The technique of laser cooling, whose basic idea was proposed in 1975 [1], provided the development of many important areas like high-resolution spectroscopy [2], atomic clocks [3] and quantum gases confined in magnetic or optical traps [4, 5]. Among the techniques applied to cooling neutral atoms is the optical molasses [6] that will be explored in this work. Here we study the standard molasses and a new alternated molasses configuration, which consists of turning on just one pair of counter-propagating laser beams per cycle, and alternating this pair between the three spatial directions. We analyse the two techniques under the lens of the radiation force, by exploring a semiclassical treatment, in order to obtain the minimum energy attained by each of them at the end of the cooling process. We compare, then, these two cooling techniques, pointing out their advantages.

We report on an investigation of a method that applies simultaneously two different mathematical models in order to optimize the design of a Zeeman Slower towards the implementation of ultra cold atoms in solid state physics. We introduce the implementation of a finite element simulation that allows us to predict with great accuracy the magnetic field intensity profile generated by the proposed design. Through the prediction of the behavior of the Zeeman Slower a greater control is acquired, which allows the optimization of the different experimental variables. We applied the method in the design of a multilayer solenoidal "Spin-Flip" Zeeman Slower for strontium atoms. The magnetic intensity profile generated by the Zeeman Slower is in agreement with the magnetic field strength profile necessary for the atom cooling and tends to zero in both end sides. The latter terms are essential in order to optimize the amount of trapped and cooled atoms.

Nosotros presentamos un método que utiliza simultaneamente dos modelos matemáticos, con el objetivo de optimizar el diseño de un desacelerador Zeeman, con miras a la implementación de átomos ultrafríos a la física del estado sólido. Proponemos la implementación novedosa de una simulación por medio de elementos finitos con la cual es posible predecir con mucha precisión el perfil de intensidad del campo magnético generado por el diseño realizado. Al poder predecir el comportamiento del desacelerador Zeeman se adquiere un mayor control, a partir del cual es posible optimizar las diferentes variables experimentales. El método propuesto es aplicado para el diseño y construcción de un desacelerador Zeeman solenoidal de tipo "Spin Flip" para átomos de estroncio. El perfil de intensidades de campo magnético generado por el desacelerador Zeeman construido concuerda con el perfil de intensidades de campo magnético necesario para el enfriamiento de átomos de estroncio y tiene además la ventaja que la intensidad de campo magnético tiende a cero en los extremos. Ambas condiciones permiten incrementar la cantidad de átomos enfriados y atrapados.

Abstract Introduction: On occasions, Combinatorial Optimization Problems (COP), like the University Course Timetabling Problem (CTTP), can be solved using Operational Research (OR) techniques; however, when the problem increases in size, finding a solution becomes more complex. This type of problem is NP-hard, requiring procedures like metaheuristic methods in order to solve the problem. This paper confronts a real world situation in Mexico concerning the Curriculum-Based Timetabling Problem (CB-CTT). Each institution have their own operationals rules due to the modeling of the problema is unique because preserve their own characteristics. First, as part of the contribution to the solution of the problem, it was implemented a Mediation Software (MS) in order to organize the raw data and eliminate a hard constraint related to curricula. Subsequently, the problem handle here was split into five instances in accordance to the courses that share the same physical space, which was solved using a typical Simulated Annealing (SA) metaheuristic. In addition, The problem was satisfactorily solved, assigning 9620 lectures in 174.5 hours approximatly, providing a solution without partitioning the problem into two subproblems, impacting positivly reducing the labor time, and providing a feasible and without errors educational timetable to the whole university. Method: The Simulated Annealing (SA) algorithm is a meta-heuristic search for global optimization problems; the overall objective of such algorithms is to find a good approximation to the optimal value of a function in a large search space. This value is called "global or local optimum".The name and inspiration comes from the process of annealing the steel and ceramics, a technique that involves heating and then slowly cooling the material to vary its physical properties. The heat causes the atoms increase their energy and can thus move from their initial (a local minimum energy) positions; slow cooling gives them more likely to recrystallize in configurations with lower energy than the initial (minimum overall) .The method was independently described by Scott Kirkpatrick, C. Daniel Gelatt and Mario P. Vecchi at 1983. Results: Concluding this work, is shown that is confronted a large real CB-CTT problem with 2507 courses conform by 1, 2, 3, 4, 5, 6, 7, or 8 lectures or hours, totalizing 9620 lectures; being able to assign into 316 rooms with different capacities, and also satisfying all the requested of 2178 professors and 1668 groups. Discussion or Conclusion: In this research were developed various instances, where 3 of 5 are considered by the research community like large instances, and solved with SA Algorithm, regarding all feasible solutions. Thereby the metaheuristic methods are relatively good depending on the instance, and for this institution can offer a good solution.

Resumen Introducción: En ocasiones, los problemas de Optimización Combinatoria (COP), tal como el Problema de Calendarización de horarios (CTTP), se puede resolver utilizando técnicas Investigación Operativa (IO); sin embargo, cuando el problema aumenta de tamaño, la búsqueda de una solución se vuelve más compleja. Este tipo de problema es NP-duro por lo que requiere de procedimientos como métodos metaheurísticos con el fin de resolver el problema. Este trabajo aborda un Problema real en una Institución de Educación Superior Mexicana acerca de la Calendarización de horarios basada en la Curricula (CB-CTT). Cada institución tiene sus propias reglas operacionales, por lo tanto la modelación del problema es único ya que conserva sus propias características. Primero como parte de la aportación a la solución del problema, se elaboró un Software de Mediación (MS) con el fin de organizar los datos en bruto y eliminar la restricción dura en relación con los planes de estudio. Posteriormente, el problema se dividió en cinco instancias, de acuerdo a los cursos que comparten el mismo espacio físico, los cuales fueron resueltos mediante el algoritmo tradicional de Recocido Simulado (SA).El problema fue resuelto de manera satisfactoria, obteniendo la asignación de 9620 sesiones en 174.5 horas aproximadamente, aportando una solución sin particionar el problema en dos subproblemas, impactando positivamente la reducción del tiempo de elaboración de los horarios, proporcionando un horario factible y sin errores para toda la universidad. Método: El Algoritmo de Recocido Simulado, cristalización simulada o enfriamiento simulado, es un algoritmo de búsqueda metaheurística para problemas de optimización; el objetivo general de este tipo de algoritmos es encontrar una buena aproximación al valor óptimo de una función en un espacio de búsqueda grande. A este valor se lo denomina "óptimo local u óptimo global". El nombre e inspiración viene del proceso de recocido del acero y cerámicas, una técnica que consiste en calentar y luego enfriar lentamente el material para variar sus propiedades físicas. El calor causa que los átomos aumenten su energía y que puedan así desplazarse de sus posiciones iniciales (un mínimo local de energía); el enfriamiento lento les da mayores probabilidades de recristalizar en configuraciones con menor energía que la inicial (mínimo global). El método fue descrito independientemente por Scott Kirkpatrick, C. Daniel Gelatt y Mario P. Vecchi en 1983. Resultados: Como conclusión este trabajo muestra la solución a un problema real de gran tamaño CB-CTT con 2507 cursos conformados por 1, 2, 3, 4, 5, 6, 7 ó 8 sesiones u horas por curso, totalizando 9620 sesiones; se logró asignar en 316 habitaciones con diferentes capacidades, y también satisfacer cada una de las solicitudes de 2178 profesores y 1668 grupos. Discusión o Conclusión: En esta investigación se han desarrollado diversas instancias, donde 3 de los 5 son considerados por la comunidad científica como instancias grandes, que se resuelve con el algoritmo SA, proporcionando todas las soluciones factibles. De esta manera se confirma que los métodos metaheurísticos son relativamente buenos dependiendo de las circunstancias y para esta institución puede ofrecer una buena solución.

Neste trabalho desenvolvemos um modelo clássico para descrever o processo de resfriamento atômico devido à interação de um átomo com uma configuração de feixes de luz laser. Derivamos uma expressão para a força de radiação sobre o átomo com a descrição detalhada da origem de cada um dos termos envolvidos. Por fim construímos um paralelo entre o aspecto clássico e as particularidades da natureza quântica da interação radiação matéria.

In this work we develop a classical model to describe the laser cooling process due to the interaction between an atom and a configuration of laser beams. We derive an expression for the radiation force exerted on the atom, detailing the origin of each term involved. Lastly, we built a parallel between the classical model and the peculiarities of the quantum nature of the interaction radiation-matter.

O desenvolvimento científico nos permite trabalhar hoje com gases em temperaturas muito inferiores aos 10-6 K. Estes gases, uma vez obtidos por técnicas de resfriamento óptico, precisam ser caracterizados com relaçãao às suas propriedades termodinâmicas. a a medida da temperatura. Dentre tais propriedades está a medida da temperatura. Neste trabalho mostramos de forma tutorial como são medidas tais baixas temperaturas, através de técnicas de tempo de voo. Tais técnicas combinam conhecimento básico de mecânica, termodinâmica dentre outros tópicos convencionalmente estudados nos cursos básicos de física.

Scientific development allows us to work today with gas at temperatures far below the 10-6 K . These gases are obtained by optical cooling techniques and need to be characterized for their thermodynamic properties. Among these properties is the temperature measurement. We show in a tutorial how low temperatures are measured using techniques called time of flight. These techniques combine basic knowledge of mechanics, thermodynamics, among other topics conventionally studied in the basic physics course.

Relógios atômicos de feixe de Césio têm sido a base para diversas aplicações em ciência e tecnologia nas últimas quatro décadas. Testes de leis fundamentais de física, buscas por mínimas variações em constantes fundamentais, sincronização de redes de telecomunicações e o funcionamento do sistema de posicionamento global, baseado em satélites de navegação, não seriam possíveis sem os relógios atômicos. A adoção de técnicas de aprisionamento e resfriamento ópticos tem permitido um grande avanço na precisão dos relógios atômicos. Chafarizes de átomos frios e relógios compactos de átomos frios também têm sido desenvolvidos. Precisões de medida de algumas partes em 1015 foram demonstradas para relógios do tipo chafariz de átomos frios. Apresentamos uma visão geral do programa de metrologia de tempo e freqüência baseado em átomos de césio, em desenvolvimento na USP de São Carlos. Estas atividades consistem na construção e caracterização de relógios do tipo feixe atômico e de outros, utilizando átomos frios. Discutimos os princípios básicos, construção, avaliação e importantes aplicações de relógios atômicos no programa brasileiro.

Cesium atomic beam clocks have been the workhorse for many demanding applications in science and technology for the past four decades. Tests of the fundamental laws of physics and the search for minute changes in fundamental constants, the synchronization of telecommunication networks, and realization of the satellite-based global positioning system would not be possible without atomic clocks. The adoption of optical cooling and trapping techniques, has produced a major advance in atomic clock precision. Cold-atom fountain and compact cold-atom clocks have also been developed. Measurement precision of a few parts in 10(15) has been demonstrated for a cold-atom fountain clock. We present here an overview of the time and frequency metrology program based on cesium atoms under development at USP São Carlos. This activity consists of construction and characterization of atomic-beam, and several variations of cold-atom clocks. We discuss the basic working principles, construction, evaluation, and important applications of atomic clocks in the Brazilian program.

We describe the experimental apparatus and the methods to achieve Bose-Einstein condensation in 87Rb atoms. Atoms are first laser cooled in a standard double magneto-optical trap setup and then transferred into a QUIC trap. The system is brought to quantum degeneracy selectively removing the hottest atoms from the trap by radio-frequency radiation. We also present the main theoretical aspects of the Bose-Einstein condensation phenomena in atomic gases.

We use the theory of coupled Gross-Pitaevskii equations to derive an expression for the current density of the propagating atoms coupled out of the condensate under the influence of gravity. By describing the propagation vector of the atoms and using a theoretical definition of the coherence length, we calculate the coherence lengths of 37K, 141Ce, and 249Fm atom lasers numerically. Our calculation method is verified with the available experimental and theoretical data in the literature. The results showed a very good agreement.

Neste trabalho apresentamos um modelo simples de resfriamento evaporativo para átomos ultrafrios aprisionados. Este processo objetiva a diminuição da temperatura da amostra gasosa a partir da retirada dos átomos mais quentes desta e conseqüente retermalização dos remanescentes em uma temperatura mais baixa. O modelo parte da distribuição de Maxwell-Boltzmann de velocidades para a amostra atômica e permite o cálculo da temperatura e número de átomos remanescentes nesta após a retirada dos átomos mais quentes e retermalização. A partir dessas expressões simulamos o processo de resfriamento evaporativo realizado usualmente em experimentos, onde são retirados átomos cada vez mais frios após cada retermalização.

In this work we present a simple model to describe evaporative cooling for ultracold trapped atoms. This process is used to achieve low temperatures of the gaseous sample by removing the hottest atoms and subsequently rethermalizing the remaining atoms at a lower temperature. The model assumes a Maxwell-Boltzmann distribution of velocities in the atomic sample and allows the calculation of the temperature and the number of remaining atoms after the hottest atoms have been removed and the rethermalization has taken place. Using these expressions we simulate the process of evaporative cooling as it is usually carried out in experiments, where colder atoms are removed after each successive rethermalization.

Since the invention of magneto-optical trap (MOT), there have been several experimental and theoretical studies of the density distribution in these devices. To the best of our knowledge, only horizontal orbital traps have been observed, perpendicular to the coil axis. In this work we report the observation of distributions of trapped atoms in pure circular orbits without a nucleus whose orbital plane is tilted up to 90° with respect to the horizontal plane. We have used a stabilized time phase optical array in our experiments and conventional equipment used for MOT.

Desde la invencion de la trampa magneto-óptica (TMO), ha habido varios estudios teóricos y experimentales sobre la distribución de densidad en tales dispositivos. Las distribuciones logradas han sido solo en forma horizontal, perpendiculares con respecto del eje de la bobina. En este trabajo, reportamos la observacion de distribuciones de trampas atómicas en órbitas circulares sin núcleo cuyo plano orbital es inclinado hasta 90° con respecto del plano horizontal. Hemos usado en nuestros experimentos un arreglo de fase optica estabilizado en tiempo y equipo convencional usado en trampas magneto-opticas.

We describe a new system for laser cooling and trapping of neutral Calcium atoms employing the ¹S0 -¹ P1 resonant transition at 423 nm. An on-axis magneto-optical trap (MOT) is loaded from a Zeeman decelerated atomic beam. When a single laser is used, in order to avoid perturbation of the trap by the deceleration laser beam, this one has been tightly focused near the MOT center, with a waist size much smaller than the atomic cloud. In order to test the efficiency of this novel technique, we have then employed a second, independent decelerating laser, with a profile mode matched to the atomic beam. For an oven temperature of 580±C this system can load 1.2 (2) x 10(7) atoms in 16 (1) ms. By the spatial extension of the atomic cloud the one dimension rms velocity was estimated to be 136 (12) cm/s, corresponding to a temperature of 9 (2) mK. The variation of the number of trapped atoms as a function of laser detuning and intensity, trap magnetic field gradient and oven temperature is analyzed. Spatial structures of the trapped atoms, like stable rings created by vortex forces, have been observed. This is the first time that these structures, already observed in alkali-metal elements, are reported in MOTs of alkaline-earth elements.