Generation of many-particle entanglement in an ion trap by adiabatic ground-state transitions

We discuss the creation of many-particle entanglement in an ion trap where all ions are simultaneously coupled to bichromatic laser fields. It is shown that in a time-averaged, coarse-grained picture the system can be mapped onto a spin ensemble with controllable collective interactions. An adiabatic change of laser parameters allows a transfer from separable to entangled eigenstates of the many-particle Hamiltonian. Of particular interest is a transition in the ground state which in some cases corresponds to a quantum phase transition. The influence of decoherence mechanisms can be substantially reduced if at all times a sufficiently large energy gap between the ground state and the first excited state is maintained.