What makes a particle detector click

TL;DR

This paper compares light-matter interaction models in free space and cavities, revealing fundamental differences in detector resonance behavior with Fock states, especially regarding monochromatic wavepackets and their physical implications.

Contribution

It uncovers key distinctions in Fock state detection between free space and cavity models, emphasizing the role of wavepacket normalizability and spatial delocalization.

Findings

Detector response in free space vanishes for monochromatic Fock wavepackets.

Cavity models show maximum absorption probability for monochromatic states.

Monochromatic Fock states are non-normalizable, affecting physical detection models.

Abstract

We highlight fundamental differences in the models of light-matter interaction between the behaviour of Fock state detection in free space versus optical cavities. To do so, we study the phenomenon of resonance of detectors with Fock wavepackets as a function of their degree of monochromaticity, the number of spatial dimensions, the linear or quadratic nature of the light-matter coupling, and the presence (or absence) of cavity walls in space. In doing so we show that intuition coming from quantum optics in cavities does not straightforwardly carry to the free space case. For example, in $(3+1)$ dimensions the detector response to a Fock wavepacket will go to zero as the wavepacket is made more and more monochromatic and in coincidence with the detector's resonant frequency. This is so even though the energy of the free-space wavepacket goes to the expected finite value of $\hbar\Omega$ in the monochromatic limit. This is in contrast to the behaviour of the light-matter interaction in a cavity (even a large one) where the probability of absorbing a Fock quantum is maximized when the quantum is more monochromatic at the detector's resonance frequency. We trace this crucial difference to the fact that monochromatic Fock states are not normalizable in the continuum, thus physical Fock states need to be constructed out of normalizable wavepackets whose energy density goes to zero in the monochromatic limit as they get spatially delocalized.