Bosonic stimulation and the irreproducibility of condensate fragmentation

It is pointed out that the quantum statistical phenomenon of Bosonic stimulation, inherent to Bose statistics and the associated Bose-Einstein correlation, can be effectively mapped on to the statistical problem of the Polya urn scheme. Thus, we predict an irreproducibility for the limiting non-degenerate values of the relative populations of two, or more equivalent but separated condensates resulting from the fragmentation of a given source condensate. Experiments are proposed that should verify this prediction − using the dilute gas Bose-Einstein condensates, or a pulsed degenerate multi-mode laser, where one would look for the run-to-run (or the pulse-to-pulse) fluctuations of the relative populations. It is a deep, but rather well known result that the indistinguishability of identical Bosons, and the associated quantum (Bose) statistics, implies a certain non-classical Bose-Einstein correlation. 1,2 Thus, the indistinguishable Bose particles emitted from a given source, or from proximate sources, are so correlated in space-time, or momentum-energy, as to imply enhanced probability of emission of the particles with small relative momentum. A direct manifestation of this Bosonic stimulation, 1,3 wherein a Bose particle is preferentially scattered (stimulated scattering) into the final single particle state which has a higher pre-existing Bosonic population. This derives straightforwardly from the usual Bose factor (n+1) in a + |n = √ n + 1|n + 1. It is now easy to see that, from the point of view of the relative population statistics, this phenomenon of Bosonic stimulation maps on to that associated with the Polya 1