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arXiv:2103.01605 · Physical Review Letters

Realization of a Townes Soliton in a Two-Component Planar Bose Gas

Brice Bakkali-Hassani, C. Maury, Y.-Q. Zou, É. Le Cerf, R. Saint-Jalm, P. C. M. Castilho, Sylvain Nascimbène, Jean Dalibard, J. Beugnon

Published Jul 9, 2021• 69 citations
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Abstract

Most experimental observations of solitons are limited to one-dimensional (1D) situations, where they are naturally stable. For instance, in 1D cold Bose gases, they exist for any attractive interaction strength g and particle number N. By contrast, in two dimensions, solitons appear only for discrete values of gN, the so-called Townes soliton being the most celebrated example. Here, we use a two-component Bose gas to prepare deterministically such a soliton: 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 explore various interaction strengths, atom numbers, and sizes and confirm the existence of a solitonic behavior for a specific value of gN and arbitrary sizes, a hallmark of scale invariance.

DOI
10.1103/physrevlett.127.023603

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•Dec 10, 2021•0 citations
Most experimental observations of solitons are limited to one-dimensional (1D) situations, where they are naturally stable. For instance, in 1D cold Bose gases, they exist for any attractive interaction strength g and particle number N. By contrast, in two dimensions, solitons appear only for discrete values of gN, the so-called Townes soliton being the most celebrated example. Here, we use a two-component Bose gas to prepare deterministically such a soliton: 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 explore various interaction strengths, atom numbers, and sizes and confirm the existence of a solitonic behavior for a specific value of gN and arbitrary sizes, a hallmark of scale invariance.
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.
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.
We report near-deterministic generation of two-dimensional (2D) matter-wave Townes solitons and a precision test on scale invariance in attractive 2D Bose gases. We induce a shape-controlled modulational instability in an elongated 2D matter wave to create an array of isolated solitary waves of various sizes and peak densities. We confirm scale invariance by observing the collapse of solitary-wave density profiles onto a single curve in a dimensionless coordinate rescaled according to their peak densities and observe that the scale-invariant profiles measured at different coupling constants g can further collapse onto the universal profile of Townes solitons. The reported scaling behavior is tested with a nearly 60-fold difference in soliton interaction energies and allows us to discuss the impact of a non-negligible magnetic dipole-dipole interaction (MDDI) on 2D scale invariance. We confirm that the effect of MDDI in our alkali cesium quasi-2D samples effectively conforms to the same scaling law governed by a contact interaction to well within our experiment uncertainty.
The form and stability of quantum vortices in Bose-Einstein condensates with attractive atomic interactions is elucidated. They appear as ring bright solitons, and are a generalization of the Townes soliton to nonzero winding number m. An infinite sequence of radially excited stationary states appear for each value of m, which are characterized by concentric matter-wave rings separated by nodes, in contrast to repulsive condensates, where no such set of states exists. It is shown that robustly stable as well as unstable regimes may be achieved in confined geometries, thereby suggesting that vortices and their radial excited states can be observed in experiments on attractive condensates in two dimensions.
We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time domain reveal detailed information about this dynamical process, from the hyperbolic growth of density waves, the formation of solitons, to the subsequent collision and collapse dynamics, demonstrating multiple universal behaviors in an attractive many-body system in association with the formation of a quasistationary state.
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.