Synthetic gauge potentials and analogue gravity in Bose-Einstein condensates
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In this thesis multi-component, spinorial cold atomic gases are studied. We investigate first the new perspectives introduced by nonlinear, that is density dependent, synthetic gauge fields in atomic Bose-Einstein condensate. Such fields stem from a collisionally induced detuning in combination with synthetic magnetism arising from the light-atom coupling. The effective mean field dynamics of the condensate shows the appearance of an exotic nonlinearity which is proportional to the current in the system. It introduces a chirality, whose effects on the stability and dynamical properties of the rotating state of a condensate is investigated. We show that by properly shaping the profile and the magnitude of the light-matter interaction parameters, it may happen that the rotating state is energetically favorable compared to the corresponding non-rotating one. Furthermore, we analyze the effects of the nonlinear field on the dynamics of a vortex in a condensate. We obtain the equation of motion for the vortex core, showing the appearance of an extra force which is explicitly depending on the number of particles that are in the system. Furthermore, we consider the implications of the same type of density-dependent fields in the context of analogue gravity. We show that they provide an extra degreeof- freedom that can be exploited in order to design effective non-trivial spacetimes experienced by phonons. In the framework of analogue models of gravity, we finally discuss the perspectives of two-dimensional systems, and address the problem of the black hole lasing effect in the spin modes of the system. By developing a Gross-Pitaevskii theory for the problem, we prove the onset of the lasing instability, and the phenomenon of mode conversion at the horizons. To this aim we consider both homogeneous and harmonically trapped condensates.