Multimode entangling interactions between transmons coupled through a metamaterial ring-resonator: experiment

Left-handed metamaterial transmission line resonators made with arrays of superconducting lumped circuit elements have unique dispersion relations resulting in densely grouped mode spectra. Forming these transmission lines into a ring allows access to these densely grouped resonances, but with a compact footprint allowing for flexible design. Superconducting qubits can be coupled to multiple modes in these left-handed metamaterial ring resonators, resulting in a novel landscape of entangling interactions between qubits. We have fabricated and characterized such a device with two superconducting transmon qubits coupled to a left-handed metamaterial ring resonator. We present results characterizing the interactions between the qubit and modes and the interactions between qubits. We find a broad range of g coupling values between the two qubits and modes that mediate the interaction between qubits. The J coupling between the two qubits exhibits high variability depending on qubit detuning and mode proximity. Similarly, the entangling ZZ interaction can be tuned over a wide range. This system thus forms a novel architecture for interaction between qubits through a multimode system.