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Multi-solitonic states in a Bose-Einstein Condensate mixture

G. Brochier

Published Mar 13, 2026• 0 citations
Publisher

Abstract

Once its phase-space density is high enough, an interacting dilute Bose gas can be described by a macroscopic wave function obeying nonlinear dynamics. Ultracold Bose gases thus form coherent quantum fluids whose behavior becomes particularly rich in one dimension, where interactions and integrability tightly guide the evolution. In this thesis, we study a two-component weakly interacting 1D Bose gas that maps onto the attractive nonlinear Schrödinger equation (NLSE) in a certain limit, and more generally onto the Landau-Lifshitz equation (LLE), governing spin-chains. This correspondence enables the controlled preparation and exploration of multi-soliton solutions of both models. We first realize NLSE multi-solitons and characterize their dynamics, including their distinctive breathing behavior. Using the full LLE mapping, we then extend this implementation to multi-solitons with arbitrary depletion, thereby accessing a broader family of solitons and revealing features intrinsic to the underlying spin-chain description. Finally, we investigate weak integrability breaking and show that it drives the decomposition of multi-solitons into their constituents, rendering their encoded scattering data experimentally accessible. This provides a controlled pathway to probe integrable structures, opening prospects for studying soliton gases, interacting nonlinear waves, and the emergence of complex dynamics from nearly integrable systems.

DOI
10.70675/06b4ec0ez4105z4f49za3a4z6b322d18796b

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Once its phase-space density is high enough, an interacting dilute Bose gas can be described by a macroscopic wave function obeying nonlinear dynamics. Ultracold Bose gases thus form coherent quantum fluids whose behavior becomes particularly rich in one dimension, where interactions and integrability tightly guide the evolution. In this thesis, we study a two-component weakly interacting 1D Bose gas that maps onto the attractive nonlinear Schrödinger equation (NLSE) in a certain limit, and more generally onto the Landau-Lifshitz equation (LLE), governing spin-chains. This correspondence enables the controlled preparation and exploration of multi-soliton solutions of both models. We first realize NLSE multi-solitons and characterize their dynamics, including their distinctive breathing behavior. Using the full LLE mapping, we then extend this implementation to multi-solitons with arbitrary depletion, thereby accessing a broader family of solitons and revealing features intrinsic to the underlying spin-chain description. Finally, we investigate weak integrability breaking and show that it drives the decomposition of multi-solitons into their constituents, rendering their encoded scattering data experimentally accessible. This provides a controlled pathway to probe integrable structures, opening prospects for studying soliton gases, interacting nonlinear waves, and the emergence of complex dynamics from nearly integrable systems.
We present a series of experimental investigations on binary mixtures of Bose-Einstein condensates. Our focus lies on the regime where the interaction parameters place the system at the threshold of miscibility. We demonstrate that the dynamics of such mixtures can be effectively reduced to a single nonlinear equation. This framework is illustrated through the discussion of stable solitonic solutions in one and two dimensions. Furthermore, we show that employing a binary mixture enables exploration beyond the dynamics governed by the nonlinear Schrödinger equation, allowing us to address other fundamental equations in nonlinear physics, such as the Landau-Lifshitz equation describing the motion of spin chains in ferromagnetic materials.
États multi-solitons dans un mélange de spin de Condensats de Bose-Einstein Pour une densité de l'espace de phase suffisamment élevée, un gaz de Bose dilué en interaction peut être décrit par une fonction d'onde macroscopique obéissant à une dynamique non linéaire. Les gaz de Bose ultrafroids forment ainsi des fluides quantiques cohérents dont le comportement devient particulièrement riche à une dimension, où les interactions et l'intégrabilité guident fortement l'évolution. Dans cette thèse, nous étudions un gaz de Bose 1D à deux composantes en interaction faible, qui se décrit par l'équation de Schrödinger non linéaire attractive (NLSE) dans un certain régime, et plus généralement par l'équation de Landau-Lifshitz (LLE), régissant la dynamique de chaînes de spin. Cette correspondance permet la préparation et l'exploration contrôlées de solutions multi-solitons des deux modèles. Nous réalisons d'abord des solitons multiples NLSE et caractérisons leur dynamique, notamment leur comportement respirant distinctif. En utilisant une description complète via LLE, nous étendons ensuite cette mise en œuvre à des solitons multiples avec une déplétion arbitraire, accédant ainsi à une famille plus large de solitons et révélant des caractéristiques intrinsèques à la description sous-jacente de la chaîne de spin. Enfin, nous étudions la brisure de l'intégrabilité et montrons qu'elle entraîne la décomposition des multi-solitons en leurs constituants, rendant ainsi leurs données de diffusion accessibles expérimentalement. Cela fournit une voie contrôlée pour sonder les structures intégrables, ouvrant des perspectives pour l'étude des gaz de solitons, des ondes non linéaires en interaction et de l'émergence de dynamiques complexes à partir de systèmes presque intégrables.
We report the deterministic experimental realization and controlled fission of magnetic multi-soliton states in a uniform quasi-one-dimensional immiscible two-component Bose gas. We explore the Manakov regime, where the spin dynamics is well described by the easy-axis Landau-Lifshitz equation (LLE). The gauge equivalence between the easy-axis LLE and the attractive nonlinear Schrödinger equation (NLSE) enables the direct construction of magnetic multi-solitons from the well-known NLSE solutions. We observe the two- and three- soliton states, which exhibit robust breathing in quantitative agreement with integrable theory. By introducing a weak, localized perturbation, we controllably break integrability and induce the splitting of a two-soliton into its fundamental constituents. This process reveals the composite structure of multi-soliton states and realizes an experimental analog of the inverse scattering transform.
At sufficiently high phase space densities, the many-body state of a degenerate Bose gas can be described by a single macroscopic wavefunction that undergoes nonlinear dynamics. Ultracold Bose gases are a prominent platform in the field of nonlinear physics, enabling the study of stable stationary wavepackets, known as solitons. In these platforms, atom interactions are often weak and treated within a mean-field approach. However, interactions play a crucial role in the physics of these Bose gases and explain for example the formation mechanism of solitons or the emergence of a remarkable phase of matter: superfluidity. This thesis describes investigations on peculiar dynamics of ultracold Bose gases, which are approximated by zero-temperature physics. After introducing our experimental setup and its theoretical characterization, we discuss the survival of the superfluid property in spatially modulated systems, in connection with Leggett's seminal work in 1970 and the spectacular supersolid phase of matter. We then explore the physics of a specific type of 1D soliton that emerges in a weakly-immiscible two-component mixture, known as the magnetic soliton. Its name originates from its appearance in 1D ferromagnetic spin chains. Magnetic solitons exhibit a captivating periodic motion under a uniform force field, similar to the Bloch oscillations of electrons in solids. Finally, we introduce a new experimental setup for studying Rydberg excitations and the realization of an all-optical Bose-Einstein-Condensate.
This thesis describes a collection of experiments that explore interacting ultracold Bose gases, both in and out of equilibrium. Our experiments are performed using a gas of 39^{39}39K or 87^{87}87Rb confined in the uniform potential of an optical box trap, a novel testbed for quantum many-body phenomena. Our work focuses on weakly interacting non-equilibrium systems, moderately interacting systems that are still in equilibrium, and the unitary Bose gas which is both strongly interacting and eludes equilibrium. We begin with studies of weakly-interacting gases far from equilibrium, which feature ties to nonlinear wave phenomena. Highlights of our experiments include the direct measurement of turbulent-cascade fluxes, which (alongside realizing a tuneable dissipation scale) allow us to demonstrate the zeroth law of turbulence, and the first observation of weak collapse, a general type of nonlinear wave collapse predicted over 40 years ago. We then turn to moderately strong interactions, confronting existing theories of interacting quantum fluids. One of our most important results is the first quantitative measurement of the quantum depletion of a Bose–Einstein condensate, confirming a 70-year-old theory first developed to describe liquid helium. The culmination of our work explores the unitary Bose gas, where interparticle interactions are as strong as allowed by the laws of quantum mechanics. This strongly-correlated state promises tantalizing possibilities, including emergent universal behavior set solely by the gas density and novel forms of superfluidity. However, the strong interactions also lead to a complex interplay between coherent and dissipative dynamics. By disentangling these two processes, we have caught a glimpse of the promises that the unitary Bose gas holds. In particular, we observe the emergence of universal behavior, and find that the gas features a well defined quasi-equilibrium state, with a non-zero condensed fraction.
Bethe strings are bound states of constituent particles in a variety of interacting many-body one-dimensional (1D) integrable quantum models relevant to magnetism, nanophysics, cold atoms and beyond. They are the quantum analogue to bright solitons. As emergent fundamental excitations, they are predicted to collectively reshape observable equilibrium and dynamical properties. Small individual Bethe strings have recently been observed in quantum magnets and superconducting qubits. However, creating states featuring intermixtures of many, including large, strings remains an outstanding experimental challenge. Here, using nearly integrable ultracold Bose gases, we realize such intermixtures of Bethe strings out of equilibrium, by dynamically tuning interactions from repulsive to attractive. We measure the average binding energy of the strings, revealing the presence of bound states of more than six particles. We find further evidence for them in the momentum distribution and in Tan's contact, connected to the correlated density. Our data quantitatively agree with predictions from generalized hydrodynamics (GHD). Manipulating intermixtures of Bethe strings opens new avenues for understanding quantum coherence, nonlinear dynamics and thermalization in strongly-interacting 1D systems.