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Communications in Theoretical Physics

Splitting of triply quantized vortices in Bose–Einstein condensates of finite temperature

Jun Yan, Jie-Xiong Mo, Lichang Mo, Shan-Quan Lan, Xiao-Bao Xu, Gu-Qiang Li, Huandian He

Published Nov 13, 2024• 1 citation
Publisher

Abstract

Abstract Utilizing the dissipative Gross–Pitaevskii equation, we investigated the splitting dynamics of triply quantized vortices at finite temperature. Through linear perturbation analysis, we determined the excitation modes of these vortices across various dissipation parameters. We identified three unstable modes with p = 2-, 3- and 4-fold rotational symmetries, revealing a significant dynamic transition of the most unstable mode. That is, as the dissipation parameter increases the most unstable mode transitions from the p = 2 mode to the p = 3 mode. Throughout the entire range of dissipation parameters, the p = 4 unstable mode is never the dominant mode. Subsequently, we performed nonlinear numerical simulations of the vortex splitting process. Under random perturbations we confirmed the dynamical transition, and under specific perturbations we confirmed the instability of the p = 4 mode. Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.

DOI
10.1088/1572-9494/ad91b5

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Abstract Utilizing the dissipative Gross–Pitaevskii equation, we investigated the splitting dynamics of triply quantized vortices at finite temperature. Through linear perturbation analysis, we determined the excitation modes of these vortices across various dissipation parameters. We identified three unstable modes with p = 2-, 3- and 4-fold rotational symmetries, revealing a significant dynamic transition of the most unstable mode. That is, as the dissipation parameter increases the most unstable mode transitions from the p = 2 mode to the p = 3 mode. Throughout the entire range of dissipation parameters, the p = 4 unstable mode is never the dominant mode. Subsequently, we performed nonlinear numerical simulations of the vortex splitting process. Under random perturbations we confirmed the dynamical transition, and under specific perturbations we confirmed the instability of the p = 4 mode. Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.
Using holographic duality, we investigate the impact of finite temperature on the instability and splitting patterns of quadruply quantized vortices, providing the first-ever analysis in this context. Through linear stability analysis, we reveal the occurrence of two consecutive dynamical transitions. At a specific low temperature, the dominant unstable mode transitions from the twofold rotational symmetry mode to the threefold one, followed by a transition from the threefold one to the fourfold one at a higher temperature. As the temperature is increased, we also observe the fivefold and sixfold rotational symmetry unstable modes get excited successively. Employing the full nonlinear numerical simulations, we further demonstrate that these two novel dynamical transitions, along with the temperature-induced instabilities for the fivefold and sixfold rotational symmetry modes, can be identified by examining the resulting distinct splitting patterns, which offers a promising route for the experimental verification in the cold atom gases.
We study the nonlinear dynamics of the splitting of a doubly quantized vortex in a trapped Bose-Einstein condensate. The dynamics is studied in detail by solving the Gross-Pitaevskii equation. The main dynamical features are explained in terms of a nonlinear three-level system, to which we find an analytical solution. This result is compared to linear Bogoliubov analysis and to the full numerical time evolution. It is concluded that the time scale for the splitting is mainly determined by the instability of the linearized system, and nonlinear effects contribute logarithmically.
A bstract The stability properties and splitting dynamics of multiply quantized vortices are the subject of interest in both theoretical and experimental investigations. Going beyond the regime of validity of Gross-Pitaevskii equation (GPE), we study the composite vortices in miscible strongly interacting binary superfluids by employing a holographic model that naturally incorporates finite temperature and dissipation. The composite vortices are classified in terms of an integer pair ( S 1 , S 2 ) of phase winding numbers and can share the same vortex core, while either co-rotating or counter-rotating, leading to very diverse vortex structures. We uncover different dynamical behaviors compared to results from GPE that is valid in weak coupling limit and zero temperature. In particular, we show that the occurrence of dynamic instabilities and the instability strength are sensitive to the temperature. We identify several temperature dependent dynamical transitions in (1, 1), (2 , ±1) and (2, 2) vortices. The splitting behaviors associated with different multipolarities are demonstrated by solving the full-time evolution for slightly perturbed composite vortices. We find that the final states of all composite vortices are generally singly quantized vortices, and no additional long living vortex is formed due to strong dissipation. Our results highlight the important role of temperature and the distinction between dynamics of composite vortices in weakly interacting superfluids without dissipation and strongly interacting superfluids with dissipation, shedding new light on the understanding of quantum vortex and dynamical instabilities in multicomponent superfluids.
The stability properties and splitting dynamics of multiply quantized vortices are the subject of interest in both theoretical and experimental investigations. Going beyond the regime of validity of Gross-Pitaevskii equation (GPE), we study the composite vortices in miscible strongly interacting binary superfluids by employing a holographic model that naturally incorporate finite temperature and dissipation. The composite vortices is classified in terms of an integer pair (S1,S2)(S_1, S_2)(S1​,S2​) of phase winding numbers and can share the same vortex core, while either co-rotating or counter-rotating, leading to very diverse vortex structures. We uncover different dynamical behaviors compared to results from GPE that is valid in weak coupling limit and zero temperature. In particular, we show that the occurrence of dynamic instabilities and the instability strength are sensitive to the temperature. We identify several temperature dependent dynamical transitions in (1,1)(1,1)(1,1), (2,±1)(2,\pm 1)(2,±1) and (2,2)(2,2)(2,2) vortices. The splitting behaviors associated with different multipolarities are demonstrated by solving the full-time evolution for slightly perturbed composite vortices. We find that the final states of all composite vortices are generally singly quantized vortices, and no additional long living vortex is formed due to strong dissipation. Our results highlight the important role of temperature and the distinction between dynamics of composite vortices in weakly interacting superfluids without dissipation and strongly interacting case with dissipation, shedding a new light on the understanding of quantum vortex and dynamical instabilities in multicomponent superfluids.
The splitting process of quadruply charged vortices into less charged vortices is studied at zero temperature. We solve the Bogoliubov-de Gennes (BdG) equation numerically and classify the excitations by angular momentum l relative to the condensates. Unstable modes having complex eigenvalues appear when l = 2-6. It is found that two excitations are coupled with each other when their total energy and angular momentum are zero and yield a pair of complex eigenvalues. The decay process is also numerically simulated by solving the time-dependent Gross-Pitaevskii equation. The behavior of a condensate shows good agreement with the results of BdG. The quadruply charged vortex splits into four singly quantized vortices, which are arranged as a line, triangle, and square according to the angular momentum of the excited eigenmode. We also observe the effect of nonlinearity.
The dynamical instabilities and ensuing dynamics of singly and doubly quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full three-dimensional numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of Leanhardt et al. [Phys. Rev. Lett. 89, 190403 (2002)].