Townes soliton and beyond: Non-miscible Bose mixtures in 2D

In these lecture notes, we discuss the physics of a two-dimensional binary mixture of Bose gases at zero temperature, close to the point where the two fluids tend to demix. We are interested in the case where one of the two fluids (the bath) fills the whole space, while the other one (the minority component) contains a finite number of atoms. We discuss under which condition the minority component can form a stable, localized wave packet, which we relate to the celebrated "Townes soliton". We discuss the formation of this soliton and the transition towards a droplet regime that occurs when the number of atoms in the minority component is increased. Our investigation is based on a macroscopic approach based on coupled Gross-Pitaevskii equations, and it is complemented by a microscopic analysis in terms of bath-mediated interactions between the particles of the minority component.Comment: 24 pages, 8 figures. Proceedings of the International School of Physics "Enrico Fermi", Course 211 - Quantum Mixtures with Ultra-cold Atoms, July 2022, directors: Rudolf Grimm, Massimo Inguscio, Sandro Stringar

Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction

The study of fractional Chern insulators and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular ultracold atoms in optical lattices, provide a promising platform to realize, manipulate, and understand such systems with a high degree of controllability. Recently, an atomic $\nu=1/2$ Laughlin state has been realized experimentally for a small system of two particles on 4 by 4 sites. The next challenge concerns the preparation of Laughlin states in extended systems, ultimately giving access to anyonic braiding statistics or gapless chiral edge-states in systems with open boundaries. Here, we propose and analyze an experimentally feasible scheme to grow larger Laughlin states by connecting multiple copies of the already existing 4-by-4-system. First, we present a minimal setting obtained by coupling two of such patches, producing an extended 8-by-4-system with four particles. Then, we analyze different preparation schemes, setting the focus on two shapes for the extended system, and discuss their respective advantages: While growing strip-like lattices could give experimental access to the central charge, square-like geometries are advantageous for creating quasi-hole excitations in view of braiding protocols. We highlight the robust quantization of the fractional quasi-hole charge upon using our preparation protocol. We benchmark the performance of our patchwork preparation scheme by comparing it to a protocol based on coupling one-dimensional chains. We find that the patchwork approach consistently gives higher target-state fidelities, especially for elongated systems. The results presented here pave the way towards near-term implementations of extended Laughlin states in quantum gas microscopes and the subsequent exploration of exotic properties of topologically ordered systems in experiments.Comment: 18 pages, 21 figure

Afonso de Albuquerque and the consumption of material culture in the Indian Ocean : 1506-1515

Nesta dissertação pretendem-se identificar as práticas de Afonso de Albuquerque enquanto consumidor de arte e avaliar até que ponto são paradigmáticas do seu tempo ou constituem um marco taxativo na periodização do consumo de arte. O governador (entre 1509 e 1515, mas na Ásia desde 1506) do que viria a ser o Estado da Índia teve um papel fundamental enquanto receptor e distribuidor de presentes diplomáticos, mas são também inteligíveis nos textos coevos apontamentos sobre as suas estratégias pessoais de usufruto e exibição de objectos artísticos. O texto explora como eram tomadas as decisões quanto à cultura material num momento de trocas intensas e sem precedentes com a Ásia. Argumenta-se que as práticas alteraram-se significativamente durante o período de governo de Albuquerque, motivadas pela sua (rápida) apreensão da geopolítica asiática. A dissertação divide-se em duas partes. Na primeira produz-se uma leitura historiográfica do interesse português na Ásia durante os anos finais do século XV e os primeiros do XVI. Esta síntese serve para mapear a conjuntura em que as situações descritas no segundo capítulo tiveram lugar. O segundo capítulo, mais extenso do que o precedente, produz uma leitura crítica das estratégias de consumo (aquisição, manutenção, exibição, e transferência de posse) de objectos por Afonso de Albuquerque. Divide-se em três tendências fundamentais que, de acordo com o que é proposto, formataram o interesse português por objectos asiáticos: os saques, as ofertas diplomáticas, e o consumo de corte. Na parte final do capítulo esboça-se uma proposta de interpretação de como foram recebidos em Portugal os objectos artísticos enviados, com diversos propósitos, por Afonso de Albuquerque.This thesis attempts to understand the practices of material culture consumption performed by Afonso de Albuquerque, and to assess if they served as a paradigm or a new tendency in sixteenth-century art consumption. The governor (from 1509-1515, but in Asia since 1506) of the future ‘Estado da Índia’ had a central role as a receiver and distributor of diplomatic gifts, but contemporary documents hint at a personal strategy in the use of art. This text explores how decisions were made in a moment of unprecedented and intensive material culture exchange with Asia. It will try to argue that practices changed in the course of Albuquerque’s government, following his (fast) apprehension of Asian geopolitics. This thesis is divided into two chapters. The first consists in a historiographical reading of the Portuguese interest in Asia during the late 15th and early 16th centuries. This summary serves as a basis to understand the stage where the episodes described in chapter II took place. Chapter II, far more extensive than the former, consists in a critical reading of the consumption strategies (acquisition, maintenance, display, and transfer) used by Afonso de Albuquerque. It is divided into three fundamental tendencies which, it is argued, shaped the Portuguese interest for Asiatica: looting, diplomatic gift-exchange, and courtly consumption. The final part of the chapter provides some suggestions on how the material culture sent by Albuquerque with various intents was received in Portugal

Test de l'invariance d'échelle dans un gaz de bosons bidimensionnel : préparation et caractérisation d'ondes solitaires

At a sufficiently large phase-space density, a Bose gas can be described by a macroscopic wave function subject to nonlinear dynamics. Degenerate Bose gases now constitute a major platform in the study of self-trapped nonlinear fields known as solitons or solitary waves. Up to now, most experimental observations of solitons have been restricted to one-dimensional situations, where they are generically stable. On the contrary, multidimensional solitary waves are more prone to instabilities and thus more challenging to observe experimentally. In this thesis, we produce solitary waves in a two-dimensional ultracold bosonic system. After presenting our experimental setup, we demonstrate our ability to produce deterministically a Townes soliton, a celebrated solution of the nonlinear Schrödinger equation in two dimensions. Our novel approach is based on a two-component mixture: starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We show that the soliton can exist with various sizes, a hallmark of the scale invariance present in the underlying model. We then confirm the relation linking the soliton atom number to the interaction strength. Our experimental observations are supported by further numerical and theoretical considerations. These studies also allow us to go beyond the simplest model sustaining a Townes soliton, by considering effects beyond the mean-field description. Finally, we propose a few experiments aimed at characterizing excited, moving, as well as colliding solitons.Lorsque la densité dans l'espace des phase d'un gaz de bosons identiques devient suffisamment élevée, il peut alors être décrit par une fonction d'onde macroscopique sujette à une dynamique non linéaire. Ces gaz quantiques sont aujourd'hui devenus des plateformes incontournables dans l'étude des solitons, objets fondamentaux de la physique non linéaire, aussi connus sous le nom d'ondes solitaires. Jusqu'à maintenant, l'essentiel des observations expérimentales de solitons a été limité à des situations unidimensionnelles, où les solitons sont stables naturellement. A l'inverse, les ondes solitaires de plus grande dimension sont généralement fragilisées par la présence d'instabilités dynamiques, rendant leur étude expérimentale plus difficile. Dans cette thèse, nous produisons des ondes solitaires à partir d'un système de bosons bidimensionnel. Après avoir présenté notre dispositif expérimental, nous montrons comment préparer de façon déterministe un soliton de Townes -- une solution remarquable de l'équation de Schrödinger non linéaire en dimension deux. Notre approche s'appuie sur l'utilisation d'un gaz à deux composantes : à partir d'un échantillon uniforme d'atomes dans un état interne donné, nous imprimons la fonction d'onde du soliton grâce à un transfert optique vers un autre état. Nous vérifions que le soliton peut exister sous diverses tailles, confirmant ainsi l'invariance d'échelle du modèle physique sous-jacent. Nous confirmons également la relation liant le nombre d'atomes contenu dans le soliton et la force des interactions. Nos observations expérimentales sont corroborées par des études numériques et théoriques. Par ailleurs, ces considérations nous permettent d'étudier la physique au-delà du modèle simple comportant un soliton de Townes, en considérant des effets allant au-delà du champ moyen. Finalement, nous proposons quelques expériences vouées à étudier les excitations, le mouvement et les collisions de tels solitons

Test de l'invariance d'échelle dans un gaz de bosons bidimensionnel : préparation et caractérisation d'ondes solitaires

At a sufficiently large phase-space density, a Bose gas can be described by a macroscopic wave function subject to nonlinear dynamics. Degenerate Bose gases now constitute a major platform in the study of self-trapped nonlinear fields known as solitons or solitary waves. Up to now, most experimental observations of solitons have been restricted to one-dimensional situations, where they are generically stable. On the contrary, multidimensional solitary waves are more prone to instabilities and thus more challenging to observe experimentally. In this thesis, we produce solitary waves in a two-dimensional ultracold bosonic system. After presenting our experimental setup, we demonstrate our ability to produce deterministically a Townes soliton, a celebrated solution of the nonlinear Schrödinger equation in two dimensions. Our novel approach is based on a two-component mixture: starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We show that the soliton can exist with various sizes, a hallmark of the scale invariance present in the underlying model. We then confirm the relation linking the soliton atom number to the interaction strength. Our experimental observations are supported by further numerical and theoretical considerations. These studies also allow us to go beyond the simplest model sustaining a Townes soliton, by considering effects beyond the mean-field description. Finally, we propose a few experiments aimed at characterizing excited, moving, as well as colliding solitons.Lorsque la densité dans l'espace des phase d'un gaz de bosons identiques devient suffisamment élevée, il peut alors être décrit par une fonction d'onde macroscopique sujette à une dynamique non linéaire. Ces gaz quantiques sont aujourd'hui devenus des plateformes incontournables dans l'étude des solitons, objets fondamentaux de la physique non linéaire, aussi connus sous le nom d'ondes solitaires. Jusqu'à maintenant, l'essentiel des observations expérimentales de solitons a été limité à des situations unidimensionnelles, où les solitons sont stables naturellement. A l'inverse, les ondes solitaires de plus grande dimension sont généralement fragilisées par la présence d'instabilités dynamiques, rendant leur étude expérimentale plus difficile. Dans cette thèse, nous produisons des ondes solitaires à partir d'un système de bosons bidimensionnel. Après avoir présenté notre dispositif expérimental, nous montrons comment préparer de façon déterministe un soliton de Townes -- une solution remarquable de l'équation de Schrödinger non linéaire en dimension deux. Notre approche s'appuie sur l'utilisation d'un gaz à deux composantes : à partir d'un échantillon uniforme d'atomes dans un état interne donné, nous imprimons la fonction d'onde du soliton grâce à un transfert optique vers un autre état. Nous vérifions que le soliton peut exister sous diverses tailles, confirmant ainsi l'invariance d'échelle du modèle physique sous-jacent. Nous confirmons également la relation liant le nombre d'atomes contenu dans le soliton et la force des interactions. Nos observations expérimentales sont corroborées par des études numériques et théoriques. Par ailleurs, ces considérations nous permettent d'étudier la physique au-delà du modèle simple comportant un soliton de Townes, en considérant des effets allant au-delà du champ moyen. Finalement, nous proposons quelques expériences vouées à étudier les excitations, le mouvement et les collisions de tels solitons

Test de l'invariance d'échelle dans un gaz de bosons bidimensionnel : préparation et caractérisation d'ondes solitaires

Lorsque la densité dans l'espace des phase d'un gaz de bosons identiques devient suffisamment élevée, il peut alors être décrit par une fonction d'onde macroscopique sujette à une dynamique non linéaire. Ces gaz quantiques sont aujourd'hui devenus des plateformes incontournables dans l'étude des solitons, objets fondamentaux de la physique non linéaire, aussi connus sous le nom d'ondes solitaires. Jusqu'à maintenant, l'essentiel des observations expérimentales de solitons a été limité à des situations unidimensionnelles, où les solitons sont stables naturellement. A l'inverse, les ondes solitaires de plus grande dimension sont généralement fragilisées par la présence d'instabilités dynamiques, rendant leur étude expérimentale plus difficile. Dans cette thèse, nous produisons des ondes solitaires à partir d'un système de bosons bidimensionnel. Après avoir présenté notre dispositif expérimental, nous montrons comment préparer de façon déterministe un soliton de Townes -- une solution remarquable de l'équation de Schrödinger non linéaire en dimension deux. Notre approche s'appuie sur l'utilisation d'un gaz à deux composantes : à partir d'un échantillon uniforme d'atomes dans un état interne donné, nous imprimons la fonction d'onde du soliton grâce à un transfert optique vers un autre état. Nous vérifions que le soliton peut exister sous diverses tailles, confirmant ainsi l'invariance d'échelle du modèle physique sous-jacent. Nous confirmons également la relation liant le nombre d'atomes contenu dans le soliton et la force des interactions. Nos observations expérimentales sont corroborées par des études numériques et théoriques. Par ailleurs, ces considérations nous permettent d'étudier la physique au-delà du modèle simple comportant un soliton de Townes, en considérant des effets allant au-delà du champ moyen. Finalement, nous proposons quelques expériences vouées à étudier les excitations, le mouvement et les collisions de tels solitons.At a sufficiently large phase-space density, a Bose gas can be described by a macroscopic wave function subject to nonlinear dynamics. Degenerate Bose gases now constitute a major platform in the study of self-trapped nonlinear fields known as solitons or solitary waves. Up to now, most experimental observations of solitons have been restricted to one-dimensional situations, where they are generically stable. On the contrary, multidimensional solitary waves are more prone to instabilities and thus more challenging to observe experimentally. In this thesis, we produce solitary waves in a two-dimensional ultracold bosonic system. After presenting our experimental setup, we demonstrate our ability to produce deterministically a Townes soliton, a celebrated solution of the nonlinear Schrödinger equation in two dimensions. Our novel approach is based on a two-component mixture: starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We show that the soliton can exist with various sizes, a hallmark of the scale invariance present in the underlying model. We then confirm the relation linking the soliton atom number to the interaction strength. Our experimental observations are supported by further numerical and theoretical considerations. These studies also allow us to go beyond the simplest model sustaining a Townes soliton, by considering effects beyond the mean-field description. Finally, we propose a few experiments aimed at characterizing excited, moving, as well as colliding solitons