A scheme for the generation of a nonclassical Bose-Einstein condensate is proposed in a Jg = 1 → Je = 0 system where ultracold atoms are populated in one ground-state sublevel |g-⟩ and form a Bose-Einstein condensate. By coupling the condensate to copropagating classical (σ-) and quantum (σ+) non-resonant travelling-wave laser fields, effective two-photon excitations between two ground-state sublevels |g-⟩ and |g+⟩ create a new condensate in |g+⟩. For an appropriate selection of the interaction time and atom-field coupling strengths, the quantum features of the quantized laser field, which may be prepared in a certain nonclassical state, can be exchanged with those of the quantum density field of the generated condensate.