Photon Blockade Strength from the Anharmonicity of the Jaynes-Cummings Ladder

When a cavity is strongly coupled to a two-level emitter, its energy levels cease to be equally spaced. A drive tuned to the first transition is then detuned from the second, so a second photon is largely excluded: the photon blockade. This study computes the quantities that follow from stated assumptions for a Jaynes-Cummings system with cavity decay corresponding to quality factor 20000 at 780 nm and coupling rates from 5 to 100 GHz in ordinary frequency units, using the relations set out in the Methods. The headline results are kappa GHz = 19.22, anharmonicity at g 20 GHz = 11.72, g2 at g 20 = 0.4021, g2 at g 5 = 0.915, g2 at g 100 = 0.0262. The central question is stated as follows: How large is the anharmonicity, and the resulting suppression of two-photon occupation, for coupling rates spanning the strong-coupling range, and at what coupling does the suppression reach a factor of one hundred? The answer obtained here is conditional on the assumptions listed in the paper and in the deposited calculation; changing an assumption changes the numbers in the way the sensitivity discussion describes. Blockade experiments report a second-order correlation well below one, often near 0.1 or lower, in systems where the anharmonicity exceeds the linewidth by a clear margin. The work is a computation, not a laboratory measurement, and it is labelled accordingly. Where the computed result is unfavourable to the device or effect under study, that outcome is reported in the same terms as a favourable one, because a bound that only appears when it is welcome is not a bound at all. All numerical statements in this abstract are reproduced by the deposited script from the stated inputs.