Exact decoherence dynamics of a detector coupled to vacuum fluctuations in bounded geometries
The properties of quantum vacuum are highly sensitive to the underlying spacetime geometry and boundary conditions. We investigate in this paper the decoherence dynamics of a two-level system (detector) coupled to a vacuum scalar field through the $\hatσ_z$-coupling scheme under various boundary environments. By rigorously evaluating the reduced density matrix of the detector, we derive an exact general expression for the detector's decoherence function, $γ(Δt)$, and use it to characterize the dynamical decoherence of a detector in three scenarios: free space, a perfectly reflecting boundary, and a cavity formed by two parallel reflecting boundaries. We find that in free space the detector's coherence decays monotonically with time, indicating that vacuum fluctuations alone inevitably lead to a complete loss of coherence. In the single-boundary case, by contrast, the detector's coherence displays non-monotonic time evolution: $γ(Δt)$ increases with time up to a maximum and then settles to a steady value, indicating that the initial coherence can be partially preserved due to the presence of the boundary. When the detector is placed inside a cavity, its coherence evolution exhibits oscillatory behavior, and a significant fraction of the initial coherence survives. Moreover, for the same detector-boundary distance, more coherence is preserved in the cavity case than in the single-boundary case. These results provide a viable route for engineering quantum coherence via boundary conditions.