• cold atoms
• microscope
• Ytterbium

Abstract
When atoms are cooled down to temperature close to the absolute zero, they can no longer be described as a classical gas of point-like particles, and it becomes necessary to use the laws of quantum mechanics to describe their properties. Thanks to the high accuracy with which cold atomic systems can be controlled and manipulated, nowadays ultracold atomic gases provide a platform to emulate other many-body quantum systems, encountered in particular in condensed matter physics. For this reason we can say that cold atoms systems are "quantum simulators" of various many-body systems with interesting properties.
This thesis describes the research work I have done within the Bose Einstein Condensates group of Laboratoire Kastler Brossel, at Collège de France in Paris. The experiment to which I took part aims to simulate for electrically neutral atoms the analogue of an electromagnetic gauge potential in a bidimensional periodic system. The presence of a magnetic field breaks the lattice periodicity, and consequently the energetic band structure of the lattice changes, with the appearance of subbands separated by finite gaps. This turns in important consequences for the transport properties of the system (e.g., in the integer Quantum Hall Effect displayed by electronic systems). In the tight binding regime, where particle motion is described by tunneling between nearest-neighbors, the presence of the magnetic field results in a complex tunneling amplitude (the so-called Peierls factor). The simulation scheme of our experiment
is based precisely on mimicking this phase factor using laser dressing of ultracold Ytterbium atoms. The ground state 1S0 = g and the metastable excited state 1P1 = e are coupled by an ultranarrow optical transition (also used in optical atomic clocks). Driving this clock transition in a special, state-dependent lattice, one can realize the Peierls factor trough laser-assisted tunneling, as I explain briefly in the thesis.
In this manuscript I will focus on the production and characterization of an Ytterbium BEC, to be used as the first step for the realization of the gauge fields. I have been involved in the reconstruction of the main setup (at my arrival the vacuum chamber was disassembled for allowing some improvements). An ultracold cloud is produced after several laser cooling steps (Zeeman slowing and magneto optical trapping) performed in the so-called MOT chamber, followed by evaporation in an optical dipole trap in the Science chamber. Here the condensate is obtained, and then charged in the optical lattice. I describe the experimental aspects of each one of these steps, and briefly sketch the theoretical elements underlining them.
An essential aspect of quantum gases experiments is the acquisition of high-resolution images that provide density maps of the quantum gases under investigation. I will present in-depth tests of the existing imaging systems in the experiment, and also the design, construction and test of a new one with much improved performances. The tests aimed to infer informations about the optical resolution, limited in general by optical aberrations. In order to minimize the presence of these aberrations, I designed using a ray tracing software (OSLO) and optically characterized an aberration-corrected microscope objective for the new imaging system, operating with diffraction-limited resolution for a numerical aperture of 0.3 (limited by the vacuum system geometry). In particular the magnification, focal length, modulation transfer function and resolution have been measured.
For completeness I also report some preliminary results in setting up a repumper for atoms in the metastable state e. In the current experiment, only atoms in the ground state can be detected. It would be extremely useful in the future to also detect atoms in the excited state directly. This requires a repumper laser in order to quickly bring back atoms from the metastable state to the ground one with good and reproducible efficiency. Unfortunately, the laser broke, and the supplier could not repair within the duration of the research stay, leaving this project on hold status. Nevertheless, I report on the basic idea, as well as on spectroscopy measurements performed to locate nearby absorption lines that could be use to lock the laser frequency.