We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong coupling regime and find that fundamental quantum optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield single- or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two-photon couplings in the dispersive regime, where two- photon interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multi-qubit two-photon quantum Rabi model and find a scaling of the critical coupling with the number of qubits. Using realistic parameters with the circuit proposed, three qubits are sufficient to reach the collapse point.
@article{arxiv.1711.10032,
title = {Two-photon quantum Rabi model with superconducting circuits},
author = {S. Felicetti and D. Z. Rossatto and E. Rico and E. Solano and P. Forn-Díaz},
journal= {arXiv preprint arXiv:1711.10032},
year = {2018}
}