Quantum dynamics of semiconductor quantum dot Josephson junctions

Josephson junctions constructed from superconductor-semiconductor-superconductor heterostructures have been used to realize a variety of voltage-tunable superconducting quantum devices, including qubits and parametric amplifiers. To date theoretical descriptions of these systems have been restricted to small quantum fluctuations of the junction phase, making them inapplicable to many experiments. In this work we relax this, employing a path-integral formulation where the phase quantum dynamics is obtained self-consistently from an underlying many-body formalism. Our method recovers previously-known results for small phase fluctuations, and predicts new effects outside of that limit: (i) system capacitances undergo a gate-voltage-dependent renormalization; and (ii) an additional charge offset appears for asymmetric junctions. Our main results can be summarized in terms of a single-particle Hamiltonian, which can be directly compared to that of an ordinary Josephson junction. This more general theory could be a first step towards designing new quantum devices that go qualitatively beyond voltage-tunable variants of previously-known circuits.