Detector of microwave photon pairs based on a Josephson photomultiplier

We propose a viable design of a microwave two-photon threshold detector. In essence, the considered scheme is an extension of the existing single-photon detector - a Josephson photomultiplier (JPM) - an absorbing microwave detector based on a capacitively-shunted rf SQUID. To implement a two-photon threshold detector, we utilize a dimer of resonators - two lumped-element resonators interacting via an asymmetric dc SQUID, with one of the resonators capacitively coupled to the JPM. By specific tuning of the resonator frequencies and the external flux through the dc SQUID coupler, we engineer a non-perturbative two-photon coupling between the resonators. This coupling results in the coherent conversion of a photon pair from one resonator into a single photon in another resonator, enabling selective response to quantum states with at least two photons. We also consider an extended coupler design that allows on-demand \textit{in situ} switching of two-photon coupling. In addition, we propose the modified JPM design to improve its performance. Our calculations demonstrate that, for realistic circuit parameters, we can achieve more than $99\%$ fidelity of photon pair detection in less than 50 ns. The considered scheme may serve as a building block for the implementation of efficient photon-number-resolving detectors in circuit QED architecture.