Two-photon quantum Rabi model with superconducting circuits

TL;DR

This paper proposes a superconducting circuit to realize a two-photon quantum Rabi model, revealing modified quantum optical phenomena and analyzing spectral collapse with multiple qubits, advancing solid-state quantum simulation capabilities.

Contribution

It introduces a novel superconducting circuit design for the two-photon quantum Rabi model and analyzes its quantum optical properties and spectral collapse phenomena.

Findings

Two-photon interactions enable photon blockade effects.

Effective Hamiltonian includes qubit-state-dependent Kerr nonlinearity.

Three qubits can reach spectral collapse with realistic parameters.

Abstract

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.