Rotation-triggered Kelvin-Helmholtz and counter-superflow instabilities in a three-component Bose-Einstein condensate

Abstract

Interfacial hydrodynamic instabilities in multicomponent superfluids provide a versatile platform to explore nonequilibrium quantum dynamics beyond classical fluid analogues. We study dynamical interfacial instabilities in a quasi-two-dimensional three-component Bose-Einstein condensate confined in a harmonic trap, where rotation is applied selectively to the intermediate component to generate controlled relative motion at two interfaces. This selective rotation protocol enables the independent tuning of shear and counterflow across the inner and outer boundaries, allowing direct control over the nature and strength of the resulting instability mechanisms. Three regimes are examined: Kelvin-Helmholtz instability in the strongly immiscible limit, counter-superflow instability in the partially miscible regime, and a parameter window where both unstable mechanisms are present. The onset condition for the Kelvin-Helmholtz instability is derived using a hydrodynamic pressure-balance approach, and the subsequent nonlinear evolution is obtained from time-dependent Gross-Pitaevskii simulations. A Bogoliubov-de Gennes analysis is performed to identify the dominant unstable modes excited during the dynamical evolution of the system. The conniving features of the collective excitations and their spatial structures have been consistent with the density modulations observed during the dynamics. The results demonstrate that the presence of two interfaces and tunable intercomponent interactions in a three-component condensate modifies the instability mechanisms relative to binary mixtures and provides a controlled parameter regime to study multicomponent quantum hydrodynamics.

Figures (9)

• Figure 1: Schematic representation of a rotating, radially phase-separated three-component BEC in a quasi-2D harmonic trap.
• Figure 2: Ground state density profile of the three components in a phase-separated BEC. The system is confined in a harmonic trap with $(\omega_r, \omega_z) = 2\pi \times (50,2500)$ Hz, and each component contains $N_j = 80,000$ atoms. The intracomponent scattering lengths are $a_{11}=92.4a_0$, $a_{22}=94.5a_0$, and $a_{33}=100.4a_0$, while the intercomponent scattering lengths are $a_{12}=a_{21}=213a_0$, $a_{13}=a_{31}=213a_0$, and $a_{23}=a_{32}=127a_0$, where $a_0$ denotes the Bohr radius.
• Figure 3: Real time evolution of the density distributions of a three-component BEC confined in quasi-2D harmonic trap are shown in panels [(a1)-(a4)], [(b1)-(b4)], and [(c1)-(c4)] for BEC-1, BEC-2 and BEC-3, respectively, following a sudden rotation to BEC-2 ($\Omega_2 = 0.4\omega_r$), while BEC-1 and BEC-3 remain stationary ($\Omega_1 = \Omega_3 = 0$). Snapshots of the density profiles at $t = 25.46$ ms, 31.83 ms, 38.19 ms, and 42.65 ms describe the interfacial deformation and vortex nucleation that accompany the development of the KHI. A full movie of the dynamics is available in the Supplemental Material.
• Figure 4: Ground state density profile of a weakly miscible three-component BEC confined in quasi-2D harmonic trap. Trap frequencies are $(\omega_r, \omega_z) = 2\pi \times (50,,2500)$ Hz, with $N_j = 80,000$ atoms in each component. The intracomponent scattering lengths are $a_{11}=92.4a_0$, $a_{22}=94.5a_0$, and $a_{33}=100.4a_0$, while the intercomponent scattering lengths are $a_{12}=a_{21}=93.4a_0$, $a_{13}=a_{31}=120a_0$, and $a_{23}=a_{32}=97a_0$, where $a_0$ denotes the Bohr radius.
• Figure 5: Real time evolution of the density distributions of a three-component BEC confined in quasi-2D harmonic trap are shown in panels [(a1)-(a4)], [(b1)-(b4)], and [(c1)-(c4)] for BEC-1, BEC-2 and BEC-3, respectively, under sudden rotation of BEC-2 with $\Omega_2 = 0.8\omega_r$, while BEC-1 and BEC-3 remain stationary ($\Omega_1 = \Omega_3 = 0$). Snapshots of the density profiles are taken at (1) $t = 22.28$ ms, (2) $t = 23.23$ ms, (3) $t = 24.82$ ms, and (4) $t = 25.46$ ms. A full movie of the dynamics is available in the Supplemental Material.