QFT in curved spacetime permits quantitative predictions for the Unruh effect with hydrogenlike atoms


We consider ionized hydrogenlike atoms accelerated by an external electric field to detect Unruh radiation. By applying quantum field theory in the Rindler space-time, we show that the first-quantized description for hydrogenlike atoms cannot always be adopted. This is due to the frame-dependent definition of particles as positive and negative frequency field modes. We show how to suppress such a frame-dependent effect by constraining the atomic ionization and the electric field. We identify the physical regimes with nonvanishing atomic excitation probability due to the Unruh electromagnetic background. We recognize the observational limits for the Unruh effect via first-quantized atomic detectors, which appear to be compatible with current technology. Notably, the nonrelativistic energy spectrum of the atom cannot induce coupling with the thermal radiation, even when special relativistic and general relativistic corrections are considered. On the contrary, the coupling with the Unruh radiation arises because of relativistic hyperfine splitting and the Zeeman effect.