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In this short review we present our recent results concerning the rotation of atomic Bose-Einstein condensates confined in quadratic or quartic potentials, and give an overview of the field. We first describe the procedure used to set an atomic gas in rotation and briefly discuss the physics of condensates containing a single vortex line. We then address the regime of fast rotation in harmonic traps, where the rotation frequency is close to the trapping frequency. In this limit the Landau Level formalism is well suited to describe the system. The problem of the condensation temperature of a fast rotating gas is discussed, as well as the equilibrium shape of the cloud and the structure of the vortex lattice. Finally we review results obtained with a quadratic + quartic potential, which allows to study a regime where the rotation frequency is equal to or larger than the harmonic trapping frequency.
We propose an inverse method to accelerate without final excitation the adiabatic transport of a Bose Einstein condensate. The method, applicable to arbitrary potential traps, is based on a partial extension of the Lewis-Riesenfeld invariants, and pr
We demonstrate theoretically the spontaneous formation of a stochastic polarization in exciton-polariton Bose-Einstein condensates in planar microcavities under pulsed excitation. Below the threshold pumping intensity (dependent on the polariton life
We study the energetic and dynamic stability of coreless vortices in nonrotated spin-1 Bose-Einstein condensates, trapped with a three-dimensional optical potential and a Ioffe-Pritchard field. The stability of stationary vortex states is investigate
We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. This is done in the framework of the 2D Gross-Pitaevskii equation and requires a symplectic reduction of the quadratic form d
We review some theories of non-equilibrium Bose-Einstein condensates in potentials, in particular of the Bose-Einstein condensate of polaritons. We discuss such condensates, which are steady-states established through a balance of gain and loss, in t