Mirror Reflectivity and Photon Storage Time in a Fabry-Perot Cavity for Single Photons

A single photon that enters a Fabry-Perot resonator leaves again after a dwell time set by how often it reflects and how much light escapes at each reflection. That dwell time decides whether the photon can be held long enough for a control operation, a heralding check, or a synchronisation delay, and it also sets the spectral width the source must match. This study computes the quantities that follow from stated assumptions for a symmetric two-mirror Fabry-Perot cavity of length 0.05 m, wavelength 780 nm, with a fixed additional round-trip loss of 0.002 in intensity, using the relations set out in the Methods. The headline results are finesse at R 0.99 = 260.7, lifetime at R 0.99 s = 1.384e-08, linewidth at R 0.99 Hz = 1.150e+07, finesse at R 0.9995 = 1.256e+03, lifetime at R 0.9995 s = 6.666e-08. Further computed values are saturation ratio lifetime = 4.817. The central question is stated as follows: How much storage time, spectral width and round-trip loss follow from a stated mirror reflectivity for a five-centimetre resonator at 780 nm, and at what reflectivity does further coating improvement stop buying useful time because other losses dominate? 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. Laboratory resonators of this size are commonly quoted with finesse values from a few hundred for coated optics to well above one hundred thousand for supermirror coatings, so a sweep across that interval tests both ordinary and demanding coatings. 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.