The physics of quantum particles in periodic potentials can be described in terms of Bloch waves and indeed many effects originally predicted for electrons moving in a lattice of ions have been observed for ultracold atoms in optical lattices. Interactions among the atoms forming the BEC are responsible for the nonlinear character of the Bloch waves, resulting in the onset of different kinds of instabilities, we have performed a detailed investigation of the stability regimes of a condensate in a moving optical lattice, separately addressing the effects and the timescales of energetic and dynamic instabilities. Spin-polarized Fermi gases are free from these effects and fundamental conduction phenomena, such as the crossover from a conducting to an insulating behaviour, the latter due to a localization of the particles in the lattice, can be observed
A Bose-Einstein condensate (BEC) is a macroscopic ensemble of atoms that collectively behaves as a single quantum-mechanical object. In this thesis I describe an apparatus built to create and study a BEC, as well as initial experiments carried out using a one-dimensional optical standing wave (optical lattice) to manipulate the BEC. In the first experiment, a weak optical lattice Bragg-reflects a BEC moving in a nearly harmonic trap. The Bragg reflection combined with the harmonic trapping potential cause the BEC to oscillate, much as light oscillates in an optical cavity. In the second experiment, a deep optical lattice applied to an atom cloud for a short duration is used to split and recombine the atomic wavefunction. By doing this we can create two different types of atom interferometer: a small-separation atom interferometer which works with either a BEC or a thermal gas, and a large-separation atom interferometer which works only with a BEC and whose interferometric arms are, in principle, separately addressable. In the third experiment, an optical lattice potential is slowly turned on. Under the influence of this lattice potential, the BEC loses its superfluid properties, but fully regains them when the lattice is turned back off. This behavior is consistent both with a reversible transition to a 1-D Mott insulator state and with mean-field effects in a deep lattice; both interpretations are discussed. In the latter part of this thesis I describe an apparatus designed to accommodate experiments involving both a BEC and an ion. The interactions between an ion and a BEC have never before been experimentally investigated. Our apparatus includes both the means to localize an ion by actively shielding against stray electric fields and to spatially image ions. This should allow future experiments in which a single ion is embedded in a BEC. In addition to imaging ions, the apparatus provides the capability to create high-resolution images of distributions of neutral atoms by photoionizing them and then quickly imaging them. I conclude the thesis with a discussion of future experiments exploring ion-BEC interactions.
An optical lattice is a periodic potential for atoms, created using a standing wave pattern of light. Due to the interaction between the light and the atoms, the atoms are attracted to either the nodes or the anti-nodes of the standing wave, depending on the exact wave lenght of the light. This means that if such a lattice is loaded with a sufficiently high number of ultracold atoms, a periodic array of atoms is obtained, we an interatomic distance of a few tenths of a micrometer. In order to obtain such a high number of cold atoms, one first has to create a so-called Bose-Einstein condensate. When an optical lattice is loaded from a Bose-Einstein condensate, it is possible to create a system in which every atom is in the lowest band of the lattice and there is on average one atom in each lattice site. Because the lattice potential is created with laser light, the depth of the lattice can easily be tuned by changing the intensity of the laser. When the intensity of the laser light is low, the atoms can tunnel from one site to the next. Due to this tunneling, the gas of atoms in the lattice will remain superfluid. However, if the intensity of the laser light is increased to above a certain critical value, a quantum phase transition occurs to a so-called Mott insulator. In this state, the atoms can no longer tunnel due to the fact that the on-site interaction between atoms becomes more important then the tunneling probability. In this PhD thesis, a description is given of the experimental setup that is being constructed in our group to create these systems in our lab. Also, a theoretical description is given of these systems and several important quantities our derived, such as the gap of the Mott-insulating state. Furthermore, an experiment is proposed that can be used to accurately measure this gap.
The first successful experimental realization of a Bose-Einstein condensate (BEC) in 1995 sparked a still growing research activity that in the meantime has led to beautiful and surprising results, such as the interference of matter waves [4], the Mott-superfluid phase transition [49] or the direct observation of Anderson localization of matter waves [10]. The strong interest in BECs arises, among others, from the possibility to investigate known but hard to study quantum systems on a rather macroscopic scale: for example one can load ultra-cold bosons into an optical lattice created by a standing light wave, and thereby simulate a solid state device. When it comes to a measurement on the BEC, however, essentially all measurement techniques result in the destruction of the condensate: for example in the so called “time of flight method” the optical lattice is switched off to observe the expansion of the trapped atoms and thereby directly visualize their momentum distribution, which highlights the condensed component [11]. In this thesis we elaborate on a means to probe a Bose-Einstein condensate from outside, with a scattering particle. The interaction between the probe particle and the bosons allows energy exchange between them, i.e., this setup includes inelastic scattering. After the scattering process, the condensate is still confined in the optical lattice and can therefore be used for further investigations. Of course, this method of probing a BEC is only then a serious alternative if the properties of the BEC can be inferred from the scattering signal. Besides outlining the scattering formalism, the central aim of this work is to show how the properties of the BEC can be deduced from those quantities accessible in a scattering experiment, like for example the transmission or the inelastic cross section. The other, equally strong motivation of this work concerns the signature of the interaction between the bosons in the scattering quantities. The dynamics of an analog classical system depends strongly on the interaction strength, which can induce a complex structure of the underlying phase space like, e.g., the appearance of a separatrix or even the emergence of chaotic dynamics in a globally mixed regular-chaotic phase space. We are interested to which extent such phase-space metamorphosis is reflected in the properties of the scattering particle. Currently light scattering (Bragg spectroscopy) on an optical lattice [78, 77] or rather on an optical lattice embedded into a cavity [62,68,19] is under intense investigation. These efforts predominantly aim at a characterization of the Mott-superfluid transition by specific scattering properties. In the present thesis we focus on condensates loaded in two and three lattice sites, with a large number of bosons. These systems exhibit a diversity of important physical effects (as we will see below) and thus are of paradigmatic relevance for a detailed understanding of multiparticle quantum dynamics in periodic potentials.
The transport of quantum particles in non ideal material media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quantum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percolation, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Understanding quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to revisit the problem of quantum conductivity and quantum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trapping of neutral atoms. Transport has been widely investigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the observation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.