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Physical Review A

Macroscopic Borromean and anti-Borromean states of quantized vortices

Wei-Can Yang, Makoto Tsubota, Muneto Nitta, Hua-Bi Zeng

Published Feb 13, 2025• 1 citation
Publisher

Abstract

Borromean states refer to a class of bound states with special topological structures, generally thought to exist only in microscopic systems. In this paper, we investigate vortex bound states in three-component Bose-Einstein condensates using coupled Gross-Pitaevskii equations. Specifically, through the competition between two-body and three-body interactions, we identify the emergence of vortex Borromean states, where only three vortices form a stable bound state while any two-vortex subsystems remain unbound. Our theoretical analysis and numerical simulations provide a comprehensive phase diagram of the vortex Borromean states. Additionally, we uncover an unconventional topological phase---a vortex anti-Borromean state---in which two vortices bind together but separate upon the addition of a third vortex. This study highlights the complex role of three-body interactions in macroscopic systems and offers different insights into the topology and phase transitions of multicomponent vortex systems.

DOI
10.1103/physreva.111.023319

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Borromean states refer to a class of bound states with special topological structures, generally thought to exist only in microscopic systems. In this paper, we investigate vortex bound states in three-component Bose-Einstein condensates using coupled Gross-Pitaevskii equations. Specifically, through the competition between two-body and three-body interactions, we identify the emergence of vortex Borromean states, where only three vortices form a stable bound state while any two-vortex subsystems remain unbound. Our theoretical analysis and numerical simulations provide a comprehensive phase diagram of the vortex Borromean states. Additionally, we uncover an unconventional topological phase---a vortex anti-Borromean state---in which two vortices bind together but separate upon the addition of a third vortex. This study highlights the complex role of three-body interactions in macroscopic systems and offers different insights into the topology and phase transitions of multicomponent vortex systems.
The three-body problem, from the chaotic motions of celestial bodies to complex microscopic particle interactions, has always been one of the most foundational yet intricate challenges in physics since its establishment. A key breakthrough in this domain is the Efimov effect, which represents a significant stride in what is now known as Efimov physics. Our study uncovers a macroscopic Efimov effect in a three-component Bose-Einstein Condensate (BEC) system. Through theoretical analysis and numerical simulation, it is verified that under certain conditions, three vortices form a bound state, while removing one vortex causes the others to unbind, demonstrating topological characteristics similar to the Borromean rings, hence termed the `vortex Efimov effect', signifying a novel topological phase transition. We propose several experimental approaches to realize this macroscopic Efimov effect, paving new paths not only in many-body physics but also in exploring quantum phase transitions and applications in quantum information.
We investigate droplet formation in three-component ultracold bosons. In particular, we identify the formation of a Borromean droplet, where only the ternary bosons can form a self-bound droplet while any binary subsystems cannot, as the first example of Borromean binding due to a collective many-body effect. Its formation is facilitated by an additional attractive force induced by the density fluctuation of a third component, which enlarges the mean-field collapse region in comparison to the binary case and renders the formation of a Borromean droplet after incorporating the repulsive force from quantum fluctuations. Outside the Borromean regime, we demonstrate an interesting phenomenon of droplet phase separation due to the competition between ternary and binary droplets. We further show that the transition between different droplets and gas phase can be conveniently tuned by boson numbers and interaction strengths. The study reveals the rich physics of a quantum droplet in three-component boson mixtures and sheds light on the more intriguing many-body bound state formed in multicomponent systems.
We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.
We numerically study the vortex-vortex interaction in multicomponent homogeneous Bose-Einstein condensates within the realm of the Gross-Pitaevskii theory. We provide strong evidence that pairwise vortex interaction captures the underlying mechanisms which determine the geometric configuration of the vortices, such as different lattices in many-vortex states, as well as the bound vortex states with two (dimer) or three (trimer) vortices. Specifically, we discuss and apply our theoretical approach to investigate intra- and intercomponent vortex-vortex interactions in two- and three-component Bose-Einstein condensates, thereby shedding light on the formation of the exotic vortex configurations. These results correlate with current experimental efforts in multicomponent Bose-Einstein condensates and the understanding of the role of vortex interactions in multiband superconductors.
We study vortex dynamics in trapped two-component Bose-Einstein condensates with a laser-induced spin-orbit coupling using the numerical analysis of the Gross-Pitaevskii equation. The spin-orbit coupling leads to three distinct ground-state phases, which depend on some experimentally controllable parameters. When a vortex is put in one or both of the two-component condensates, the vortex dynamics exhibits very different behaviors in each phase, which can be observed in experiments. These dynamical behaviors can be understood by clarifying the stable vortex structure realized in each phase.
We show the existence of Borromean bound states in a one-dimensional quantum three-body system composed of two identical bosons and a distinguishable particle. It is assumed that there is no interaction between the two bosons, while the mass-imbalanced two-body subsystems can be tuned to be either bound or unbound. Within the framework of the Faddeev equations, the three-body spectrum and the corresponding wave functions are computed numerically. In addition, we identify the parameter-space region for the two-body interaction, where the Borromean states occur, evaluate their geometric properties, and investigate their dependence on the mass ratio.