In this paper, we show that it is possible to manipulate the many-body wave function of an isolated dot with a few electrons by locally applying magnetic and electric fields. We polarize the dot at a level crossing, where the sensitivity is at its maximum. Time-dependent fields produce a superposition of the states involved in the avoided crossing. In the case of N = 2 and N =3 electrons, the results of exact diagonalisation give information about the nature of these states and allow us to construct an effective Hamiltonian describing the coupling. The formalism for evaluating the Berry phase arises naturally. We argue that a quantum dot, capacitively coupled to a quantum point contact, can influence its conductance. The quantum superposition of the states produced by cycling the fields on the dot can be measured this way.