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

The use of Left-Handed-Transmisson lines allows a very high mode denisty at frequencies above the IR cutoff due to its disperson relation. We theoretically support an experiment on coupling two qubits to the device and calculate the g-coupling to the modes, which exhibit different frequency dependency when compared to the right-handed case. A careful analysis of these couplings leads to the effective coupling between the qubits, which can be very large, since the modes are very dense and therefore transmit high interaction. In general this causes the ZZ-interaction between the qubits to be large, but we can still acurately predict static qubit-qubit interaction both for only a few kHz aswell as for tens of MHz. In this talk we will present the modeling of this Left-Handed system and compare it to experimental measurements.