Multicomponent condensates: a flexible platform for soliton physics

TL;DR

Multicomponent Bose-Einstein condensates provide a versatile platform to study soliton physics by mapping the coupled Gross-Pitaevskii dynamics onto effective single-component equations or spin-chain models. The analysis identifies regimes—the Manakov regime, the low-depletion GPE limit, and arbitrary depletion—where the two-component system reduces to a single GPE with an effective interaction $g_{\text{eff}}$ or to a Landau-Lifshitz equation describing ferromagnetic spin dynamics. The work demonstrates stable 1D dark-bright solitons, 1D and 2D bright solitons (including Townes) in immiscible mixtures, and magnetic solitons in easy-plane and easy-axis configurations, with experimental realizations and phase-sensitive measurements. By enabling controlled preparation, dynamic tuning via Feshbach resonances, and coherent coupling, the platform provides access to beyond-NLS nonlinear equations and to spin-chain physics, offering a versatile quantum simulator for nonlinear dynamics.

Abstract

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.

Figures (7)

• Figure 1: a Realization of a single dark-bright soliton in a harmonic trap (adapted from Ref. Becker2008). A two-photon Raman transfer is used to spin-flip a wave packet of atoms from component $F=1$ to component $F=2$ in a spatially resolved way. A phase jump in component $F=1$, centered at the position of the wave packet, is also imprinted. The time evolution of the dark-bright soliton in the trap is represented by a set of double-exposure absorption images showing the density distributions of both components over time. As expected in the Manakov regime, it can be seen that the total density remains approximately constant. b Realization of a soliton train of dark-bright solitons in a harmonic trap (adapted from Ref. Hamner2011). A magnetic field gradient induces a counterflow between the two components, resulting in the formation of solitons. For each time of evolution in the harmonic trap, the two pictures correspond to the two components of the gas.
• Figure 2: Spin-resolved density profile of a bright soliton realized in an immiscible spin mixture evolving in one dimension (adapted from Rabec24). The minority component forms a stationary localized wave packet within a bath of majority atoms.
• Figure 3: Dynamics of the minority component, starting with a quasi-uniform density background and following the application of a localized perturbation. The latter induces the formation of a Peregrine soliton, characterized by a transient density enhancement localized in both space and time (adapted from Romero-Ros2024).
• Figure 4: Dynamics of a localized wave packet of minority atoms evolving within a majority-atom bath in two dimensions. a When the initial density is prepared according to the Townes soliton profile, the wave packet remains stationary provided that the total atom number matches the critical value $N_{2,\text{c}} = A / |g_{\text{eff}}|$. b When the initial density instead follows a Gaussian profile, the root-mean-square width $\sigma$ can be made stationary Pitaevskii97, but the density profile deforms over time (adapted from Bakkali-Hassani2021).
• Figure 5: Measurement of the density and phase profiles of a pair of easy-plane magnetic solitons. The $y$ coordinate corresponds to the longitudinal direction (i.e., the $x$ coordinate in the main text). a Optical density (OD) of component 1. b Optical density of component 2. c Measurement of the relative phase $\varphi(x)$. A Ramsey interferometric scheme maps $\cos{ \varphi(x) }$ to the optical density. The relative phase changes by $\pi$ across each soliton, with opposite phase evolution for the two solitons (adapted from Farolfi2020).