Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates

Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.Comment: 18 pages, 10 figure

Faraday waves in binary non-miscible Bose-Einstein condensates

We show by extensive numerical simulations and analytical variational calculations that elongated binary non-miscible Bose-Einstein condensates subject to periodic modulations of the radial confinement exhibit a Faraday instability similar to that seen in one-component condensates. Considering the hyperfine states of $^{87}$Rb condensates, we show that there are two experimentally relevant stationary state configurations: the one in which the components form a dark-bright symbiotic pair (the ground state of the system), and the one in which the components are segregated (first excited state). For each of these two configurations, we show numerically that far from resonances the Faraday waves excited in the two components are of similar periods, emerge simultaneously, and do not impact the dynamics of the bulk of the condensate. We derive analytically the period of the Faraday waves using a variational treatment of the coupled Gross-Pitaevskii equations combined with a Mathieu-type analysis for the selection mechanism of the excited waves. Finally, we show that for a modulation frequency close to twice that of the radial trapping, the emergent surface waves fade out in favor of a forceful collective mode that turns the two condensate components miscible.Comment: 13 pages, 10 figure

Exact stationary solutions of the parametrically driven and damped nonlinear Dirac equation

Two exact stationary soliton solutions are found in the parametrically driven and damped nonlinear Dirac equation. The parametric force considered is a complex ac force. The solutions appear when their frequencies are locked to half the frequency of the parametric force, and their phases satisfy certain conditions depending on the force amplitude and on the damping coe cient. Explicit expressions for the charge, the energy, and the momentum of these solutions are provided. Their stability is studied via a variational method using an ansatz with only two collective coordinates. Numerical simulations con rm that one of the solutions is stable, while the other is an unstable saddle point. Consequently, the stabilization of damped Dirac solitons can be achieved via time-periodic parametric excitations.Junta de Andalucía and Ministerio de Economía y Competitividad of Spain FIS2017-89349-PMinisterio de Ciencia, Innovación y Universidades of Spain PGC2018-093998-BI0

Faraday waves on a bubble Bose-Einstein condensed binary mixture

By studying the dynamic stability of Bose-Einstein condensed binary mixtures trapped on the surface of an ideal two-dimensional spherical bubble, we show how the Rabi coupling between the species can modulate the interactions leading to parametric resonances. In this spherical geometry, the discrete unstable angular modes drive both phase separations and spatial patterns, with Faraday waves emerging and coexisting with an immiscible phase. Noticeable is the fact that, in the context of discrete kinetic energy spectrum, the only parameters to drive the emergence of Faraday waves are the $s-wave$ contact interactions and the Rabi coupling. Once analytical solutions for population dynamics are obtained, the stability of homogeneous miscible species is investigated through Bogoliubov-de Gennes and Floquet methods, with predictions being analysed by full numerical solutions applied to the corresponding time-dependent coupled formalism.Comment: 17 pages, 15 figure

Patterning by dynamically unstable spin-orbit-coupled Bose-Einstein condensates

In a two-dimensional atomic Bose-Einstein condensate, we demonstrate Rashba spin-orbit coupling can always introduce dynamical instability into specific zero-quasimomentum states in all parameter regimes. During the evolution of the zero-quasimomentum states, such spin-orbit-coupling-induced instability can fragment the states and lead to a dynamically patterning process. The features of formed patterns are identified from the symmetries of the Bogoliubov-de Gennes Hamiltonian. We show that spin-orbit-coupled Bose-Einstein condensates provide an interesting platform for the investigation of pattern formations.Comment: Accepted for publication in Chao, Solitons & Fractal

Faradejevi talasi u ultrahladnim dipolnim Boze gasovima

Nakon pionirskih eksperimenata sa sistemima ultrahladnih atoma u kojima je realizovana Boze-Ajnčtajn kondenzacija sa slabom kontaktnom interakcijom, bila je potrebna čitava decenija...After pioneering experiments that realized Bose-Einstein condensates in systems of ultracold atoms with weak contact interactions, it took a decade for experimental techniques to advance and enable measurement of effects of the dipole-dipole interaction that exist between atoms or molecules with a permanent or induced electric or magnetic dipole moment..