Excitation spectrum of vortex-lattice modes in a rotating condensate with a density-dependent gauge potential

TL;DR

This paper analyzes the excitation spectrum of vortex modes in a rotating Bose-Einstein condensate influenced by a density-dependent gauge potential, revealing how nonlinear rotation affects mode frequencies and symmetry.

Contribution

It provides analytical and numerical insights into vortex mode frequencies and their dependence on nonlinear rotation, highlighting deviations from traditional theorems and symmetry properties.

Findings

Dipole mode frequency depends on interaction strength, violating Kohn's theorem.

Derived analytical expressions for dipole and breathing modes show width dependence on nonlinear rotation.

Identified four vortex displacement modes with frequencies sensitive to nonlinear rotation.

Abstract

We investigate the collective excitation spectrum of a quasi-2D Bose-Einstein condensate trapped in a harmonic confinement with nonlinear rotation induced by a density-dependent gauge field. 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. Further utilizing the variational analysis, we derive analytical expressions for the dipole and breathing modes, which suggests a strong dependence of the condensate's width on the nonlinear rotation resulting from the density-dependent gauge potential. We identify four different vortex displacement modes -- namely Tkachenko, circular, quadratic, and rational-whose frequencies are sensitive to the nonlinear rotation. In addition to the numerical analysis, we also derive an analytical expression for the Tkachenko mode frequency using a Hydrodynamic approach that agrees well with the frequencies obtained by the Fourier analysis of the transverse and longitudinal vortex dynamics induced by a Gaussian perturbation as well as the frequencies from the BdG excitation spectrum. Our findings also reveal that the excitation spectrum remain symmetric around the angular quantum number $l=0$, with modified energy splitting between $l$ and $-l$ as the nonlinear rotation changes from negative to positive values. Finally, we demonstrate that the surface mode excitation frequency increases (decreases) with an increase in the positive (negative) nonlinear rotation strength.