  We calculate the transmission spectrum of a superconducting circuit
realization of the Dicke model and identify spectroscopic features that can
serve as signatures of the superradiant phase. In particular, we calculate the
resonance frequencies of the system as functions of the bias term, which is
usually absent in studies on the Dicke model but is commonly present in
superconducting qubit circuits. To avoid over-complicating the proposed
circuit, we assume a fixed coupling strength. This situation precludes the
possibility of observing signatures of the phase transition by varying the
coupling strength across the critical point. We show that the spectrum obtained
by varying the bias point under fixed coupling strength can contain signatures
of the normal and superradiant phases: in the normal phase one expects to
observe two spectral lines, while in the superradiant phase four spectral lines
are expected to exist close to the qubits' symmetry point. Provided that
parameter fluctuations and decoherence rates are sufficiently small, the four
spectral lines should be observable and can serve as a signature of the
superradiant phase.
