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arXiv:2501.06119 · Physical review. B./Physical review. B

Vortex stability in interacting Bose-Einstein condensates

Ajay Srinivasan, Aaron Wirthwein, Stephan Haas

Published Sep 10, 2025• 0 citations
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Abstract

We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.

DOI
10.1103/9ggl-ycdv

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We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.
Summary form only given. I present results of the detailed asymptotic and numerical results on stability of unit and higher order vortices in coupled Gross-Pitaevskii equations, which model the experimental work. Low lying eigenfrequencies, including ones generating instability of the unit vortex placed in one component of a binary mixture of BEC, have been calculated applying perturbative theory in the limit of the weak interparticle interaction. Results of the perturbative theory have been verified and significantly extended using numerical analysis of the linearised equations for excitations and direct numerical simulation of the coupled Gross-Pitaevskii equations. Two main instability mechanisms have been identified and their dependencies on the relative number of the particles in the condensates and on the strength of the inter-species interaction have been studied. The first mechanism is the drift instability induced by the vortex free component of the condensate and resulting in the motion of the vortex out of the condensate center to its periphery. The second mechanism is the splitting of the higher order vortices into unit ones. Absolute and/or relative increase of the number of particles in the vortex free condensate component has been found to have stabilizing effect on both drift and splitting instabilities. Different scenarios of the splitting instabilities have been found.
We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices. Published by the American Physical Society 2024
In this work, we consider vortex lattices in rotating Bose–Einstein condensates composed of two species of bosons having different masses. Previously (Barnett et al 2008 New J. Phys. 10 043030), it was claimed that the vortices of the two species form bound pairs and the two vortex lattices lock. Remarkably, the two condensates and the external drive all rotate at different speeds owing to the disparity of the masses of the constituent bosons. In this paper, we study the system by solving the full two-component Gross–Pitaevskii equations numerically. Using this approach, we verify the stability of the putative locked state that is found to exist within a disc centered on the axis of rotation and that depends on the mass ratio of the two bosons. We also derive a refined estimate for the locking radius tailored to the experimentally relevant case of a harmonic trap and show that this agrees with the numerical results. Finally, we analyze in detail the rotation rates of the different components in the locked and unlocked regimes.
The dynamics and interaction of quantized vortices in Bose-Einstein condensates (BECs) are investigated by using the two-dimensional Gross-Pitaevskii equation (GPE) with/without an angular momentum rotation term. If all vortices have the same winding number, they would rotate around the trap center but never collide. In contrast, if the winding numbers are different, their interaction highly depends on the initial distance between vortex centers. The analytical results are presented to describe the dynamics of the vortex centers when β=0. While if β≠0, there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs. Finally, the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented.
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the 'https://creativecommons.org/licenses/by/4.0/'Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices.
We study the structure and stability of vortex lattices in two-component rotating Bose-Einstein condensates with intrinsic dipole-dipole interactions and contact interactions. To address experimentally accessible coupled systems, we consider $^{164}\mathrm{Dy}\ensuremath{-}^{162}\mathrm{Dy}$ and $^{168}\mathrm{Er}\ensuremath{-}^{164}\mathrm{Dy}$ mixtures, which feature different miscibilities. The corresponding dipole moments are ${\ensuremath{\mu}}_{\mathrm{Dy}}=10{\ensuremath{\mu}}_{\mathrm{B}}$ and ${\ensuremath{\mu}}_{\mathrm{Er}}=7{\ensuremath{\mu}}_{\mathrm{B}}$, where ${\ensuremath{\mu}}_{\mathrm{B}}$ is the Bohr magneton. For comparison we also discuss a case where one of the species is nondipolar. Under a large aspect ratio of the trap, we consider mixtures in the pancake-shaped format, which are modeled by effective two-dimensional coupled Gross-Pitaevskii equations, with a fixed polarization of the magnetic dipoles. Then, the miscibility and vortex-lattice structures are studied by varying the coefficients of the contact interactions (assuming the use of the Feshbach-resonance mechanism) and the rotation frequency. We present phase diagrams for several types of lattices in the parameter plane of the rotation frequency and the ratio of inter- and intraspecies scattering lengths. The vortex structures are found to be diverse for the more miscible $^{164}\mathrm{Dy}\ensuremath{-}^{162}\mathrm{Dy}$ composition, with a variety of shapes, whereas for the less miscible case of $^{168}\mathrm{Er}\ensuremath{-}^{164}\mathrm{Dy}$, the lattice patterns mainly feature circular or square formats.