Unconventional geometric phase gate and multiqubit entanglement for hot ions with a frequency-modulated field

We present an alternative scheme for implementing the unconventional geometric two-qubit phase gate and preparing multiqubit entanglement by using a frequency-modulated laser field to simultaneously illuminate all ions. Selecting the index of modulation yields selective mechanisms for coupling and decoupling between the internal and the external states of the ions. By the selective mechanisms, we obtain the unconventional geometric two-qubit phase gate, multiparticle Greenberger--Horne--Zeilinger states and highly entangled cluster states. Our scheme is insensitive to the thermal motion of the ions.