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The emergence of transient checkerboard and stripe patterns in a stack of driven quasi-one-dimensional homogeneous dipolar condensates is studied. The parametric driving of the $s$-wave scattering length leads to the excitation of the lowest collective Bogoliubov mode. The character of the lowest mode depends critically on the orientation of the dipoles, corresponding to out-of-phase and in-phase density modulations in neighboring condensates, resulting in checkerboard and stripe patterns. Further, we show that a dynamical transition between the checkerboard and stripe patterns can be realized by quenching the dipole orientation either linearly or abruptly once the initial pattern is formed via periodic driving., Comment: 8 pages, 7 figures

We analyze the formation of transient patterns and spin-spin correlations in quasi-two-dimensional spin-1 homogeneous Bose-Einstein condensates subjected to parametric driving of $s$-wave scattering lengths. The dynamics for an initial ferromagnetic phase is identical to that of a scalar condensate. In contrast, intriguing dynamics emerges for an initial polar state. For instance, we show that competition exists between density patterns and spin-mixing dynamics. Dominant spin-mixing dynamics lead to a gas of polar core vortices and anti-vortices of different spin textures. The density modes of the Bogoliubov spectrum govern the wavenumber selection of Faraday patterns. The spin modes determine the vortex density and the spatial dependence of spin-spin correlation functions. When the density patterns outgrow the spin-mixing dynamics, the spin-spin correlations decay exponentially with a correlation length of the order a spin healing length; otherwise, they exhibit a Bessel function dependence. Strikingly, competing instabilities within density and spin modes emerge when both scattering lengths are modulated at different frequencies and appropriate modulation amplitudes. The competing instability leads to a superposition of density patterns or correlation functions of two distinct wavelengths. Our studies reveal that fine control over the driven dynamics can be attained by tuning interaction strengths, quadratic Zeeman field, driving frequencies, and amplitudes., Comment: 11 pages, 13 figures

We analyze the dynamics of both population and spin densities, emerging from the spatial overlap between two distinct polar bright solitons in Spin-1 Spinor Condensates. The dynamics of overlapping solitons in scalar condensates exhibits soliton fusion, atomic switching from one soliton to another and repulsive dynamics depending on the extent of overlap and the relative phase between the solitons. The scalar case also helps us understand the dynamics of the vector solitons. In the spinor case, non-trivial dynamics emerge in spatial and spin degrees of freedom. In the absence of spin changing collisions, we observe Josephson-like oscillations in the population dynamics of each spin component. In this case, the population dynamics is independent of the relative phase, but the dynamics of the spin-density vector depends on it. The latter also witnesses the appearance of oscillating domain walls. The pair of overlapping polar solitons emerge as four ferromagnetic solitons irrespective of the initial phase difference for identical spin-dependent and spin-independent interaction strengths. But the dynamics of final solitons depends explicitly on the relative phase. Depending on the ratio of spin-dependent and spin-independent interaction strengths, a pair of oscillatons can also emerge as the final state. Then, increasing the extent of overlap may lead to the simultaneous formation of both a stationary ferromagnetic soltion and a pair of oscillatons depending on the relative phase., Comment: 11 Pages and 16 Figures