Quantum swapping of immiscible Bose-Einstein condensates as an alternative to the Rayleigh-Taylor instability

Abstract

We consider a two-component Bose-Einstein condensate in a quasi-one-dimensional harmonic trap, where the immiscible components are pressed against each other by an external magnetic force. The zero-temperature nonstationary Gross-Pitaevskii equations are solved numerically; analytical models are developed for the key steps in the process. We demonstrate that if the magnetic force is strong enough, then the condensates may swap their places in the trap due to dynamic quantum interpenetration of the nonlinear matter waves. The swapping is accompanied by development of a modulational instability leading to quasiturbulent excitations. Unlike the multidimensional Rayleigh-Taylor instability in a similar geometry of two-component quantum fluid systems, quantum interpenetration has no classical analog. In a two-dimensional geometry a crossover between the Rayleigh-Taylor instability and the dynamic quantum interpenetration is investigated.

Parametric resonance of capillary waves at the interface between two immiscible Bose-Einstein condensates

“…In all calculations, we keep the scaled system size R 0 = 30 and the repulsion parameter γ = 0.01, which implies a sufficiently small thickness of the interface ∼1/ √ γ R 0 ≈ 0.3 and a much smaller healing length ∼1/R 0 ≈ 3.3 × 10 −2 [11]. The unperturbed planar distribution of BEC density has been obtained numerically similar to Refs.…”

“…As an example of such interplay, we can mention works on shock fronts in Bose-Einstein condensates (BECs), nonlinear optics, and quantum plasmas [7][8][9]: the quantum shocks propagate as soliton trains due to Bohm-de Broglie dispersion instead of the monotonic transition between low-density and high-density gases (fluids, plasmas) in a classical shock. Development of quantum solitons has been also obtained experimentally and theoretically in the process of dynamical quantum interpenetration of both miscible and immiscible BECs [2,10,11].…”

“…We study a ribbon-shaped two-dimensional (2D) geometry where the BEC components are initially placed in the domains y < 0 and y > 0, respectively. The BEC is tightly confined in the z direction; in the y direction it is trapped so that the Thomas-Fermi (TF) approximation for each component holds well [11]; finally, it is not confined in the x direction. The system of widthλ along the x direction is shown in Fig.…”

“…[4][5][6][18][19][20][21]. With the help of the instabilities, one can produce rather complicated quantum vortex structures in BECs like skyrmions, for which the intrinsically empty vortex core in one BEC component is filled by the other component [11,21]. The system of a two-component BEC can be realized experimentally by blocking the spin-recombination process |1,−1 + |1,1 → |1,0 + |1,0 by the quadratic Zeeman effect, as discussed in Ref.…”

“…As an alternative to the RT instability, Ref. [11] found the possibility of reducing the excess of potential energy by one-dimensional (1D) dynamical quantum interpenetration; still, it has been also shown that the RT instability dominates for interface perturbations of a sufficiently large wavelength.…”