Entangling Interactions Between Artificial Atoms Mediated by a Multimode Left-Handed Superconducting Ring Resonator

Superconducting metamaterial transmission lines implemented with lumped circuit elements can exhibit left-handed dispersion, where the group and phase velocity have opposite sign, in a frequency range relevant for superconducting artificial atoms. Forming such a metamaterial transmission line into a ring and coupling it to qubits at different points around the ring results in a multimode bus resonator with a compact footprint. Using flux-tunable qubits, we characterize and theoretically model the variation in the coupling strength between the two qubits and each of the ring-resonator modes. Although the qubits have negligible direct coupling between them, their interactions with the multimode ring resonator result in both a transverse exchange coupling and a higher-order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>Z</a:mi><a:mi>Z</a:mi></a:math> interaction between the qubits. As we vary the detuning between the qubits and their frequency relative to the ring-resonator modes, we observe significant variations in both of these interqubit interactions, including zero crossings and changes of sign. The ability to modulate interaction terms such as the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mi>Z</d:mi><d:mi>Z</d:mi></d:math> scale between zero and large values for small changes in qubit frequency provides a promising pathway for implementing entangling gates in a system capable of hosting many qubits. Published by the American Physical Society 2024