Finite-Frequency Boson-Number Bounds Across the Quantum Rabi Transition
This research derived rigorous upper and lower bounds for ground-state energy and boson occupation number across the quantum Rabi model's phase transition for finite frequency ratios. The results characterize subcritical, critical, and supercritical regimes, establishing scaling behavior for the boson occupation near the critical point. These bounds offer testable predictions for trapped-ion quantum simulators.