Realizing higher Josephson harmonics in a double-junction transmon

Engineering the harmonic content of superconducting devices allows the implementation of interesting elements such as protected qubits [1] and superconducting diodes [2]. Recently, it has been shown that higher Josephson harmonics can be engineered using two standard superconducting junctions in series [3]. We realize the double-junction transmon, consisting of a single junction in series with a SQUID, which allows tuning between an approximately sinusoidal potential and higher harmonic content through flux. The harmonics are experimentally extracted from higher-order qubit transitions using spectroscopy measurements. We match the measurements to a model that includes an internal mode arising from the superconducting middle island. We observe that the internal mode dispersively interacts with the readout resonator and enables flux tuning to a balance point where the net dispersive shift is zero. The combination of Josephson harmonics engineering and the interaction of the internal mode with the readout resonator makes for a useful building block in superconducting qubit systems.

[1] T. Larsen et al., Phys. Rev. Lett. 125, 056801 (2020)

[2] C. Ciaccia et al., Phys. Rev. Res. 5, 033131 (2023)

[3] A. M. Bozkurt et al., SciPost Phys. 15.5.204 (2023)