# Engineering the Floquet spectrum of superconducting multiterminal quantum dots

## TL;DR

This paper theoretically explores the Floquet spectrum in multiterminal superconducting quantum dots, revealing how time-periodic dynamics produce observable spectral features and proposing an analytical model validated by Green's function calculations.

## Contribution

It introduces a novel analytical model for Floquet spectra in superconducting quantum dots and links Floquet-Wannier-Stark ladders to measurable current fluctuations.

## Key findings

- Floquet-Wannier-Stark ladders manifest as peaks in current fluctuations.
- Analytical model accurately predicts resonance features.
- Green's function calculations confirm the spectral structures.

## Abstract

Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Stark ladder spectra, we have developed an analytical model relying on the sharpness of the resonances. The charge-charge correlation function is obtained as a factorized form of the Floquet wave-function on the dot and the superconducting reservoir populations. We confirm these findings by Keldysh Green's function calculations, in particular regarding the voltage and frequency dependence of the resonance peaks in the current-current correlations. Our results open up a road-map to quantum correlations and coherence in the Floquet dynamics of superconducting devices.