Synthetic gauge potentials and analogue gravity in Bose-Einstein condensates
Abstract
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.