Scheme for realizing ancilla-free 1→M economic phase-covariant quantum cloning of qubits and qutrits

We propose an experimental scheme to realize the ancilla-free 1→M economic phase-covariant quantum cloning of the equatorial qubit and qutrit. The cloning is implemented by the resonant interaction of the atoms with cavity field of a high-Q cavity. The scheme is deterministic and basic quantum operations to realize schemes may be realized with the current experimental technology.