Collective dynamics of internal states in a Bose-Einstein gas

A theory for the Rabi and internal Josephson effects in an interacting, homogeneous Bose-Einstein gas in the cold collision regime is presented. By using the microscopic transport equation for the density matrix the problem is mapped onto a problem of precession of two coupled classical spins. In the absence of an external excitation field our results agree with the theory of density induced frequency shifts in atomic clocks. In the presence of the external field, the internal Josephson effect occurs in a condensed Bose-Einstein gas as well as in a noncondensed gas. The crossover from Rabi oscillations to Josephson oscillations as a function of interaction strength is studied in detail.