Strongly correlated bosons and fermions in optical lattices

These lectures are an introduction to the physics of strongly correlated fermions and bosons. They are specially targeted for the experimental realizations that have been provided by cold atomic gases in optical lattices.Comment: Lectures presented at the Les Houches summer school 2010: "Many-Body Physics with Ultracold Gases", organized by C. Salomon and G. V. Shlyapniko

How many double squares can a string contain?

Counting the types of squares rather than their occurrences, we consider the problem of bounding the number of distinct squares in a string. Fraenkel and Simpson showed in 1998 that a string of length n contains at most 2n distinct squares. Ilie presented in 2007 an asymptotic upper bound of 2n - Theta(log n). We show that a string of length n contains at most 5n/3 distinct squares. This new upper bound is obtained by investigating the combinatorial structure of double squares and showing that a string of length n contains at most 2n/3 double squares. In addition, the established structural properties provide a novel proof of Fraenkel and Simpson's result.Comment: 29 pages, 20 figure

Modeling and simulation of drying operation in PVC powder production line: a pneumatic dryer model

A one-dimensional steady-state model is developed to simulate drying of PVC powder in a pneumatic dryer. In this model, a two-phase continuum model was used to describe the steady-state flow of a dilute dispersed phase (wet PVC powder) and a continuous phase (humid air) through dryer. The particle scale kinetics was obtained by immersion of a fixed mass of wet PVC’s particles (cake) in a batch dense fluidized bed containing inert hot particles (glass bead). The drying kinetics was described by a shrinking core type model and integrated in pneumatic dryer model. The results show that the inlet temperature is the most important parameter in the operation. The drying rate is controlled by a two-stage process. The first stage corresponds to the surface water evaporation, and the second to the pore water evaporation

Experimental observation of a strong mean flow induced by internal gravity waves

We report the experimental observation of a robust horizontal mean flow induced by internal gravity waves. A wave beam is forced at the lateral boundary of a tank filled with a linearly stratified fluid initially at rest. After a transient regime, a strong jet appears in the wave beam, with horizontal recirculations outside the wave beam. We present a simple physical mechanism predicting the growth rate of the mean flow and its initial spatial structure. We find good agreement with experimental results

Measurement of the Angular Dependence of the Dipole-Dipole Interaction Between Two Individual Rydberg Atoms at a F\"orster Resonance

We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a F\"orster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the F\"orster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantization axis. Our results show good agreement with the expected angular dependence $\propto(1-3\cos^2\theta)$, and represent an important step towards quantum state engineering in two-dimensional arrays of individual Rydberg atoms.Comment: 5 pages, 4 figure

Direct measurement of the van der Waals interaction between two Rydberg atoms

We report on the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. By working in a regime where the single-atom Rabi frequency of the laser used for excitation to the Rydberg state is comparable to the interaction energy, we observe a \emph{partial} Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. A quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and to observe its characteristic $C_6/R^6$ dependence. The magnitude of the measured $C_6$ coefficient agrees well with an \emph{ab-initio} theoretical calculation, and we observe its dramatic increase with the principal quantum number $n$ of the Rydberg state. Our results not only allow to test an important physical law, but also demonstrate a degree of experimental control which opens new perspectives in quantum information processing and quantum simulation using long-range interactions between the atoms.Comment: 4 pages, 3 figures, published versio