Molecular Orbital Theory of the gaseous Bose-Einstein condensate: Natural Orbital analysis of strongly correlated ground and excited states of an atomic condensate in a double well

The possibility, envisaged in 1925 by Einstein following the suggestion of Bose, of a dilute gas of atoms being condensed into a single quantum state was experimentally achieved in 1995 following decades of research. An avalanche of experiment and theory has followed, leading to the awarding of the 2001 Nobel Prizes in Physics to three of the pioneering experimentalists. Theory, mostly couched in the language and formalism of condensed matter physics, has developed apace. What we point out here is that a condensate in a double well trap may be thought of exactly as a diatomic molecule with delocalized molecular orbitals (MOs) filled with Bosons, rather than electrons. As in quantum chemistry, configuration interaction must be included to supplement the MO picture if dissociation is to be correctly described. Such dissociation is called condensate fragmentation in the condensed matter theory literature. Natural orbitals and their occupation numbers provide a clear and succinct way of determining where the atoms are in highly correlated states as fragmentation occurs, and are particularly helpful in understanding what is actually happening when energy levels with macroscopic occupancy cross as a function of breaking the symmetry between the trap wells. It is seen that only a few particles are actually active in the level crossing. Recent experiments in super-conductive Josephson loops showing tunneling of macroscopic quantum states are easily included in this picture.