Asymptotic Decoherence of an Unruh--DeWitt Detector in de Sitter Spacetime: Conformal versus Minimal Coupling

Abstract

We investigate the loss of coherence of a two-level Unruh--DeWitt detector coupled to massless real scalar fields in $(1+3)$-dimensional de Sitter spacetime. Treating the detector--field interaction perturbatively to second order, we derive analytic expressions for the real asymptotic coherence-decay coefficients for conformally and minimally coupled scalar fields. For the conformally coupled field, the coefficient remains finite in the small-gap limit and grows linearly with the detector energy gap in the large-gap regime. For the massless minimally coupled field, the logarithmic sector of the Wightman function produces an additional positive contribution. This provides an explicit analytic extension of the previously known infrared enhancement of detector transition responses to the asymptotic coefficient governing detector coherence. The explicitly average-time-dependent sector does not contribute to the real nonzero-frequency asymptotic coefficient under the adiabatically regulated half-line prescription adopted here, when the regulator is removed at fixed average time and fixed positive detector gap. This asymptotic result does not describe the complete finite-time dynamics, which depends on the switching function and observation interval. Within the stated prescription, the coefficients satisfy $Γ_{\rm MMC}>Γ_{\rm CC}$ for $ω>0$, with $Γ_{\rm MMC}/Γ_{\rm CC} =1+(H/ω)^2$. The distinction is most pronounced in the small-gap regime, whereas the two coefficients approach one another for large detector gaps.