What makes a particle detector click

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 Ω 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.

Anti-particle detector models in QFT

“…We then take the T → ∞ limit. The adiabatic limit yields the physical behaviour of a detector switched on for long times preventing spurious UV divergences, as discussed, e.g., in [30,32,33]. Under the long time limit assumption, both the vacuum contribution and the counter-rotating contribution form the wavepacket vanish (see, e.g.…”

“…( 13) is normalized. These calculations are analogous to those performed in [30] for the linear model, although we allow the field to be massive.…”

“…Regarding the field, following [30], we will assume that its initial state is a general one-particle wavepacket |ϕ , given by…”

“…( 16), it is possible to identify the vacuum contribution to the excitation probability, and separate it from the one-particle content contribution, associated with the F (x )F * (x) and F * (x )F (x) terms. Note that the F * (x )F (x) term is usually referred to as the counterrotating term [30,31], this is because in the transition probability these terms are proportional to e iΩτ u * k (x) (counter-rotating phase) whereas the term F (x )F * (x) is proportional to e iΩτ u k (x) (co-rotating phase). In other words, the counter-rotating terms can be associated with the coupling of the positive phase terms of the detector with the negative frequency modes of the field.…”

“…In other words, the counter-rotating terms can be associated with the coupling of the positive phase terms of the detector with the negative frequency modes of the field. It can be shown that there is a variety of scenarios where the counter-rotating terms vanish [30,31], and the overall contribution of the co-rotating term tends to be larger. As a matter of fact, in Appendix E we show that the counter-rotating contribution from the wavepacket terms is always smaller than the vacuum contribution of the field.…”