Quantum Limits to Linewidth Narrowing in Single‐ and Few‐Atom Cavity Electromagnetically Induced Transparency

ABSTRACT 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 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 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.