Sinusoidal Excitations in Two Component Bose-Einstein Condensates

The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit pure sinusoidal, propagating wave solutions in quasi one dimensional geometry. These solutions, which exist for a wide parameter range, are then investigated in the presence of a harmonic oscillator trap with time dependent scattering length. This illustrates the procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. We subsequently analyzed this system in an optical lattice, where the occurrence of an irreversible phase transition from superfluid to insulator phase is seen.