What makes a particle detector click

We highlight fundamental differences in the models of light-matter interaction between the behavior of Fock state detection in free space versus optical cavities. To do so, we study the phenomenon of the resonance of detectors with Fock wave packets 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 wave packet will go to zero as the wave packet 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 wave packet goes to the expected finite value of h Omega in the monochromatic limit. This is in contrast to the behavior 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 wave packets whose energy density goes to zero in the monochromatic limit as they get spatially delocalized.

Automated summary

The study reveals fundamental differences in the behavior of Fock state detection in free space versus optical cavities, particularly in terms of monochromaticity, spatial dimensions, nature of light-matter coupling, and the presence of cavity walls. It is found that monochromatic Fock states are not normalizable in free space, with their energy density approaching zero as they become spatially delocalized, contrasting the behavior in optical cavities.