This paper gives a historical perspective to the gestation and birth of Bose-Einstein (BE).As is known today, particles whose spin is an even multiple of
hslash/2 obey BE statistics, those whose spin is an odd multiple of
hslash/2 obey FD statistics. (These particles may be elementary or composite.) Both statistics are derived from the fact that particles in the quantum realm are indistinguishable, the difference being that in the FD case at most one particle can occupy any given quantum state (Pauli principle) while in the BE case any number of particles can be in a particular state. Little of this was known when the statistics were first developed by Bose. The paper gives the background of attempts to explain the black-body spectrum, which led eventually to Bose's combinatorical derivation of the Planck law using the concept of indistinguishability. (Bose was professor of physics at Dacca, in what is now Bangladesh, then India.) Einstein was the first to appreciate Bose's work, translating the paper into German for publication in Zeitschrift für Physik, and applying the methods to a quantum gas (hence, "Bose-Einstein condensation", which explains the bizarre behavior of liquid
rmHe4). \n\n
We calculate the spectrum of the scattered light from quantum degenerate atomic gases obeying Bose-Einstein statistics. The atoms are assumed to occupy two ground states, which are optically coupled through a common excited state by two low-intensity off-resonant light beams. In the presence of a Bose condensate in both ground states, the atoms may exhibit light-induced oscillations between the two condensates analogous to the Josephson effect. The spectrum of the scattered light is calculated in the limit of a low oscillation frequency. In the spectrum we are able to observe qualitative features depending on the phase difference between the macroscopic wave functions of the two condensates. Thus, our optical scheme could possibly be used as an experimental realization of the spontaneous breakdown of the U(1) gauge symmetry in the Bose-Einstein condensation.