Two-Photon Emission from an Accelerated Detector with Gaussian Switching

We present a closed-form analysis of second-order two-photon emission from a uniformly accelerated Unruh-DeWitt detector with a smooth Gaussian switch and derivative coupling. The time-ordered Dyson integrals are evaluated exactly, yielding a single spectral amplitude that simultaneously covers all four channels--right-travelling/right-travelling (RR), left-travelling/left-travelling (LL), right-travelling/left-travelling (RL), and left-travelling/right-travelling (LR). The spectra are organized by narrow kinematic gates (sum-frequency for RR/LL, difference-frequency for RL/LR) and a causal resonant denominator encoded by the Faddeeva function. As the gate time increases, the Gaussian factors sharpen into delta constraints and recover the eternal-interaction response. We map scaling with acceleration, gap, and duration, and show that the single-particle marginal combines a sharp nonthermal resonance with an Unruh thermal tail.