  In this work we show the simplest and integrable model for Bose-Einstein
condensates loaded in a triple well potential where the tunneling between two
wells can be controlled by the other well showing a behavior similar to an
electronic field effect transistor. Using a classical analysis, the Hamilton's
equation are obtained, a threshold indicating a discontinuous phase transition
is presented and the classical dynamics is computed. Then, the quantum dynamics
is investigated using direct diagonalisation. We find well agreement in both
these analysis. Based on our results, the switching scheme for tunneling is
shown and the experimental feasibility is discussed.
