Emergence of quasi-charge in an ultra-high-impedance superconducting circuit: Design

We introduce an ultra-high-impedance superconducting circuit where the role of phase difference across a Josephson junction is replaced by quasi-charge. This Hamiltonian is dual to that of the transmon, in which the kinetic energy term associated with the charging energy is replaced by the inductive energy. Our circuit consists of a small-area Josephson junction shunted by a large linear inductance exceeding one micro-Henry. In such a circuit, the sensitivity of the ground to the first excited state transition is virtually flux insensitive while the flux-tunability of the transitions to higher excited states is largely preserved. Proper circuit design and choice of the fabrication techniques enable the mitigation of the parasitic capacitance previously associated with such large shunting inductances. In this talk, we demonstrate how the device spectra can be adequately described by the dual Hamiltonian and show that the flux dispersion of the qubit transition is reduced down to less than 100 MHz across the entire flux quantum. We also put a limit on the loss tangent of the inductor to be 5×10^-6.