Causality issues of particle detector models in QFT and Quantum Optics

We analyze the constraints that causality imposes on some of the particle detector models employed in quantum field theory in general, and in particular on those used in quantum optics (or superconducting circuits) to model atoms interacting with light. Namely, we show that disallowing faster-than-light communication can impose severe constraints on the applicability of particle detector models in three different common scenarios: 1) when the detectors are spatially smeared, 2) when a UV cutoff is introduced in the theory and 3) under one of the most typical approximations made in quantum optics: the rotating-wave approximation. We identify in which scenarios the models' causal behaviour can be cured and in which it cannot.

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