Quantum Limits to Linewidth Narrowing in Single- and Few-Atom Cavity Electromagnetically Induced Transparency
Electromagnetically induced transparency (EIT) in cavities can narrow the transmission resonance below the empty-cavity linewidth. We investigate the limits of this narrowing from a single emitter to the few-atom regime. Using a Lindblad master equation for $N_{at}$ identical three-level atoms coupled to a cavity mode, driven by coherent probe and control fields, we compute the full width at half maximum (FWHM) of the transparency feature. In the strictly low-excitation limit, we derive an analytical cubic polynomial that captures the narrowing and recovers the known linear-response scaling. For finite probe powers, the achievable linewidth faces a quantum bound on the minimum achievable linewidth. Contrasting our model with a semiclassical approximation, we show this limitation arises from the unavoidable excitation of higher-order multiphoton states. Their intrinsically larger decay rates destroy the ideal single-excitation EIT dark state. Increasing $N_{at}$ enhances collective cooperativity, creating a multiphoton blockade that suppresses these detrimental excitations and yields a stepwise reduction of the minimum FWHM. Our results provide analytical boundaries for cavity-EIT linewidth control, guiding the optimization of narrowband filters and highly coherent light-matter interfaces.