Indirect Measurements of a Harmonic Oscillator

TL;DR

This paper models the quantum measurement process of a harmonic oscillator coupled to a field, analyzing conditions under which the measurement aligns with ideal expectations using quantum stochastic differential equations.

Contribution

It introduces a quantum model of system and apparatus interaction and derives conditions for consistent measurement outcomes.

Findings

Established conditions for measurement compatibility

Solved quantum stochastic differential equations for the model

Demonstrated the measurement process aligns with ideal observables

Abstract

The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model describing both system and apparatus and consisting of a harmonic oscillator coupled to a field. The equation of motion is a quantum stochastic differential equation. By solving it we establish the conditions ensuring that the two perspectives are compatible, in that the apparatus indeed measures the observable it is ideally supposed to.