We give a classification of all irreducible completely pointed $U_q(mathfrak{sl}_{n+1})$ modules over a characteristic zero field in which $q$ is not a root of unity. This generalizes the classification result of Benkart, Britten and Lemire in the no
n quantum case. We also show that any infinite-dimensional irreducible completely pointed $U_q(mathfrak{sl}_{n+1})$ can be obtained from some irreducible completely pointed module over the quantized Weyl algebra $A_{n+1}^q$.
In this paper we discuss in detail an experimental scheme to test the universality of free fall (UFF) with a differential $^{87}$Rb / $^{85}$Rb atom interferometer applicable for extended free fall of several seconds in the frame of the STE-QUEST mis
sion. This analysis focuses on suppression of noise and error sources which would limit the accuracy of a violation measurement. We show that the choice of atomic species and the correctly matched parameters of the interferometer sequence are of utmost importance to suppress leading order phase shifts. In conclusion we will show the expected performance of $2$ parts in $10^{15}$ of such an interferometer for a test of the UFF.
We report on a simple novel trapping scheme for the generation of Bose-Einstein condensates of $^{87}$Rb atoms. This scheme employs a near-infrared single beam optical dipole trap combined with a weak magnetic quadrupole field as used for magneto-opt
ical trapping to enhance the confinement in axial direction. Efficient forced evaporative cooling to the phase transition is achieved in this weak hybrid trap via reduction of the laser intensity of the optical dipole trap at constant magnetic field gradient.
