  We study the quantum phase transition in a spin chain with variable Ising
interaction and position-dependent coupling to a resonator field. Such a
complicated model, usually not present in natural physical systems, can be
simulated by an array of qubits based on man-made devices and exhibits
interesting behavior. We show that, when the coupling between the qubit and
field is strong enough, a super-radiant phase transition occurs, and it is
possible to pick a particular field mode to undergo this phase transition by
properly modulating the strength of the Ising interaction. We also study the
impact of the resonator field on the magnetic properties of the spin chain, and
find a rich set of phases characterized by distinctive qubit correlation
functions.
