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We study photonic signatures of symmetry broken and topological phases in adriven, dissipative circuit QED realization of spin-1/2 chains. Specifically,we consider the transverse-field XY model and a dual model with 3-spininteractions. The former has a ferromagnetic and a paramagnetic phase, whilethe latter features, in addition, a symmetry protected topological phase. Usingthe method of third quantization, we calculate the non-equilibrium steady-stateof the open spin chains for arbitrary system sizes and temperatures. We findthat the bi-local correlation function of the spins at both ends of the chainprovides a sensitive measure for both symmetry-breaking and topological phasetransitions of the systems, but no universal means to distinguish between thetwo types of transitions. Both models have equivalent representations in termsof free Majorana fermions, which host zero, one and two topological Majoranaend modes in the paramagnetic, ferromagnetic, and symmetry protectedtopological phases, respectively. The correlation function we study retains itsbi-local character in the fermionic representation, so that our results areequally applicable to the fermionic models in their own right. We propose aphotonic realization of the dissipative transverse-field XY model in a tunablesetup, where an array of superconducting transmon qubits is coupled at bothends to a photonic microwave circuit.

Signatures of topological quantum phase transitions in driven and dissipative qubit-arrays