Based on cavity QED, we first propose the unified scheme to implement the 1→2 optimal universal quantum cloning machine for arbitrary input state, the asymmetric 1→2 phase-covariant cloning and the 1→3 optimal asymmetric economical phase-covariant quantum cloning machine for the equatorial input state. During the cloning process, due to atoms interacting with a highly detuned cavity mode, thus the scheme is insensitive to the cavity decay and thermal field.
