In this Letter we report the investigation of transport and static properties of a Bose-Einstein condensate in a large-spaced optical lattice. The lattice spacing can be easily tuned starting from few micrometers by adjusting the relative angle of two partially reflective mirrors. We have performed in-situ imaging of the atoms trapped in the potential wells of a 20 microm spaced lattice. For a lattice spacing of 10 microm we have studied the transport properties of the system and the interference pattern after expansion, evidencing quite different results with respect to the physics of BECs in ordinary near-infrared standing wave lattices, owing to the different length and energy scales.
In this Letter we report the investigation of transport and static properties of a Bose-Einstein condensate in a large-spaced optical lattice. The lattice spacing can be easily tuned starting from few micrometers by adjusting the relative angle of two partially reflective mirrors. We have performed in-situ imaging of the atoms trapped in the potential wells of a 20 microm spaced lattice. For a lattice spacing of 10 microm we have studied the transport properties of the system and the interference pattern after expansion, evidencing quite different results with respect to the physics of BECs in ordinary near-infrared standing wave lattices, owing to the different length and energy scales.
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.
We study the phase coherence property of Bose−Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza–Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.
Bose-Einstein condensates (BECs) have proven to be remarkable systems with which to study some of the foundational models of condensed matter physics. The observation of a critical velocity for the breakdown of superfluidity in a BEC and the superfluid to Mott insulator transition observed in a BEC trapped by an optical lattice are but two examples of the, by now, dozens of exciting results in this field, which combines theoretical tools from condensed matter physics with state-of-the-art experimental techniques from ultra-cold atomic physics. However, any real condensed matter system has to contend with the effects of disorder, a phenomena notably absent in the inherently clean BEC systems. We have developed and implemented a way to add well characterized disorder in a controlled way to the otherwise clean BEC system using the light field from a laser speckle pattern. Using this system, we have investigated the effects of disorder or a single Gaussian defect, on the collective dipole motion of a BEC of 7Li in an optical trap. In addition, we perform transport experiments on a weakly interacting BEC expanding in a disordered one-dimensional atom wave-guide. We have observed that in such a system, the wave nature of matter can lead to spectacular and counterintuitive phenomena. Specifically, we verify that this system exhibits Anderson localization, a phenomena fundamentally resulting from the interference of multiply scattered matter waves. In such a state, the localized gas behaves as an insulator in a regime where it is classically expected to be conducting.\nWe also present results of experiments regarding a repulsive BEC scattering from a semi-permeable, single defect potential. We investigate the transport properties of such a system with special emphasis on the velocity and defect strength dependent dissipation of the collective dipole motion of the BEC. Finally, we present the results of our experiments on the scattering properties of bright matter wave solitons. We have observed fragmentation of the soliton in a disordered potential as well as both splitting and recombination of a soliton after interacting with a single repulsive defect potential.
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.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.
We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation $\ensuremath{\Delta}t$ are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on $\ensuremath{\Delta}t$ and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate.