Dynamics of the center of mass in rotating Bose–Einstein condensates

I. Corro, R. G. Scott, A. Martin

Qingzhou Shu

This paper investigates the dynamics of the center of mass in three-dimensional arbitrary-angle rotating Bose-Einstein condensates (ARotBECs), which are governed by the Gross-Pitaevskii equation (GPE) with an arbitrary-angle angular momentum rotation term. The second-order ordinary differential equations (ODEs) which govern the motion of the center of mass of ARotBECs are analytically solved. Subsequently, a novel numerical scheme, which is mass conservative — i.e. the Lagrangian multiplier-based Crank-Nicolson leap-frog (LagM-CNLF) method, integrated with Fourier pseudo-spectral spatial discretization, is proposed to efficiently and accurately simulate the GPE with arbitrary-angle rotation term. Finally, distinct motion patterns of the center of mass are systematically categorized based on analytical solutions and rigorously validated through direct numerical simulations of the GPE, demonstrating robust consistency between theoretical predictions and numerical computational results. The dynamics of quantized vortices is also studied to show the effectiveness of the LagM-CNLF method.

Wu‐Ming Liu

Wen-Kai Bai, Jian-Chong Xing, Tao Yang +2 more

We study the nonlinear dynamics of a three-dimensional Bose-Einstein condensate (BEC) excited by a vortex ring phase imprinting. We identify independent, integrated, and stationary modes of the center-of-mass oscillation of the condensate with respect to the vortex ring movement. We show that the oscillation amplitude of the center-of-mass of the condensate depends strongly on the initial radius of the vortex ring, the nonlinear inter-atomic interaction, and the aspect ratio of the trap, while the oscillation frequency is fixed and equals to the frequency of the harmonic trap in the direction of the ring movement. However, when applying Kelvin wave perturbations on the vortex ring, the center-of-mass oscillation of the BEC is changed non-trivially with respect to the perturbation modes, the long-scale perturbation strength as well as the wave number of the perturbations. The parity of the wave number of the Kelvin perturbations plays an important role on the mode of the center-of-mass oscillation of the condensate.

Benjamin Schlein

I. Corro, R. G. Scott, A. Martin

The dynamics of two-component Bose-Einstein condensates in rotating traps is investigated. In the Thomas-Fermi limit, equations of motion are derived showing multiple static solutions for a vortex-free condensate. Dynamic stability analysis of these solutions and comparison to truncated Wigner simulations enable us to identify the regimes for which vortex states will occur. In addition, our analysis predicts center-of-mass oscillations that are induced by interspecies interactions and affect each component separately. For attractive interspecies interactions, these oscillations lead to a stable symmetry-broken state.