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Chaos Solitons & Fractals

Dynamics of the breathing mode with rotational symmetry in two-dimensional Bose–Einstein condensates

Zhendong Li, Huanyu Cao, Zhen Cao, Siying Li, Xinyi Liu, Yueheng Lan, Mingyuan Sun

Published Apr 30, 2026• 0 citations
Publisher
DOI
10.1016/j.chaos.2026.118344

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We show that the breathing mode of a rapidly rotating, harmonically trapped Bose-Einstein condensate may be described by a generalized lowest Landau level (LLL) wave function, in which the oscillator length is treated as a variable. Using this wave function in a variational Lagrangian formalism, we show that the frequency of the breathing mode for a two-dimensional cloud is $2{\ensuremath{\omega}}_{\ensuremath{\perp}}$, where ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ is the trap frequency. We also study large-amplitude oscillations and confirm that the above result is not limited to linear oscillations. The resulting mode frequency can be understood in terms of orbits of a single particle in a harmonic trap. The mode frequency is also calculated for a cloud in three dimensions and the result for the axial breathing mode frequency agrees with recent experimental data in the rapid rotation regime.
We studied the collective modes of a Bose-Einstein condensate (BEC) with spin-orbit coupling. We developed the hydrodynamic equations for spin-orbit coupled BECs and used them to study collective modes in the plane-wave phase and large Rabi coupling regime for both a uniform BEC and a BEC in a harmonic trap. In the homogeneous situation, we obtained energy spectra of elementary excitations and found that the spin-orbit coupling can increase the effective mass of the atoms, which will suppress the sound velocity. The spin-orbit coupling can also change the spin mixing, which will modify the interaction energy, and may lead to an enhancement of sound velocity. The competition between these two effects gives the behavior of sound velocity. In a harmonic trap, we found that the dipole mode and the breathing mode are coupled together in the plane-wave phase, and these two modes have a $\ensuremath{\pi}/2$ phase difference, because the spin-orbit coupling and the interaction are not invariant under spin rotation. However, in the large Rabi coupling regime, the dipole mode and the breathing mode are decoupled due to the symmetry restriction.
We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential, the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.