Nanomechanical effects in an Andreev quantum dot

TL;DR

This paper investigates how mechanical vibrations influence the charge and flux detection capabilities of a superconducting quantum dot system, revealing optimal conditions for flux sensitivity and entanglement effects.

Contribution

It introduces a detailed analysis of phonon coupling effects on charge sensitivity and entanglement in a superconducting quantum dot with mechanical degrees of freedom.

Findings

Identification of parameter regions with high charge-phase sensitivity.

Demonstration of phonon coupling impact on flux detection.

Analysis of electron-phonon entanglement via von Neumann entropy.

Abstract

We consider a quantum dot with mechanical degrees of freedom which is coupled to superconducting electrodes. A Josephson current is generated by applying a phase difference. In the absence of coupling to vibrations, this setup was previously proposed as a detector of magnetic flux and we wish here to address the effect of the phonon coupling to this detection scheme. We compute the charge on the quantum dot and determine its dependence on the phase difference in the presence of phonon coupling and Coulomb interaction. This allows to identify regions in parameter space with the highest charge to phase sensitivity, which are relevant for flux detection. Further insight about the interplay of such couplings and subsequent entanglement properties between electron and phonon degrees of freedom are gained by computing the von Neuman entropy.