Academic literature on the topic 'Ultracold atoms'

This article reviews the development in our laboratory of magnetic lattices comprising periodic arrays of magnetic microtraps created by patterned magnetic films to trap periodic arrays of ultracold atoms. Recent achievements include the realisation of multiple Bose-Einstein condensates in a 10 \(\mu\)m-period one-dimensional magnetic lattice; the fabrication of sub-micron-period square and triangular magnetic lattice structures suitable for quantum tunnelling experiments; the trapping of ultracold atoms in a sub-micron-period triangular magnetic lattice; and a proposal to use long-range interacting Rydberg atoms to achieve spin-spin interactions between sites in a large-spacing magnetic lattice.

The recent experimental progress in laser cooling and trapping of neutral atoms brings the atomic samples into the ultracold regime where the bosonic atoms and fermionic atoms are expected to have different dynamic behaviours in the laser fields. In this paper we systematically introduce the theoretical study of interaction of an ultracold atomic ensemble with a light wave in the frame of a vector quantum field theory. The many-body quantum correlation in the ultracold regime of atom optics is studied in terms of vector quantum field theory. A general formalism of nonlinear atom optics for a coherent atomic beam is developed.

Ultracold neutral atoms can be trapped in spatially inhomogeneous magnetic fields. In this paper, we present a theoretical model and demonstrate by using Landau-Zener tool that if the magnetic resonant transition region is very narrow, "potential barriers" appear and quantum reflection of such ultracold atoms can be observed in this region.

This thesis describes the dipole trapping of both metastable and ground state argon atoms. Metastable argon atoms are first Doppler-cooled down to ∼80 μK in a magneto- optical trap (MOT) on the 4s[3/2]2 to 4p[5/2]3 transitions. These were loaded into dipole traps formed both within the focus of a high-power CO2 laser beam and within an optical build-up cavity. The optical cavity’s well depth could be rapidly modulated: allowing efficient loading of the trap, characterisation of trapped atom temperature, and reduction of intensity noise. Collisional properties of the trapped metastable atoms were studied within the cavity and the Penning and associative losses from the trap calculated. Ground state noble gas atoms were also trapped for the first time. This was achieved by optically quenching metastable atoms to the ground state and then trapping the atoms in the cavity field. Although the ground state atoms could not be directly probed, we detected them by observing the additional collisional loss from co-trapped metastable argon atoms. This trap loss was used to determine an ultra-cold elastic cross section between the ground and metastable states. Using a type of parametric loss spectroscopy we also determined the polarisability of metastable argon at the trapping wavelength of 1064 nm.

Diese Dissertation widmet sich der theoretischen Beschreibung ultrakalter Atome in einem optischen Einschluss. Das Hauptaugenmerk liegt hierbei auf inelastischen Resonanzen, die durch die Kopplung von Schwerpunkts- und Relativbewegung durch Anharmonizitäten im externen Potenzial Zustande kommen, der Entwicklung einer Methode zur theoretischen Beschreibung von ultrakalten Wenigteilchensystemen in einem vielseitigen Einschlusspotenzial und der Quantensimulation von Attosekundenphysik mit ultrakalten Atomen.
This thesis aims for a theoretical description of ultracold trapped atoms. The main focus are resonance phenomena due to the coupling of center-of-mass and relative motion, the development of a theoretical approach to treat ultracold few-body systems in versatile trap potentials, and the quantum simulation of attosecond physics with ultracold atoms.

La teoria que descriu la Mecànica Quàntica ens ha permès el descobriment de molts fenòmens que prèviament eren ocults dins la seva naturalesa probabilística. Concretament, la Mecànica Quàntica va permetre veure l'ara anomenada dualitat ona-partícula en objectes extremadament petits. Aquest comportament apareix típicament en sistemes aïllats i per tant, els experiments on les partícules no interactuen amb l'ambient son fonamentals per l'estudi de sistemes i fenòmens quàntics. Els àtoms ultrafreds són sistemes en els quals els àtoms són refredats a temperatures de l'ordre dels nanokelvin i, en general, continguts en cambres d'ultra buit, d'aquesta manera els àtoms es poden estudiar en ambients altament controlables. Dins d'aquest camp, els condensats de Bose—Einstein (CBE) són un estat de la matèria particularment interessant. En els CBE totes les partícules d'un gas ultrafred de bosons ocupen de manera macroscòpica un mateix estat quàntic. Aquest comportament fa que els CBE siguin ideals per estudiar fenòmens quàntics a escala macroscòpica. En aquesta tesis, investiguem sistemes on, un fenomen quàntic sense anàleg a la mecànica clàssica, l'efecte túnel, és, o té el potencial de ser, el mecanisme que inicia la dinàmica. Podem dir que una partícula massiva pateix efecte túnel, quan aquesta és capaç d'accedir a una regió clàssicament prohibida sense tenir l'energia cinètica necessària per fer-ho. Aquest fenomen pot aparèixer en diferents formes, per exemple, una partícula pot creuar per efecte túnel una barrera quan hi col·lisiona o pot simplement oscil·lar entre dos pous de potencial separats per una barrera. En aquest context, primer hem considerat la implementació d'un interferòmetre amb solitons de matèria brillants en el qual el mecanisme de divisió ve donat per la col·lisió amb una barrera d'amplada finita. Fem servir solitons de matèria brillants en CBE en una dimensió ja que aquests presenten propietats, com ara un comportament no dispersiu, que els fa ideals per interferometria. Com hem comentat abans, també estem interessats en sistemes on l'efecte túnel apareix entre potencials propers. En aquests casos, per tal d'estimar l'amplitud d'acoblament entre els auto-estats de les trampes locals, és necessari conèixer el perfil de densitat de manera analítica, especialment a les zones de baixa densitat. Particularment, estudiem els perfils de densitat en CBE de dues components atrapats en potencials harmònics els quals es troben en fase miscible. La formulació analítica d'aquests perfils de densitat per a cada component al voltant de les regions de baixa densitat ve donada per equacions universals. Seguidament, ens fixem en la dinàmica d'àtoms individuals en potencials acoblats a través de l'efecte túnel. Primer estudiem processos de passatge adiabàtic que representen una eina robusta i eficient pel transport i la càrrega d'àtoms entre potencials cilíndricament simètrics i concèntrics. Els dos processos que hem investigat estan basats en els anàlegs en matèria del passatge adiabàtic ràpid (RAP en anglès) i de la transferència adiabàtica Raman estimulada (STIRAP en anglès). Amb aquestes dues tècniques, som capaços de transportar l'àtom entre dos i tres anells i de carregar un àtom ultrafred des d’un potencial harmònic a un anell concèntric. Tot seguit, continuem estudiant anells, però aquest cop en comptes de fer servir una configuració concèntrica, fem servir potencials acoblats lateralment, on demostrem que amplituds d'acoblament complexes apareixen de manera natural en la dinàmica dels estats de moment angular de l'àtom. També proposem com fer servir aquesta propietat per dissenyar estats obscurs espacials a través de la interferència quàntica. Finalment, demostrem com aquests estats obscurs es poden fer servir per crear estats de vora en una banda òptica de trampes harmòniques, tant fent servir el conjunt d'estat fonamentals de les trampes com amb els estats que porten moment angular. Primerament, mostrem que aquests estats són robustos i que poden ser obtinguts en altres geometries. A més, també suggerim que fent servir el número quàntic associat al moment angular com a dimensió sintètica, s’obre la possibilitat de simular sistemes quàntics tridimensionals amb xarxes de dues dimensions.
The theory of Quantum Mechanics led to the discovery of many phenomena that were previously hidden by its probabilistic nature. In particular, Quantum Mechanics brought to light the so-called wave-particle duality behavior of extremely small objects. This behavior is typically obtained in isolated systems, therefore experiments where particles do not interact with the environment are basic to study quantum systems and quantum phenomena. Ultracold atoms are systems where atoms are cooled down to temperatures of the order of nanokelvin and, in general, kept in ultrahigh vacuum chambers, such that they can be studied in a highly controlled environment. Within this field, Bose—Einstein condensates (BECs) are a particular appealing state of matter where all the particles of an ultracold bose gas, macroscopically occupy a single quantum state. This behavior makes BECs ideal for studying quantum phenomena at a macroscopic scale. In this thesis, we investigate systems where, a quantum phenomenon that has no analogue in classical mechanics, the quantum tunneling is, or has the potential to be, the mechanism that triggers the dynamics. A tunneling event occurs whenever a massive particle is able to access a classically forbidden region of space without having the necessary kinetic energy to do it. Note that this phenomenon can arise in different scenarios, for instance a particle can tunnel when colliding with a potential barrier or it can simply oscillate between two separated wells separated by a potential barrier. In this context, first, we consider the implementation of a matter-wave bright soliton interferometer whose splitting mechanism is based on tunneling through a finite width barrier. We use bright matter-wave solitons in one dimensional BECs as they present properties, such as their dispersionless behavior, that are ideal for interferometric purposes. As mentioned previously, we are also interested on systems where tunneling occurs between neighboring potentials. For those cases, in order to estimate the tunneling amplitudes that couple the eigenstates of the local traps, the analytical density profiles of the eigenstates are required, especially around the low density regions. In particular, we study the density profiles of harmonically trapped two-component BECs within the miscible phase. The analytical formulation of the density profiles of each component around the low density regions is given by means of universal equations. We then turn our attention to the dynamics of single atoms in tunnel-coupled potentials. First, we study spatial adiabatic passage processes as a robust and efficient technique to transport and load single atoms between cylindrically symmetric concentric potentials. The two processes investigated are based on the matter-wave analogues of the rapid adiabatic passage and of the stimulated Raman adiabatic passage. With these techniques, we are able to transport the atom between two and three rings and to load an ultracold atom from a harmonic potential to a concentric ring. Next, we continue investigating ring potentials, but instead of using concentric rings, we use sided-coupled rings and we demonstrate that in this system, complex tunneling amplitudes appear naturally in the dynamics of single atom angular momentum states. We also propose to use this feature to engineer spatial dark states through quantum interference. Finally, we demonstrate how spatial dark states can be used to create edge-like states in an optical ribbon either for the manifold of ground states of the traps forming the ribbon or for states carrying orbital angular momentum. We show that these states are robust and that can be extended to other geometries. In addition, we suggest to use the winding number associated to the angular momentum as a synthetic dimension opening the possibility to quantum simulate three dimensional systems with two dimensional lattices.

Time-varying fields are widely used to extend the accessible range of trapping potentials for ultracold atoms. This work explores two very different examples of such fields, in the radiofrequency and optical regimes, whose interactions with trapped atoms can both be described in terms of the dressed atom picture. Forming the basis of this work are radiofrequency dressed adiabatic potentials based on macroscopic trapping coils. Atoms are confined at the south pole of the resultant oblate spheroidal trapping surfaces. This work describes the extension of these potentials by two different methods: the application of multiple dressing radiofrequencies, and addition of a rapidly-scanned optical dipole trap. This is the first experimental demonstration of a multiple-radiofrequency dressed adiabatic potential, explored using ultracold ⁸⁷Rb atoms confined in a highly configurable double well. Due to the independent generation of each constituent dressing frequency, the depth of each trapping well and the height of the barrier are easily manipulated, enabling precise and reliable transfer of atoms between the available trapping geometries. Experimental work includes an exploration of the potential-shaping capabilities of the three-radiofrequency system, and characterisation of the potential landscape using radiofrequency spectroscopy with good agreement to the eigenvalues numerically calculated using Floquet theory. This initial exploration of multiple-radiofrequency techniques lays the groundwork for applications in studying double well physics in a two-dimensional system, and independent state or species selective manipulation of trapped atoms. The potential shaping capabilities of this method can also be extended by applying additional trapping frequencies. In a supplementary line of experimental work, an optical dipole trapping system has been constructed, and the trapping beam aligned to the lower surface of the radiofrequency dressed trapping shell in order to sculpt the radial confinement. Beam shaping is achieved using an acousto-optic deflector, which can be used to produce either a composite array of static deflected beams, a rapidly-scanned painted potential, or some combination of the two approaches. The development and extension of the experimental apparatus required to implement these enhanced dressed state potentials is explored, and the challenges of their experimental implementation considered.

Die vorliegende Arbeit befasst sich mit der Wechselwirkung ultrakalter Atome mit der Mode eines optischen Resonators hoher Güte. Die Atome sind dabei in einem periodischen Potenzial gefangen, dessen Periodizität nicht kommensurabel mit der Wellenlänge des Resonators ist. Ein Laser regt die Atome an und sie streuen Photonen in die Resonatormode, wobei die Emission inkohärent ist, falls die Laue- Bedingung nicht erfüllt ist. Dieser Fall wird betrachtet und es werden Bedingungen ermittelt, für welche nichtlineare optische Prozesse auftreten können. Die Eigenschaften des Lichtes werden untersucht, wenn sich das System entweder wie ein parametrischer Verstärker verhält oder wie eine Lichtquelle mit "Antibunching"- Statistik. Weiterhin kann eine stationäre Verschränkung zwischen Licht und Spinwellen der Atome erzeugt werden. Im zweiten Teil wird die Situation betrachtet, in der die Nullpunktsbewegung der Atome für die Atom-Licht-Wechselwirkung relevant ist. Für große Parameterbereiche zeigen numerische Berechnungen, dass die Rückwirkung des Resonators die Formierung eines lokalen Schachbrettmusters in der atomaren Dichteverteilung erzeugt. Die einzelnen Atomgruppe dieses Musters stehen zueinander in fester Phasenbeziehung, was zur Erhöhung der Zahl der Resonatorphotonen führt.
In this thesis we investigate the interactions between ultracold atoms confined by a periodic potential and a mode of a high-finesse optical cavity whose wavelength is incommensurate with the potential periodicity. The atoms are driven by a probe laser and can scatter photons into the cavity field. When the von-Laue condition is not satisfied, there is no coherent emission into the cavity mode. We consider this situation and identify conditions for which different nonlinear optical processes can occur. We characterize the properties of the light when the system can either operate as a degenerate parametric amplifier or as a source of antibunched light. Moreover, we show that the stationary entanglement between the light and spinwavemodes of the array can be generated. In the second part we consider the regime in which the zero-point motions of the atoms become relevant in the dynamics of atom-photon interactions. Numerical calculations show that for large parameter regions, cavity backaction forces the atoms into clusters with a local checkerboard density distribution. The clusters are phase-locked to one another so as to maximize the number of intracavity photons.

The present thesis studies a variety of cold atomic systems in artificial gauge fields. In the first part we focus on fractional quantum Hall effects, asking whether interesting topological states can be realized with cold atoms. We start by making a close connection to solid-state systems and first consider fermionic atoms with dipolar interactions. Assuming the system to be in the Laughlin state, we evaluate the energy gap in the thermodynamic limit as a measure for the robustness of the state. We show that it can be increased by additionally applying a non-Abelian gauge field squeezing the Landau levels. We then switch to bosonic systems with repulsive contact interactions. Artificial magnetic fields for cold bosons have extensively been discussed before in the context of rotating Bose gases. We follow a different approach where the gauge field is due to an atom-laser coupling. Thus, transitions between different dressed states have to be included. They are shown to break the cylindrical symmetry of the system. Modifying the Laughlin state and the Moore-Read state accordingly, we determine the parameter regimes where they are good representations for the ground state of the system obtained via exact diagonalization. One of the most interesting feature of fractional quantum Hall states is the anyonic behavior of their excitations. We therefore also study quasiholes in the Laughlin state and the modified Laughlin state. They are shown to posses anyonic properties, which become manifest even in small systems. Moreover, the dynamics of a single quasihole causes visible traces in the density of the system which allow to clearly distinguish the Laughlin regime from less correlated phases. In the latter, a sequence of collapses and revivals of the quasihole can be observed, which is absent in the Laughlin regime. Extending our study to bosonic systems with a pesudospin-1/2 degree of freedom, we discuss the formation of strongly correlated spin singlets. Strikingly, at filling v=4/3, the system is described by a state with non-Abelian excitations, which is constructed as the zero-energy ground state of repulsive three-body contact interactions. Systems with internal degrees of freedom also allow for implementing artificial spin-orbit coupling. It is shown to give rise to a variety of incompressible states. In the second part of the thesis, we concentrate on condensed system. Bose-Einstein condensates with spin-orbit coupling are shown to have a degeneracy on the mean-field level, which is lifted by quantum and thermal fluctuations. The system becomes experimentally feasible in three dimensions, where the condensate depletion remains finite, and thus allow for an experimental observation of this order-by-disorder mechanism. Finally, we study the influence of Abelian and non-Abelian gauge fields on the quantum phase transitions of bosons in a square optical lattice. Re-entrant superfluid phases and superfluids at finite momenta are interesting properties featured by such systems.

A causa de la gran flexibilitat que ofereixen en la seva manipulació i control, els sistemes d’àtoms ultrafreds són ideals per simular un ampli ventall de models de matèria condensada i constitueixen una plataforma molt prometedora per a la implementació de noves tecnologies quàntiques. En aquest context, l’atomtrònica s’ha establert recentment com un nou camp de recerca que té per objectiu crear circuits d’ones de matèria amb àtoms ultrafreds en micro trampes òptiques versàtils, amb el doble propòsit d’explorar nous fenòmens físics i de construir dispositius quàntics com ara sensors o ordinadors. Els circuits atomtrònics més senzills estan formats per potencials en forma d’anell, els quals proporcionen camins tancats pels àtoms que admeten de manera natural estats de Moment Angular Orbital (MAO). Inspirats per aquests avenços, en aquesta tesi investiguem diversos sistemes que comparteixen la característica d’estar formats per àtoms ultrafreds en estats amb MAO en potencials amb simetria cilíndrica. El nostre interès es centra en tres aspectes dels estats amb MAO: el seu potencial per fabricar sensors, les seves aplicacions en la simulació de models de magnetisme quàntic, i les possibilitats que ofereixen per obtenir estats topològics. Primerament, considerem un Condensat de Bose-Einstein (CBE) atrapat en un únic potencial en forma d’anell i preparat en una superposició d’estats amb MAO que roten en direccions oposades. El perfil d’aquesta superposició mostra una línia de mínima densitat que gira a causa de la interacció no lineal entre els àtoms. Després de derivar una expressió que relaciona la freqüència d’aquesta rotació amb la força de les interaccions, proposem protocols que permeten fer servir el sistema com un sensor d’interaccions a dos cossos, camps magnètics i rotacions. A continuació, explorem diferents configuracions de potencials acoblats lateralment en les quals els àtoms ultrafreds experimenten una dinàmica d’efecte túnel governada per amplituds complexes amb fases que es poden variar modificant la geometria del sistema. En primer lloc, estudiem una xarxa en forma de cadena de diamant carregada amb àtoms no interactuants en estats amb MAO. En aquest sistema, les fases de les amplituds d’efecte túnel complexes donen lloc a una estructura de bandes topològica amb els seus corresponents estats de vora. A més, ajustant de manera adequada les amplituds d’efecte túnel es pot obtenir un espectre d’energies composat únicament de bandes planes. En aquest cas, el sistema mostra confinament d’Aharonov-Bohm. A continuació, analitzem una família de sistemes consistent en distribucions de potencials d’anell amb una geometria flexible plenes amb bosons fortament correlacionats en estats amb MAO. Ens centrem en el règim d’aïllant de Mott amb un àtom per trampa, en el qual es pot establir una correspondència entre estats amb MAO i d’espín-1/2. Mostrem que, ordenant les trampes de manera adequada, aquests sistemes poden simular diferents models d’espí d’interès relacionats amb un model de Heisenberg general. Seguidament, ens tornem a fixar en la cadena de diamant per investigar la física de dos bosons amb interacció atractiva en el límit en el qual totes les bandes són planes. En aquesta situació, l’energia cinètica no juga cap paper i les propietats del sistema venen determinades únicament per les interaccions. Mostrem que el sector de baixa energia de l’espectre d’estats de dos bosons es pot descriure en termes de models efectius d’una sola partícula que són topològicament no trivials. Finalment, estudiem una xarxa quadrada en dues dimensions amb diferents separacions fora i dintre de la cel·la unitat. Demostrem que aquest sistema constitueix un exemple d’aïllant topològic de segon ordre, presentant un moment quadrupolar finit i estats de cantonada protegits.
Debido a la gran flexibilidad que ofrecen en su manipulación y control, los sistemas de átomos ultrafríos son ideales para simular un amplio abanico de modelos de materia condensada y constituyen una plataforma muy prometedora para la implementación de nuevas tecnologías cuánticas. En este contexto, la atomtrónica se ha establecido recientemente como un nuevo campo de investigación cuyo objetivo es crear circuitos de ondas de materia con átomos ultrafríos manipulados mediante micro trampas ópticas versátiles, con el doble propósito de explorar nuevos fenómenos físicos y de construir dispositivos cuánticos como sensores u ordenadores. Los circuitos atomtrónicos más sencillos están formados por potenciales en forma de anillo, los cuales proporcionan caminos cerrados para los átomos que admiten de manera natural estados con Momento Angular Orbital (MAO). Inspirados por estos avances, en esta tesis investigamos diversos sistemas que comparten la característica de estar formados por átomos ultrafríos con carga de MAO en potenciales con simetría cilíndrica. Nuestro interés se centra en tres aspectos de los estados con MAO: su potencial para fabricar sensores, sus aplicaciones en la simulación de modelos de magnetismo cuántico, y las posibilidades que ofrecen para obtener estados topológicos. Empezamos considerando un condensado de Bose-Einstein (CBE) atrapado en un único potencial en forma de anillo y preparado en una superposición de estados con MAO que rotan en direcciones opuestas. El perfil de esta superposición muestra una línea de mínima densidad que gira debido a la interacción no lineal entre los átomos. Después de deducir una expresión que relaciona la frecuencia de esta rotación con la fuerza de las interacciones, proponemos protocolos que permiten utilizar el sistema como un sensor de interacciones a dos cuerpos, campos magnéticos y rotaciones. A continuación, estudiamos diferentes configuraciones de potenciales acoplados lateralmente en las que los átomos ultrafríos experimentan una dinámica de efecto túnel gobernada por amplitudes complejas con fases que se pueden variar modificando la geometría del sistema. En primer lugar, exploramos una red en forma de cadena de diamante llena con átomos no interactuantes en estados con MAO. En este sistema, las fases de las amplitudes de efecto túnel complejas dan lugar a una estructura de bandas topológica con sus correspondientes estados de borde. Además, ajustando de forma adecuada las amplitudes de efecto túnel, se puede obtener un espectro de energías compuesto únicamente de bandas planas. En este caso, el sistema muestra confinamiento de Aharonov-Bohm. En segundo lugar, analizamos una familia de sistemas consistente en distribuciones de potenciales de anillo con una geometría flexible llenas con bosones fuertemente correlacionados en estados de MAO. Nos centramos en el régimen de aislante de Mott con un átomo por trampa, en el que se puede establecer una correspondencia entre estados con MAO y de espín-1/2. Mostramos que, ordenando las trampas de manera adecuada, estos sistemas pueden simular diferentes modelos de espín de interés relacionados con un modelo de Heisenberg general. Seguidamente nos volvemos a fijar en la cadena de diamante para investigar la física de dos bosones con interacción atractiva en el límite en el que todas las bandas son planas. En esta situación, la energía cinética no juega ningún papel y las propiedades del sistema vienen determinadas únicamente por las interacciones. Mostramos que el sector de baja energía del espectro de estados de dos bosones se puede describir en términos de modelos efectivos de una sola partícula que son topológicamente no triviales. Finalmente, estudiamos una red cuadrada en dos dimensiones con diferentes separaciones fuera y dentro de la celda unidad. Demostramos que este sistema constituye un ejemplo de aislante topológico de segundo orden, presentando un momento cuadrupolar finito y estados de esquina protegidos.
Due to their high degree of tunability and controllability, ultracold atom systems constitute an ideal playground for simulating a wide variety of condensed matter models and are one of the most promising platforms for the implementation of novel quantum technologies. In this context, the emerging field of atomtronics aims at realizing matter-wave circuits with ultracold atoms in versatile optical micro-traps. These efforts have a two-fold purpose: exploring new fundamental physics and constructing quantum devices such as sensors or computers. The simplest atomtronic circuits are formed by ring-shaped potentials, which provide closed loops for the atoms that naturally support Orbital Angular Momentum (OAM) states. Motivated by these advances, in this thesis we investigate different systems that have the common characteristic of being formed by ultracold atoms carrying OAM in cylindrically symmetric potentials. Our interest is focused on three aspects of OAM states: their potential use for sensing purposes, their applications as quantum simulators of models of quantum magnetism, and the possibilities that they offer for realizing topological phases of matter. We start by considering a Bose Einstein Condensate (BEC) trapped in a single ring potential and prepared in a superposition of counter-rotating OAM states. The density profile of this state has a minimal line that rotates due to the non-linear interaction between the atoms. After deriving an expression that relates the frequency of this rotation with the strength of the interactions, we propose protocols to use the system as a device for sensing two-body interactions, magnetic fields and rotations. Next, we explore several configurations of side-coupled potentials where ultracold atoms in OAM states experience tunnelling dynamics that are governed by complex amplitudes with phases that can be tuned by modifying the geometry of the system. First, we study a lattice with a diamond chain shape filled with non-interacting ultracold atoms carrying OAM. In this system, the phases in the tunnelling rates give rise to a topological band structure with its corresponding protected edge states. Furthermore, a proper tuning of the tunneling parameters may lead to an energy spectrum composed entirely of flat bands. In this scenario, the system exhibits Aharonov-Bohm caging. We then analyse a family of systems consisting of arrays of ring potentials with a flexible geometry filled with strongly correlated bosons in OAM states. We focus on the Mott insulator regime at unit filling, for which one can establish a correspondence between OAM and spin-1/2 states. We demonstrate that by properly arranging the traps, these systems can realize different spin models of interest related to a general Heisenberg model. Then, we turn our attention back to the diamond chain to examine the physics of two attractively interacting bosons in the limit when all bands are flat. In this situation, the kinetic energy is frozen and the properties of the system are solely determined by the interactions. We show that the low-energy sector of the two-boson spectrum can be described in terms of effective single-particle models that are topologically non-trivial. Finally, we investigate a two-dimensional square lattice with different intra- and inter-cell spacings in the non-interacting limit. We show that this system constitutes an example of a second-order topological insulator, displaying a finite quadrupole moment and protected corner states.

Recent advances in optical stopping and trapping of particles now permit the investigation of atom collision dynamics at temperatures below 1 mK. We discuss three specific examples of inelastic processes appropriate for study in this new energy domain: radiative association; collisional heating; and associative ionization. Theoretical study of radiative association and collisional heating demonstrate new quantal features apparent in the total inelastic cross section due to the small number of partial waves contributing to the nuclear motion. We present the first experimental observation of an inelastic process, associative ionization between excited sodium atoms, and report a measure of the absolute cross section ~3 orders of magnitude larger than the cross section measured in conventional conditions.