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arXiv:2607.19840

Emergence of giant vortices under nonlinear rotation with attractive interactions in a toroidal condensate

Rony Boral, Swarup K. Sarkar, Matthew Edmonds, Paulsamy Muruganandam, Pankaj Kumar Mishra

Published Jul 22, 2026• 0 citations
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Abstract

We numerically investigate the effects of a density-dependent gauge potential which induces nonlinear rotation on a Bose-Einstein condensate confined in a toroidal trapping geometry. By focusing on the resulting vortex lattice configurations, we demonstrate that increasing the strength of the nonlinear rotation leads to a structural transition from a ring-shaped vortex lattice to a giant vortex state. The quantum circulation associated with the giant vortex is found to be highly sensitive to the strength of the nonlinear rotation and the giant vortex appears in the regime of negative chemical potential. Additionally, we identify the parameter regime in which the Thomas-Fermi density profile remains valid by mapping the solution space based on the strength of the nonlinear rotation and the radius of the confining potential. Based on the Bogoliubov de Gennes analysis, we investigate the impact of nonlinear rotation on the collective excitation spectrum. Our results reveal a violation of the Kohn theorem, accompanied by changes in the breathing mode frequency that indicate radial deformation of the condensate. Our findings are further substantiated through a comprehensive hydrodynamic analysis. Finally, we analyze the stability of multiply quantized vortices under nonlinear rotation. Our findings indicate that while nonlinear rotation can enhance the global stability of these states, it does not necessarily ensure their local stability.

DOI
10.48550/arxiv.2607.19840

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We numerically investigate the effects of a density-dependent gauge potential which induces nonlinear rotation on a Bose-Einstein condensate confined in a toroidal trapping geometry. By focusing on the resulting vortex lattice configurations, we demonstrate that increasing the strength of the nonlinear rotation leads to a structural transition from a ring-shaped vortex lattice to a giant vortex state. The quantum circulation associated with the giant vortex is found to be highly sensitive to the strength of the nonlinear rotation and the giant vortex appears in the regime of negative chemical potential. Additionally, we identify the parameter regime in which the Thomas-Fermi density profile remains valid by mapping the solution space based on the strength of the nonlinear rotation and the radius of the confining potential. Based on the Bogoliubov de Gennes analysis, we investigate the impact of nonlinear rotation on the collective excitation spectrum. Our results reveal a violation of the Kohn theorem, accompanied by changes in the breathing mode frequency that indicate radial deformation of the condensate. Our findings are further substantiated through a comprehensive hydrodynamic analysis. Finally, we analyze the stability of multiply quantized vortices under nonlinear rotation. Our findings indicate that while nonlinear rotation can enhance the global stability of these states, it does not necessarily ensure their local stability.
We investigate the collective excitation spectrum of a quasi-two-dimensional Bose-Einstein condensate trapped in a harmonic confinement with nonlinear rotation induced by a density-dependent gauge potential. Using a Bogoliubov--de Gennes (BdG) analysis, we show that the dipole mode frequency depends strongly on the nonlinear interaction strength, violating Kohn's theorem which is also well complemented by the analytical expression for the dipole and breathing modes obtained employing a variational analysis. We identify four different vortex displacement modes, Tkachenko, circular, quadratic, and rational, whose frequencies are rotation sensitive. An analytical Tkachenko mode frequency from a hydrodynamic approach agrees well with that computed using BdG and Fourier analysis. The excitation spectrum remains symmetric around the angular quantum number l=0l=0l=0, but energy splitting between lll and $\ensuremath{-}l$ varies with the sign and strength of the nonlinear rotation. Finally, we demonstrate that the surface mode excitation frequency increases (decreases) with an increase in the positive (negative) nonlinear rotation strength.
Motivated by recent experiments, we study theoretically a gas of atomic bosons confined in an elliptical harmonic trap, forming a quasi-two-dimensional atomic Bose-Einstein condensate subject to a density-dependent gauge potential which realizes an effective density-angular-momentum coupling. We present exact Thomas-Fermi solutions which allow us to identify the stable regimes of the full parameter space of the model. Accompanying numerical simulations reveal the effect of the interplay of the rigid body and density-angular-momentum coupling for the elliptically confined condensate. By varying the strength of the gauge potential and trap anisotropy, we explore how the superfluid state emerges in different experimentally accessible geometries, while for large rotation strengths dense vortex lattices and concentric vortex ring arrangements are obtained.
We have studied the ground state configurations of a rotating Bose—Einstein condensation in a toroidal trap as the radius of the central Gaussian potential expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the gaussian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.
We investigate the rotational properties of a zero-temperature Bose-Einstein condensed gas, which is confined in a hard-wall potential. For weak interactions the gas carries its angular momentum via vortices of multiple quantization. As the coupling increases and for sufficiently slow rotational frequencies of the trap, the multiply-quantized vortex states become unstable against a mixed state. For stronger couplings, as the angular frequency of the trap increases, there is a transition from a vortex lattice, to a vortex lattice with a hole at the trap center, and finally to a giant vortex. For weak effective attractive interactions we still have vortices of multiple quantization. These states become unstable towards states which break the axial symmetry of the problem and resemble center-of-mass excitation, as the coupling becomes more negative. Finally, for even more attractive forces, the system becomes unstable against collapse.
We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$ values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional sss-wave scattering lengths through the strength of nonlinear rotation, C\mathit{C}C, such that ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}>0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}=0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}<0)$. In an analogous manner, the critical ellipticity (${\ensuremath{\epsilon}}_{\text{cr}}$) for vortex nucleation during an adiabatic introduction of trap ellipticity ($\ensuremath{\epsilon}$) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.
We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.