# The effect of noise fluctuation of a quantum tunneling device coupled to a substrate

## TL;DR

This paper provides a theoretical analysis of how substrate coupling affects noise spectra in quantum tunneling devices, confirming experimental observations and comparing different coupling models.

## Contribution

It derives a non-Markovian noise spectrum for a quantum point contact coupled to a substrate and compares position and momentum coupling models, highlighting the role of backaction.

## Key findings

- Numerical results match experimental data.
- Backaction transmits momentum and position fluctuations.
- Markovian approximation underestimates noise floor.

## Abstract

The recent experiment of Stettenheim, et al. showed that, contrary to conventional belief, the coupling of a quantum electronic device to its substrate can have important effects on the noise power spectrum, since the substrate functions as a mechanical oscillator. We carry out a theoretical analysis of this coupling in the case of a quantum point contact (QPC). First we derive the noise power spectrum from the Hamiltonian without making the Markovian approximation, and obtain numerical results that reproduce the experimental data. Next we investigate the nature of the coupling. In most previous analyses, the coupling of an electronic device to a mechanical oscillator has been modeled as a position coupling. We model it both as a position coupling and as a momentum coupling and compare the results. We find that, as long as one includes backaction between position and momentum, the assumed mode of coupling makes little difference, since the backaction transmits momentum fluctuations to position fluctuations and vice versa. Finally, we ask whether the salient features of the model persist in the Markovian approximation. We find that a Markovian analysis confirms the QPC-substrate coupling, but underestimates the noise floor and leads to excessively sharp and narrow noise peaks around the resonant frequencies.