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arXiv:1510.00207 · Journal of Physics B Atomic Molecular and Optical Physics

Faraday waves in Bose–Einstein condensates with engineering three-body interactions

F Kh Abdullaev, A Gammal, Lauro Tomio

Published Dec 16, 2015• 12 citations
arXivHTMLPDF

Abstract

Abstract We consider Bose–Einstein condensates with two- and three-body interactions periodically varying in time. Two models of time-dependent three-body interactions, with quadratic and quartic dependence on the two-body atomic scattering length a s , are studied. It is shown that parametric instabilities in the condensate lead to the generation of Faraday waves (FWs), with wavelengths depending on the background scattering length, as well as on the frequency and amplitude of the modulations of a s . From an experimental perspective, this opens a new possibility to tune the period of Faraday patterns by varying not only the frequency of modulations and background scattering length, but also the amplitude of the modulations. The latter effect can be used to estimate the parameters of three-body interactions from the FW experimental results. Theoretical predictions are confirmed by numerical simulations of the corresponding extended Gross–Pitaevskii equation.

DOI
10.1088/0953-4075/49/2/025302

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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.
A mechanism leading to spontaneous breaking of the space symmetry, and to the appearance of spatial patterns in the most recently created state of matter, the Bose-Einstein condensate (BEC), is proposed. The pattern formation are due to a periodic modulation in time of the scattering length of the condensed atoms. Experimentally this can be achieved via the Feshbach resonance, or, for low dimensional (1D or 2D) condensates, also by modulation of the trapping potential along a spatial coordinate normal to the "working" space. The parametric excitation of patterns in condensates by considering the mean-field Gross-Pitaevskii equation, and its dissipative generalization are investigated.
Abstract Faraday waves in mixtures of Bose gases are studied by taking into account quantum fluctuations beyond the Gross–Pitaevskii mean-field formalism with the Lee–Huang–Yang term. For that, a Bose–Einstein condensed binary atomic mixture is assumed trapped in cigar-type geometry, having the inter- and intra-species scattering lengths periodically varying in time. The period of the Faraday patterns is shown to be quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. By studying the influence of the above nonlinear periodic modulations on quantum droplet dynamics, we also show that nonlinear resonances are excited in the oscillation widths of the quantum droplets. Variational predictions confirm numerical simulations for the corresponding formalism.