initial condition. From this analysis a prediction of the nature of the entire phase space is possible.