All condensate atoms in a BEC (say like Rb, etc) effectively occupy the lowest energy-state. If it is that the case, then how are such bosons in a BEC encoded as a qubit? In particular, when Grover Search is done using a BEC, it is said in arxiv.org/abs/1303.0371: that each condensate atom does an effective log(N) bit (or n-bit) query on the oracle in parallel. That is, each condensate atom is modelled as a n-qubit system (n=log(N)).
But, since a BEC has all the condensate atoms in the ground state, how is this log(N) bit query implemented by each of the atoms? Being an undergrad, I didn't come across bosonic qubit states until now. How are these realized in comparison with the "usual" qubits with many energy "levels"?