  For a Bose condensate in a double-well potential or with two
Josephson-coupled internal states, the condensate wavefunction is a
superposition. Here we consider coupling two such Bose condensates, and suggest
the existence of a joint condensate wavefunction, which is in general a
superposition of all products of the bases condensate wavefunctions of the two
condensates. The corresponding many-body state is a product of such superposed
wavefunctions, with appropriate symmetrization. These states may be potentially
useful for quantum computation. There may be robustness and stability due to
macroscopic occupation of a same single particle state. The nonlinearity of the
condensate wavefunction due to particle-particle interaction may be utilized to
realize nonlinear quantum computation, which was suggested to be capable of
solving NP-complete problems.
