Entanglement in the Dicke model

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Abstract
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.

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