Stability of a Bose-Einstein condensate revisited for composite bosons

It is known that elementary bosons condense in a unique state, not so much because this state has the lowest free particle energy but because it costs a macroscopic amount of energy to put the particles into different states which can then interact through quantum particle exchanges. Since individual exchanges between the two fermions of a composite boson are ignored when composite particles are replaced by elementary bosons, it is of importance to reconsider the exchange energy argument for the stability of the Bose-Einstein condensate in the case of composite bosons. We do this here in the light of the new many-body theory which allows us to take exactly into account all possible exchanges between the fermionic components of the composite bosons. We confirm that the condensate of composite bosons is made of a unique state, this state being moreover pure: a coherent superposition of states close in energy is shown to be less favorable for both elementary and composite bosons.