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arXiv:2405.20695

Macroscopic Efimov effect of quantized vortex

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

Published May 31, 2024• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2405.20695

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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.
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.
Phase transitions abound in the physical world, from the subatomic length scales of quark condensation to the decoupling forces in the early universe. In the Bose-Einstein condensation phase transition, a gas of trapped bosonic atoms is cooled to a critical temperature. Below this temperature, a macroscopic number of atoms suddenly starts to occupy a single quantum state; these atoms comprise the Bose-Einstein condensate (BEC). The dynamics of the BEC phase transition are the focus of this dissertation and the experiments described here have provided new information on the details of BEC formation. New theoretical developments are proving to be valuable tools for describing BEC phase transition dynamics and interpreting new experimental results. With their amenability to optical manipulation and probing along with the advent of new microscopic theories, BECs provide an important new avenue for gaining insight into the universal dynamics of phase transitions in general.Spontaneous symmetry breaking in the system's order parameter may be one result of cooling through a phase transition. A potential consequence of this is the spontaneous formation of topological defects, which in a BEC appear as vortices. We experimentally observed and characterized the spontaneous formation of vortices during BEC growth. We attribute vortex creation to coherence length limitations during the initial stages of the phase transition. Parallel to these experimental observations, theory collaborators have used the Stochastic Gross-Pitaevski Equation formalism to simulate the growth of a condensate from a thermal cloud. The experimental and theoretical statistical results of the spontaneous formation of vortex cores during the growth of the condensate are in good quantitative agreement with one another, supporting our understanding of the dynamics of the phase transition. We believe that our results are also qualitatively consistent with the Kibble-Zurek mechanism, a universal model for topological defect formation.Ultimately, our understanding of the dynamics of the BEC phase transition may lead to a broader understanding of phase transitions in general, and provide new insight into the development of coherence in numerous systems.
We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system.
The production of quantized vortices having diverse structures is a remarkable effect of rotating Bose-Einstein condensates. Vortex formation described by the mean-field theory is valid only in the regime of weak interactions. The exploration of the rich and diverse physics of strongly interacting BEC requires a more general approach. This study explores the vortex formation of strongly interacting and rapidly rotating BEC from a general ab initio many-body perspective. We demonstrate that the quantized vortices form various structures that emerge from an intricate interplay between the angular momentum and many-body interaction. We examine the distinct impact of the angular velocity and interaction energy on the vortex formation. Our analysis shows that, while the angular rotation generally augments the vortex formation, the interactions can enhance as well as impede the vortices production.
We investigate the zero-temperature properties of an impurity particle interacting with a Bose-Einstein condensate (BEC), using a variational wave function that includes up to two Bogoliubov excitations of the BEC. This allows one to capture three-body Efimov physics, as well as to recover the first nontrivial terms in the weak-coupling expansion. We show that the energy and quasiparticle residue of the dressed impurity (polaron) are significantly lowered by three-body correlations, even for weak interactions where there is no Efimov trimer state in a vacuum. For increasing attraction between the impurity and the BEC, we observe a smooth crossover from atom to Efimov trimer, with a superposition of states near the Efimov resonance. We furthermore demonstrate that three-body loss does not prohibit the experimental observation of these effects. Our results thus suggest a route to realizing Efimov physics in a stable quantum many-body system for the first time.
We numerically study the dynamics of quantized vortices in two-dimensional two-component Bose-Einstein condensates (BECs) trapped by a box potential. For one-component BECs in a box potential, it is known that quantized vortices form Onsager vortices, which are clusters of same-sign vortices. We confirm that the vortices of the two components spatially separate from each other-even for miscible two-component BECs-suppressing the formation of Onsager vortices. This phenomenon is caused by the repulsive interaction between vortices belonging to different components, hence, suggesting a new possibility for vortex phase separation.