Parametric instability of a two-component Bose-Einstein condensate driven by a strong time-dependent magnetic field

We investigate the behavior of a two-component Bose-Einstein condensate (BEC) driven by a strong time-dependent resonant magnetic field. The external resonant field couples two hyperfine states via a one-photon transition. It is shown that a first-order parametric instability of a BEC appears if the local atomic number density exceeds a threshold value that is proportional to the driving field. It is shown that the spatial-dependent increment of instability is proportional to the square of the local atomic density. This instability is determined by the nonlinearity of the BEC associated with the short-range interactions between the atoms.