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Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study both theoretically and experimentally, especially in the quantum case. Here we explore a paradigmatic problem, the diffusion of a wavepacket, by employing ultra-cold atoms in a disordered lattice with controlled noise and tunable interaction. The presence of disorder leads to Anderson localization, while both interaction and noise tend to suppress localization and restore transport, although with completely different mechanisms. When only noise or interaction are present we observe a diffusion dynamics that can be explained by existing microscopic models. When noise and interaction are combined, we observe instead a complex anomalous diffusion. By combining experimental measurements with numerical simulations, we show that such anomalous behavior can be modeled with a generalized diffusion equation, in which the noise- and interaction-induced diffusions enter in an additive manner. Our study reveals also a more complex interplay between the two diffusion mechanisms in regimes of strong interaction or narrowband noise., Comment: 11 pages, 10 figures

We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow expansion with a subdiffusive behavior when a controlled repulsive interaction is added. The measured features of the subdiffusion are compared to numerical simulations and a heuristic model. The observations confirm the nature of subdiffusion as interaction-assisted hopping between localized states and highlight a role of the spatial correlation of the disorder., Comment: 8 pages, to be published on Physical Review Letters

One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization, and the realization of the disordered Bose-Hubbard model. There are however still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass., Comment: 16 pages, 8 figures

Clarifying the interplay of interactions and disorder is fundamental to the understanding of many quantum systems, including superfluid helium in porous media, granular and thin-film superconductors, and light propagating in disordered media. One central aspect for bosonic systems is the competition between disorder, which tends to localize particles, and weak repulsive interactions, which instead have a delocalizing effect. Since the required degree of independent control of the disorder and of the interactions is not easily achievable in most available physical systems, a systematic experimental investigation of this competition has so far not been possible. Here we employ an ultracold atomic Bose-Einstein condensate with tunable repulsive interactions in a quasi-periodic lattice potential to study this interplay in detail. We characterize the entire delocalization crossover through the study of the average local shape of the wavefunction, the spatial correlations, and the phase coherence. Three different regimes are identified and compared with theoretical expectations: an exponentially localized Anderson glass, the formation of locally coherent fragments, as well as a coherent, extended state. Our results illuminate the role of weak repulsive interactions on disordered bosonic systems and show that the system and the techniques we employ are promising for further investigations of disordered systems with interactions, also in the strongly correlated regime., Comment: 8 pages, 10 figures

In 1970 V. Efimov predicted a puzzling quantum-mechanical effect that is still of great interest today. He found that three particles subjected to a resonant pairwise interaction can join into an infinite number of loosely bound states even though each particle pair cannot bind. Interestingly, the properties of these aggregates, such as the peculiar geometric scaling of their energy spectrum, are universal, i.e. independent of the microscopic details of their components. Despite an extensive search in many different physical systems, including atoms, molecules and nuclei, the characteristic spectrum of Efimov trimer states still eludes observation. Here we report on the discovery of two bound trimer states of potassium atoms very close to the Efimov scenario, which we reveal by studying three-particle collisions in an ultracold gas. Our observation provides the first evidence of an Efimov spectrum and allows a direct test of its scaling behaviour, shedding new light onto the physics of few-body systems., Comment: 10 pages, 3 figures, 1 table

We study the role played by the magnetic dipole interaction in an atomic interferometer based on an alkali Bose-Einstein condensate with tunable scattering length. We tune the s-wave interaction to zero using a magnetic Feshbach resonance and measure the decoherence of the interferometer induced by the weak residual interaction between the magnetic dipoles of the atoms. We prove that with a proper choice of the scattering length it is possible to compensate for the dipolar interaction and extend the coherence time of the interferometer. We put in evidence the anisotropic character of the dipolar interaction by working with two different experimental configurations for which the minima of decoherence are achieved for a positive and a negative value of the scattering length, respectively. Our results are supported by a theoretical model we develop. This model indicates that the magnetic dipole interaction should not represent a serious source of decoherence in atom interferometers based on Bose-Einstein condensates., Comment: 4 pages, 3 figures

Guided-wave atom interferometers measure interference effects using atoms held in a confining potential. In one common implementation, the confinement is primarily two-dimensional, and the atoms move along the nearly free dimension under the influence of an off-resonant standing wave laser beam. In this configuration, residual confinement along the nominally free axis can introduce a phase gradient to the atoms that limits the arm separation of the interferometer. We experimentally investigate this effect in detail, and show that it can be alleviated by having the atoms undergo a more symmetric motion in the guide. This can be achieved by either using additional laser pulses or by allowing the atoms to freely oscillate in the potential. Using these techniques, we demonstrate interferometer measurement times up to 72 ms and arm separations up to 0.42 mm with a well controlled phase, or times of 0.91 s and separations of 1.7 mm with an uncontrolled phase., Comment: 14 pages, 6 figures

We demonstrate the effectiveness of a guided-wave Bose-Einstein condensate interferometer for practical measurements. Taking advantage of the large arm separations obtainable in our interferometer, the energy levels of the 87Rb atoms in one arm of the interferometer are shifted by a calibrated laser beam. The resulting phase shifts are used to determine the ac polarizability at a range of frequencies near and at the atomic resonance. The measured values are in good agreement with theoretical expectations. However, we observe a broadening of the transition near the resonance, an indication of collective light scattering effects. This nonlinearity may prove useful for the production and control of squeezed quantum states., Comment: 5 pages, three figures

The use of off-resonant standing light waves to manipulate ultracold atoms is investigated. Previous work has illustrated that optical pulses can provide efficient beam-splitting and reflection operations for atomic wave packets. The performance of these operations is characterized experimentally using Bose-Einstein condensates confined in a weak magnetic trap. Under optimum conditions, fidelities of up to 0.99 for beam splitting and 0.98 for reflection are observed, and splitting operations of up to third order are achieved. The dependence of the operations on light intensity and atomic velocity is measured and found to agree well with theoretical estimates., Comment: 5 pages, 3 figures. Revised text, fixed error in figure

A Michelson interferometer using Bose-Einstein condensates is demonstrated with coherence times of up to 44 ms and arm separations up to 0.18 mm. This arm separation is larger than that observed for any previous atom interferometer. The device uses atoms weakly confined in a magnetic guide and the atomic motion is controlled using Bragg interactions with an off-resonant standing wave laser beam., Comment: 4 pages, 3 figures

We describe a novel atom trap for Bose-Einstein condensates of 87Rb to be used in atom interferometry experiments. The trap is based on a time-orbiting potential waveguide. It supports the atoms against gravity while providing weak confinement to minimize interaction effects. We observe harmonic oscillation frequencies omega_x, omega_y, omega_z as low as 2 pi times (6.0,1.2,3.3) Hz. Up to 2 times 10^4 condensate atoms have been loaded into the trap, at estimated temperatures as low as 850 pK. We anticipate that interferometer measurement times of 1 s or more should be achievable in this device., Comment: 9 pages, 3 figures

We propose a novel method for trapping Bose-condensed atoms using a white-light interference fringe. Confinement frequencies of tens of kHz can be achieved in conjunction with trap depths of only a few micro-K. We estimate that lifetimes on the order of 10 s can be achieved for small numbers of atoms. The tight confinement and shallow depth permit tunneling processes to be used for studying interaction effects and for applications in quantum information., Comment: 10 pages with 3 figures