Dynamical tunnelling is a quantum phenomenon where a classically forbidden process occurs, that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunnelling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunnelling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.
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