Quantum dynamics of superconductor-quantum dot-superconductor (super-semi) Josephson junctions*

We consider capacitively shunted gatemon qubit based on superconductor-semiconductor quantum dot-superconductor (SC-QD-SC=super-semi) Josephson junction, where the superconducting phase variables may experience large quantum fluctuations. In this case a self-consistent quantization of the system is performed following the program of Ambegaokar, Eckern, and Schön [1] (via path-integral formulation), extended to a voltage tunable QD with a single electron level, embedded into the junction. In the effective Hamiltonian, the Josephson potential for the Andreev bound states reproduces earlier results for static phases [2], whereas the charging energy term has new features: (i) the system’s capacitance is renormalized by the junction gate voltage, an effect which depends on the strength of the tunneling rates as well, and (ii) an additional charge offset appears for asymmetric junctions. These results are important to understand future experiments and quantum devices incorporating super-semi junctions in arbitrary impedance environments.

[1]  V. Ambegaokar, U. Eckern, and G. Schön, Phys. Rev. Lett. 48, 1745 (1982)

[2]  P. D. Kurilovich et al., Phys. Rev. B 104, 174517 (2021)