Density-matrix approach to a strongly coupled two-component Bose-Einstein condensate

The time evolution equations for average values of population and relative phase of a strongly coupled two-component Bose-Einstein condensate (BEC) are derived analytically. The two components are two hyperfine states, which are coupled by an external laser that drives fast Rabi oscillations between these states. Specifically, this derivation incorporates the two-mode model proposed in J. Williams et at, e-print cond-mat 9904399 for the strongly coupled hyperfine states \1,-1 > and \2,1 > of Rb-87. The fast Rabi cycles are averaged out and the rate equations so derived represent the slow dynamics of the system. These include the collapse and revival of Rabi oscillations and their dependence on detuning and trap displacement as reported in experiments of J. Williams. A procedure for stabilizing vortices is also suggested.