# Bosonic qubits using BEC versus usual qubit implementations based on energy levels

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"?

BEC qubits are set up by splitting one harmonic condensate trap into a double-well trap by means of a suitable laser or microwave field. See for instance pg.6 on these LANL slides: Quantum dynamics, measurement and decoherence in Bose-Einstein condensates. Under strong enough separation the overall ground state becomes two-fold degenerate and the two distinct levels can be used to encode one qubit. Several juxtaposed double-traps will provide a multi-qubit system. The paper simply assumes a system of $log_2N$ such qubits, evolving overall according to the Gross-Pitaevskii nonlinear dynamics Schroedinger equation.