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Physica D Nonlinear Phenomena

On the instability of standing waves for 3D dipolar Bose–Einstein condensates

Van Duong Dinh

Published Feb 6, 2021• 8 citations
Publisher
DOI
10.1016/j.physd.2021.132856

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We study the emergence of density waves in quasi-one-dimensional dipolar Bose-Einstein condensates (BECs) when the strength of dipole-dipole atomic interactions is periodically varied in time. The proposed theoretical model based on the evolution of small perturbations of the background density allows one to calculate the instability growth rate for an arbitrary set of input parameters, thereby identifying instability regions with respect to density waves. We find that among other modes of the system the roton mode is most effectively excited due to a significant contribution of subharmonics of the excitation frequency. The frequency of temporal oscillations of emerging density waves coincides with half of the driving frequency, which is the hallmark of the parametric resonance and is characteristic of Faraday waves. The possibility to create density waves in dipolar BECs, which can persist after emergence, is demonstrated. The existence of a standing-wave solution of the nonlocal Gross-Pitaevskii equation is revealed from numerical simulations. The effect of three-body atomic interactions, which is relevant to condensates with increased density, upon the properties of emerging waves is analyzed too. Significant modification of the condensate's excitation spectrum owing to three-body effects is shown.
The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar Bose-Einstein condensates, which is followed by collapse in 3D geometries. We show that in 2D, the nature of the post-instability dynamics is fundamentally different, due to the stabilization of 2D solitons. As a result, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic trap, the post-instability dynamics is characterized by a transient pattern formation followed by the creation of stable 2D solitons. This dynamics should be observable in ongoing experiments, allowing for the creation of stable 2D solitons for the first time ever in quantum gases.