Measuring the quantum state of a nanomechanical oscillator

TL;DR

This paper presents a method to directly measure the quantum state of a nanomechanical oscillator using a modified atomic homodyning technique, enabling access to its Wigner function.

Contribution

It introduces a novel measurement scheme combining magnetic coupling and Raman transitions to determine the quantum state of a nanomechanical oscillator.

Findings

The probability of atomic excitation directly relates to the oscillator's Wigner function.

The scheme allows measurement of the quantum state near the ground state.

Backaction effects on the oscillator's state are analyzed.

Abstract

We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector-atom that is simultaneously coupled to the cantilever via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the excited state is a direct measure of the Wigner characteristic function of the nanomechanical oscillator. We also investigate the backaction effect of this destructive measurement on the state of the cantilever.