Experimental Verification of Time-Dependent Flux Allocation in Fluxonium

External flux in the fluxonium Hamiltonian is generally allocated entirely to the inductor or to the Josephson junction, both of which are equally valid in the case of static external flux. However, recent theory work has shown that given a time-dependent external flux, allocation of the flux to the junction leads to terms proportional to the time derivative of the flux appearing in the Hamiltonian [1]. When the flux is allocated to the inductor, the usual fluxonium Hamiltonian is recovered. Here, we experimentally verify the theory predictions by rapidly modulating the external flux and recording qubit state transfer. We find results consistent with grouping the flux with the inductor, and inconsistent with grouping the flux with the junction while ignoring the derivative term.

 

[1] X. You, et. al, Phys. Rev. B (2019).