Faraday Patterns in Spinor Spin-1 Bose-Einstein Condensates

Abstract

Vertical vibrations in classical liquids give rise to non-linear standing waves called Faraday waves when the driving frequency is greater than a critical value. An analogous phenomenon is seen in Bose-Einstein Condensates when the system’s non-linearity is modulated and the uniform state loses it’s stability to spatially modulated states. We study Faraday Patterns in Spin-1 Spinor Bose-Einstein Condensate on periodic modulation of the different s-wave scattering lengths, a0 and a2. The size of these patterns depends upon Bogoliubov mode resonant with half of the driving frequency. In the case of Spin-1 Bose-Einstein Condensate, the nature of the Bogoliubov spectrum of spinor BECs depends explicitly on the magnetic ground state and also they are multi-branched with both spin and density modes, or coupling between them. The excitations of the spin-modes in some of the ground states leads to spin dynamics and formation of interesting spin-structures which have wavenumber indicative of the corresponding Bogoliubov mode. We find that by modulating the two scattering channels of spin-1 BEC with varied frequencies and amplitudes we can excite and explore different Bogoliubov modes of the spinor BEC.