Fluctuations of the Casimir-Polder force between an atom and a conducting wall

TL;DR

This paper investigates the quantum fluctuations of the Casimir-Polder force between an atom and conducting surfaces, proposing a method to measure these fluctuations and analyzing their dependence on measurement duration.

Contribution

It introduces a time-averaged force operator to accurately quantify Casimir-Polder force fluctuations, addressing ultraviolet divergences and exploring experimental observability.

Findings

Force fluctuations depend on measurement duration

Time-averaged operator avoids ultraviolet divergences

Fluctuations are potentially observable experimentally

Abstract

We consider the quantum fluctuations of the Casimir-Polder force between a neutral atom and a perfectly conducting wall in the ground state of the system. In order to obtain the atom-wall force fluctuation we first define an operator directly associated to the force experienced by the atom considered as a polarizable body in an electromagnetic field, and we use a time-averaged force operator in order to avoid ultraviolet divergences appearing in the fluctuation of the force. This time-averaged force operator takes into account that any measurement involves a finite time. We also calculate the Casimir-Polder force fluctuation for an atom between two conducting walls. Experimental observability of these Casimir-Polder force fluctuations is also discussed, as well as the dependence of the relative force fluctuation on the duration of the measurement.