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.
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.
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.
Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we
The analogy between nonlinear optics and Bose-Einstein condensates (BECs) is a fascinating area of study due to the similarities in their underlying physical principles. Both systems are governed by similar nonlinear partial differential equations, which allow researchers to draw parallels between the behaviors observed in these two distinct fields. Among the phenomena observed, the soliton is of particular interest. In this chapter, we demonstrate the possibility of controlling the formation and dynamics of soliton molecules in binary dipolar Bose-Einstein condensates (BECs) with spin-orbit (SO) coupling. The study is carried out analytically using the variational approach and validated numerically through split-step Fourier simulations. Our results reveal that the integrity and stability of the soliton molecules are highly sensitive to the system’s physical parameters, particularly the interplay between local (contact) and nonlocal (dipolar) interactions in the presence of SO coupling. By appropriately tuning these interactions, one can effectively control the binding, oscillatory dynamics, and potential dissociation of the soliton molecules.
Vector solitons are a type of solitary or nonspreading wave packet occurring in a nonlinear medium composed of multiple components. As such, a variety of synthetic systems can be constructed to explore their properties, from nonlinear optics to ultracold atoms, and even in metamaterials. Bose-Einstein condensates have a rich panoply of internal hyperfine levels, or spin components, which make them a unique platform for exploring these solitary waves. However, existing experimental work has focused largely on binary systems confined to the Manakov limit of the nonlinear equations governing the soliton behavior, where quantum magnetism plays no role. Here we observe, using a "magnetic shadowing" technique, a new type of soliton in a spinor Bose-Einstein condensate, one that exists only when the underlying interactions are antiferromagnetic and which is deeply embedded within a full spin-1 quantum system. Our approach opens up a vista for future studies of "solitonic matter" whereby multiple solitons interact with one another at deterministic locations.
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 study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, width, position, and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility that can be interpreted as a phase diagram that depends on the harmonic trap's strength and the interspecies coupling parameter. We numerically illustrate the bifurcation scenario whereby nontopological, phase-separated states of increasing complexity emerge out of a symmetric state as the interspecies coupling is increased. The symmetry-breaking dynamical evolution of some of these states is numerically monitored and the associated asymmetric states are also explored.