Parallel Quantum Circuit in a Tunnel Junction

TL;DR

This paper investigates the effective electronic coupling in parallel quantum buses within tunnel junctions, revealing limitations of quantum transduction and proposing a refined understanding of electrical contacts at the quantum level.

Contribution

It introduces a new analysis of quantum coupling in parallel buses and highlights the limitations of current quantum transduction models in tunnel junctions.

Findings

Effective coupling varies with the number of parallel lines, showing linear and square root regimes.

Quantum transduction in tunnel junctions cannot fully follow the oscillation frequency variations.

A quadratic power law is preserved at low coupling and small N.

Abstract

The spectrum of 1-state and 2-states per line quantum buses is used to determine the effective $V_{ab}(N)$ electronic coupling between emitter and receiver states through the bus as a function of the number $N$ of parallel lines in the bus. When the calculation of $V_{ab}(N)$ is spectrally difficult, an Heisenberg-Rabi time dependent quantum exchange process can be triggered through the bus by preparing a specific initial non-stationanry state and identifying a target state to capture the effective oscillation frequency $\Omega_{ab}(N)$ between those. For $\Omega_{ab}(N)$ (for $V_{ab}(N)$), two different regimes are observed as a function of $N$: linear and $\sqrt{N}$ more moderate increases. This state preparation was remplaced by electronically coupling the quantum bus to two semi-infinite electrodes. The native quantum transduction process at work in this tunnel junction is not faithfully following the $\Omega_{ab}(N)$ variations with $N$. Due to normalisation to unity of the electronic transparency of the quantum bus and to the low pass filter character of the transduction, large $\Omega_{ab}(N)$ cannot be followed by the tunnel junction. At low coupling and when $N$ is small enough not to compensate the small through line coupling, an $N^2$ power law is preserved for $\Omega_{ab}(N)$. The limitations of the quantum transduction in a tunnel junction is pointing how the broadly used concept of electrical contact between a metallic nanopad and a molecular wire can be better described as a quantum transduction process.