Seminar - Luca Chirolli, Istituto Nanoscienze CNR, Pisa

Coherence and topology in Josephson circuits featuring multi-harmonic elements

Josephson elements with high harmonic content have emerged as a novel tool that can provide augmented freedom in engineering of superconducting circuits. In ordinary superconducting circuits based on Josephson junctions, the dependence of the energy spectrum on the offset charges on different islands is 2e periodic through the Aharonov-Casher effect and resembles a crystal band structure. We show that employment of higher harmonic Josephson elements enables tailoring the Josephson potential and band engineering of the spectrum, thus allowing for the isolation of peculiar spectral features such as Dirac points and flat bands. The latter provide us with noise-insensitive energy levels and their engineering can therefore be used to enhance the circuit coherence. In particular, the employment of short series of Josephson junctions can be employed to introduce long wavelength modulations of the Josephson potential, whereas cos(2φ) Josephson junctions describing two-Cooper pair tunneling can be exploited to engineer short wavelength modulations. The latter show suppression of individual Cooper pair tunneling and result in parity-protected superconducting qubits, thus offering the opportunity to topologically characterize Josephson circuits.