Wavepacket detection with the Unruh-DeWitt model

In this paper we deal with several issues regarding the localization properties of the Unruh-DeWitt (UdW) detector model. Since its original formulation as a pointlike detector, the UdW model has been used to study extensively the physics of quantum fields in presence of accelerations or curved backgrounds. Natural extensions of it have tried to take into account the spatial profile of such detectors, but all of them have met a series of problems in their spectral response which render them useless to study some of the most interesting physical scenarios. In this paper we provide a derivation of the smeared UdW interaction from QED first principles, then we analyze the spectral response of spatially smeared UdW detectors, and discuss the kind of spatial profiles which are useful for the study of relevant cases.

Figure 1

A highly localized $\widehat{F}(k)$ centered in 0 would practically suppress the possibility of detection for the resonance frequencies to which the detector is most responsive, $k=\pm \Omega /c$. This results in a vanishing transition probability no matter what frequency we use to illuminate the detector.

Figure 2

A not so localized $\widehat{F}(k)$ centered in 0 would introduce an asymmetry in the detection of frequencies ${\omega }_k=\Omega \pm \delta$, $k=\pm \Omega /c$.

Figure 3

A localized $\widehat{F}(k)$ can be not centered in 0 by introducing an oscillating term in the spatial profile seen in the inset. The figure shows symmetric detection zones centered in $k=\pm \Omega /c$.