Stability of atomic-molecular coherent states of hybrid Bose-Einstein condensates

We study the stability of coherent atomic-molecular states of hybrid Bose-Einstein condensates in the framework of the parametrically coupled Gross-Pitaevskii equations with a weak 'short-correlated' noise, also taking into account the self-interaction effects described by the cubic nonlinearity. We show that the stationary states of the hybrid atomic-molecular condensates are much more robust against the effect of noise than the condensate in the critical regime, describing a complete transformation of the atomic fraction into a molecular condensate, where instability develops essentially faster, with the characteristic time proportional to the logarithm of the noise amplitude.