Faraday waves in binary nonmiscible Bose-Einstein condensates

Abstract

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.

Quantum gas mixtures in different correlation regimes

“…In the semiclassical limit it is known that symmetrybreaking eigenstates exist, which can have an energy very close to the energy of the symmetric ground state [26][27][28][29][30]. While in the few atom limit and for the symmetric Hamiltonian discussed above, the lowest energy state is the one shown in Figs.…”

Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures

“…Numerical solutions of the ODE model (13) are presented in Fig. 1 for parameters corresponding to the BCS regime.…”

“…Other examples are the patterns in the Bose-Einstein condensates (BECs) with an atomic scattering length or a radial confinement (a transverse frequency of the trap) periodically varying in time. For BECs the cases of one- [8][9][10][11] and two-component condensates [12,13], as well as dipolar condensates [14,15], have been investigated. Related parametric amplifications in an optical lattice have been studied in Ref.…”

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

“…Recently, the authors became aware of the work [45] on the Faraday resonance in two-component BEC confined to a quasi 1D geometry. The main difference between the current work and Ref.…”

“…[45] is in the geometry (multidimensional versus 1D, respectively) and in the nature of the surface waves amplified by the oscillating external force. Here we study interfacial capillary modes on the common surface of two BECs, while in the work [45] these are the surface modes at the edges of each BEC facing vacuum.…”