On the stability of the coherent state of a two-level atom Bose gas in the resonant laser field at zero temperature

It is shown that a Bose gas of two-level atoms in the intense resonant laser field at zero temperature is a mixture of two condensates with a definite ratio of the densities. The criteria of stability are found for the stationary states of such system against the increment of the amplitudes of quasi Bogoliubov elementary excitations. Besides the usual acoustic mode the gap mode is shown to exist and the magnitude of the gap is proportional to the laser field amplitude. The involvement of the gas nonideality under definite conditions results in an instability and decay of the condensates.