Measuring the Momentum of a Nanomechanical Oscillator through the Use of Two Tunnel Junctions

TL;DR

This paper introduces a quantum measurement method for nanomechanical oscillator momentum using a two tunnel junction setup influenced by Aharonov-Bohm flux, enabling momentum detection through finite-frequency noise analysis.

Contribution

It presents a novel p-measurement technique employing two tunnel junctions and phase tuning, revealing momentum information from linear position coupling.

Findings

Finite-frequency noise contains momentum spectrum information.

Phase tuning by Aharonov-Bohm flux enables p-sensitive detection.

Method feasible with current nanomechanical and quantum tunneling technologies.

Abstract

We propose a way to measure the momentum p of a nanomechanical oscillator. The p-detector is based on two tunnel junctions in a Aharonov-Bohm-type setup. One of the tunneling amplitudes depends on the motion of the oscillator, the other one not. Although the coupling between the detector and the oscillator is assumed to be linear in the position x of the oscillator, it turns out that the finite-frequency noise output of the detector will in general contain a term proportional to the momentum spectrum of the oscillator. This is a true quantum phenomenon, which can be realized in practice if the phase of the tunneling amplitude of the detector is tuned by the Aharonov-Bohm flux Phi to a p-sensitive value.