Controlling coupling strength between transmons with Left-Handed metamaterials

Metamaterial resonators exhibit an inverse dispersion relation and therefore have a high density of modes near the typical transmon frequency. Each mode contributes to the qubit-qubit coupling and the interaction transmitted by different modes can either enhance or cancel out the total interaction [1]. We study the effect of the relative position of the qubits along the transmission line and their flux-tuned frequency on the coupling strength between them. Lastly, we show that this can be used to increase or decrease the ZZ-interaction by several orders of magnitude by changing the qubit frequency by only tens of megahertz [1].