We have studied a Bose-Einstein condensate of 87 Rb atoms under an oscillatory excitation. For a fixed frequency of excitation, we have explored how the values of amplitude and time of excitation must be combined in order to produce quantum turbulence in the condensate. Depending on the combination of these parameters different behaviors are observed in the sample. For the lowest values of time and amplitude of excitation, we observe a bending of the main axis of the cloud. Increasing the amplitude of excitation we observe an increasing number of vortices. The vortex state can evolve into the turbulent regime if the parameters of excitation are driven up to a certain set of combinations. If the value of the parameters of these combinations is exceeded, all vorticity disappears and the condensate enters into a different regime which we have identified as the granular phase. Our results are summarized in a diagram of amplitude versus time of excitation in which the different structures can be identified. We also present numerical simulations of the Gross-Pitaevskii equation which support our observations.

We report on the creation of three-vortex clusters in a 87 Rb Bose-Einstein condensate by oscillatory excitation of the condensate. This procedure can create vortices of both circulation, so that we are able to create several types of vortex clusters using the same mechanism. The three-vortex configurations are dominated by two types, namely, an equilateral-triangle arrangement and a linear arrangement. We interpret these most stable configurations respectively as three vortices with the same circulation, and as a vortex-antivortex-vortex cluster. The linear configurations are very likely the first experimental signatures of predicted stationary vortex clusters.

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Phase transitions are well understood and generally followed by the behavior of the associated thermodynamic quantities, such as in the case of the λ-point superfluid transition of liquid He, which is observed in its heat capacity. In the case of a trapped Bose-Einstein condensate, the heat capacity cannot be directly measured. In this work, we present a technique capable of determining the global heat capacity from the density distribution of a weakly interacting gas trapped in an inhomogeneous potential. This approach represents an alternative to models based on the local density approximation. By defining a pair of global conjugate variables, we determine the total internal energy and its temperature derivative, the heat capacity. We then apply the technique to a trapped 87 Rb BEC, and a λ-type transition dependent on the atom number is observed, and the deviations from the noninteracting, ideal gas case are discussed. Finally, we discuss the chances of using this method to study the heat capacity at T → 0.