Two-photon emission from an accelerated detector with Gaussian switching

We study second-order two-quantum emission from a uniformly accelerated Unruh–DeWitt detector coupled to a massless scalar field in ( 1 + 1 ) dimensions, using derivative coupling and a smooth Gaussian switching function. The time-ordered Dyson integrals are evaluated exactly, yielding a closed-form spectral kernel that covers all four emission channels: RR, LL, RL, and LR. The spectrum is shaped by narrow kinematic gates and a finite-time causal resonance profile encoded by the Faddeeva function. As the interaction time increases, the gates sharpen and the corresponding rate-type kernel approaches the causal resonance structure of the eternal-interaction limit. We analyze the dependence on acceleration, detector gap, and interaction duration, show that the single-particle marginal contains both a sharp nonthermal resonance and an Unruh-type high-frequency tail, and derive spacetime-smeared coincidence amplitudes from the exact spectral kernel.