Anomalous Josephson current through a driven double quantum dot

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 ${\phi }_0$-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.

16 pages, 12 figures

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• Solving the Transient Dyson Equation with Quasilinear Complexity via Matrix Compression
• Tunable diode effect in a superconducting tunnel junction with biharmonic drive
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Properties of multiterminal superconducting nanostructure with double quantum dot
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