Quantum nondemolition measurements of a particle in electric and gravitational fields

TL;DR

This paper develops a quantum nondemolition measurement framework for a charged particle in electric and gravitational fields, analyzing measurement probabilities and the influence of mass and field strengths.

Contribution

It introduces a nondemolition variable for a charged particle in combined electric and gravitational fields and explores continuous measurement effects using the restricted path integral formalism.

Findings

Derived a nondemolition variable for the system

Calculated measurement probabilities and propagator dependence

Analyzed the role of mass and field strength in measurement outcomes

Abstract

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields are commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.