Superstrong coupling between a transmon and a metamaterial resonator

A high density of modes can be produced using metamaterial resonant structures made from arrays of lumped circuit elements, to which a flux-tunable transmon qubit can be coupled. For such a system, we have measured the coupling strength of the qubit to multiple modes by tuning the flux and observing the splitting in the transmission of each mode. To enhance the coupling strength in our next generation devices, we can increase the resonator impedance and the number of unit cells of the metamaterial resonator. In addition, by increasing the coupling capacitance between the qubit and metamaterial resonator, our simulations indicate that it will be possible to reach the superstrong coupling regime, where the coupling strengths exceed the inter-mode spacing and the qubit can thus be coupled to multiple modes simultaneously. The inclusion of on-chip flux-bias lines can enable the non-adiabatic modulation of the qubit transition or parametric modulation, which can be used to swap excitations between the qubit and the metamaterial. Superstrong coupling with fast qubit modulation will have a variety of applications in analog quantum simulations and multi-mode cQED. We report on our progress with implementing metamaterial devices with enhanced qubit coupling.