We propose a method to achieve photon pair propagation in an array of three-level superconducting circuits. Assuming experimentally accessible three-level artificial atoms with strong anharmonicity coupled via microwave transmission lines in both one and two dimensions we analyze the circuit quantum electrodynamics (QED) of the system. We explicitly show that, for a suitable choice of the coupling ratio between different levels, the single-photon propagation is suppressed and the propagation of photon pairs emerges. This propagation of photon pairs leads to the pair superfluid of polaritons associated with the system. We compute the complete phase diagram of the polariton quantum matter revealing the pair superfluid phase which is sandwiched between the vacuum and the Mott insulator state corresponding to the polariton density equal to 2 in the strong-coupling regime.

• Received 10 March 2020
• Revised 16 July 2020
• Accepted 25 September 2020

DOI:https://doi.org/10.1103/PhysRevA.102.043710