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Faraday patterns in coupled one-dimensional dipolar condensates

We study Faraday patterns in quasi-one-dimensional dipolar Bose-Einstein condensates with parametrically driven dipolar interactions. We show that in the presence of a roton minimum in the excitation spectrum, the emergent Faraday waves differ substantially in two- and one-dimensional geometries, providing a clear example of the key role of confinement dimensionality in dipolar gases. Moreover, Faraday patterns constitute an excellent tool to study non-local effects in polar gases, as we illustrate for two parallel quasi-one-dimensional dipolar condensates. Non-local interactions between the condensates give rise to an excitation spectrum characterized by symmetric and anti-symmetric modes, even in the absence of hopping. We show that this feature, absent in non-dipolar gases, results in a critical driving frequency at which a marked transition occurs between correlated and anti-correlated Faraday patterns in the two condensates. Interestingly, at this critical frequency, the emergent Faraday pattern stems from a spontaneous symmetry breaking mechanism.