Quantum Measurement of Phonon Shot Noise

TL;DR

This paper presents a quantum mechanical analysis of weak energy measurements in a driven mechanical resonator, demonstrating the detection of phonon shot noise and the significance of third moment measurements for revealing quantum effects.

Contribution

It introduces a method to detect phonon shot noise using weak measurements and highlights the importance of third moment analysis for quantum signatures.

Findings

Weak measurements can detect phonon shot noise without resolving individual Fock states.

The third moment of energy fluctuations is more sensitive to quantum effects than the second moment.

Measuring the third moment via phase shift in optomechanics aligns with full-counting statistics theory.

Abstract

We provide a full quantum mechanical analysis of a weak energy measurement of a driven mechanical resonator. We demonstrate that measurements too weak to resolve individual mechanical Fock states can nonetheless be used to unambiguously detect the non-classical energy fluctuations of the driven mechanical resonator, i.e. "phonon shot noise". We also show that the third moment of the oscillator's energy fluctuations provides a far more sensitive probe of quantum effects than the second moment, and that measuring the third moment via the phase shift of light in an optomechanical setup directly yields the type of operator ordering postulated in the theory of full-counting statistics.