Condensates and Bose-Einstein correlations

We discuss the conditions under which Bose-Einstein correlation can be used to determine the presence of condensates. One starts from the fact that any condensate is a coherent state and uses then the formalism of quantum optics. The case of final state interactions is considered explicitly in a Landau-Ginzburg type approach as used in laser physics. By applying a mean field Hartree approximation for the many mode problem we find that the second order correlation function for identical bosons $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{=0)}$ does effectively not depend on the phenomenological coupling constant g and thus C₂(0) can be used to determine the amount of coherence and hence the existence of condensates. On the other hand $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{≠0)}$ does depend on g and therefore its measurement provides information about g. The implications of these findings for the determination of the size and lifetime of the source á la Hanbury-Brown-Twiss are discussed. Our conclusions apply both to condensates in nuclear (pion condensates, alpha and deuteron condensates) and hadronic matter.