  The Dicke model describes N qubits (or two-level atoms) homogenously coupled
to a bosonic mode. Here we examine an open-system realization of the Dicke
model, which contains critical and chaotic behaviour. In particular, we extend
this model to include an additional open transport qubit (TQ) (coupled to the
bosonic mode) for passive and active measurements. We illustrate how the
scaling (in the number of qubits N) of the superradiant phase transition can be
observed in both current and current-noise measurements through the transport
qubit. Using a master equation, we also investigate how the phase transition is
affected by the back-action from the transport qubit and losses in the cavity.
In addition, we show that the non-integrable quantum chaotic character of the
Dicke model is retained in an open-system environment. We propose how all of
these effects could been seen in a circuit QED system formed from an array of
superconducting qubits, or an atom chip, coupled to a quantized resonant cavity
(e.g., a microwave transmission line).
