Multiterminal ballistic Josephson junctions coupled to normal leads

TL;DR

This paper investigates the behavior of quartet signals in multiterminal Josephson junctions with quantum dots, revealing how relaxation effects induce sharp peaks and variability in the signal, with implications for quantum circuit engineering.

Contribution

It introduces a simplified non-Hermitian model for multiterminal Josephson junctions, highlighting the impact of relaxation on quartet signals and their voltage sensitivity.

Findings

Relaxation causes sharp peaks and log-normal variations in quartet signals.

The device behavior resembles a resonantly driven harmonic oscillator.

Voltage sensitivity exhibits inverse proportionality to damping and noise parameters.

Abstract

Multiterminal Josephson junctions have aroused considerable theoretical interest recently and numerous works aim at putting the predictions of correlations among Coopers (i.e. the so-called quartets) and simulation of topological matter to the test of experiments. The present paper is motivated by recent experimental investigation from the Harvard group reporting $h/4e$-periodic quartet signal in a four-terminal configuration containing a loop pierced by magnetic flux, together with inversion controlled by the bias voltage, i.e. the quartet signal can be larger at half-flux quantum than in zero magnetic field. Here, we theoretically focus on devices consisting of finite-size quantum dots connected to four superconducting and to a normal lead. In addition to presenting numerical calculations of the quartet signal within a simplified modeling, we reduce the device to a non-Hermitian Hamiltonian in the infinite-gap limit. Then, relaxation has the surprising effect of producing sharp peaks and log-normal variations in the voltage-sensitivity of the quartet signal in spite of the expected moderate fluctuations in the two-terminal DC-Josephson current. The phenomenon is reminiscent of a resonantly driven harmonic oscillator having amplitude inverse proportional to the damping rate, and of the thermal noise of a superconducting weak link, inverse proportional to the Dynes parameter. Perspectives involve quantum bath engineering multiterminal Josephson junctions in the circuits of cavity quantum electrodynamics.