  We show how an ion trap, configured for the coherent manipulation of external
and internal quantum states, can be used to simulate the irreversible dynamics
of a collective angular momentum model known as the Dicke model. In the special
case of two ions, we show that entanglement is created in the coherently driven
steady state with linear driving. For the case of more than two ions we
calculate the entanglement between two ions in the steady state of the Dicke
model by tracing over all the other ions. The entanglement in the steady state
is a maximum for the parameter values corresponding roughly to a bifurcation of
a fixed point in the corresponding semiclassical dynamics. We conjecture that
this is a general mechanism for entanglement creation in driven dissipative
quantum systems.
