Anomalous Josephson current through a driven double quantum dot

TL;DR

This paper studies a microwave-driven double quantum dot Josephson junction, revealing how phase shifts and symmetry breaking induce tunable anomalous currents, phase transitions, and rectification effects.

Contribution

It introduces a method to control Josephson currents via microwave phase shifts, creating a tunable Floquet $ ext{ϕ}_0$-junction with novel current-phase relations.

Findings

Finite anomalous Josephson current arises from particle-hole symmetry breaking.

Driving frequency near sub-gap state energy maximizes critical current.

Interaction induces a 0-$ ext{π}$ transition in the anomalous current.

Abstract

Josephson junctions based on quantum dots offer a convenient tunability by means of local gates. Here we analyze a Josephson junction based on a serial double quantum dot in which the two dots are individually gated by phase-shifted microwave tones of equal frequency. We calculate the time-averaged current across the junction and determine how the phase shift between the drives modifies the current-phase relation of the junction. Breaking particle-hole symmetry on the dots is found to give rise to a finite average anomalous Josephson current with phase bias between the superconductors fixed to zero. This microwave gated weak link thus realizes a tunable "Floquet $\varphi_{0}$-junction" with maximum critical current achieved for driving frequencies slightly off-resonance with the energy cost of exciting a sub-gap state on each dot. We provide numerical results supported by an analytical analysis for infinite superconducting gap and weak inter-dot coupling. We identify an interaction driven $0-\pi$ transition of anomalous Josephson current as a function of driving phase difference. Finally, we show that this junction can be tuned so as to provide for complete rectification of the time-averaged Josephson current phase relation.