Gate-tunable fluxonium demonstrates linear flux-charge coupling via modulated Josephson junction

The experiment employs a voltage-tunable Josephson junction whose critical current is parametrically modulated to mediate interaction between a classical charge variable and the quantum flux operator of the fluxonium loop. Parity selection rules in the hybrid device suppress unwanted capacitive terms, allowing isolation of the target interaction. Coherent control is demonstrated by driving transitions whose strength scales linearly with modulation amplitude while the qubit transition energy remains first-order insensitive to gate voltage. This architecture directly addresses the absence of native two-terminal flux-charge elements in standard superconducting circuit theory.

Standard capacitive and inductive couplings preserve conjugate-variable separation; the new term enables circuit primitives for non-reciprocity and protected encodings previously requiring three-wave mixing or external elements. The result aligns with earlier theoretical proposals for conjugate-variable mixing but supplies the first experimental calibration of coupling strength versus drive parameters in a fluxonium. Compared with prior fluxonium implementations focused on coherence times, the present work prioritizes interaction engineering at the single-device level.

Scaling implications include compact non-reciprocal elements and readout schemes that avoid auxiliary resonators. Next steps require embedding multiple such junctions in larger lattices while preserving the observed linearity and voltage insensitivity. Integration with existing fluxonium fabrication flows appears feasible, yet junction uniformity across wafers remains the dominant engineering constraint.