Mode Volume Required for Strong Coupling Between a Single Emitter and an Optical Cavity

Strong coupling appears when the coherent exchange rate between one emitter and one cavity mode exceeds both the cavity decay rate and the emitter decay rate. Because the exchange rate grows as the mode volume shrinks, the threshold can be expressed as a maximum volume for stated decay rates. This study computes the quantities that follow from stated assumptions for a single two-level emitter at 780 nm, dipole moment 3e-29 coulomb metre, cavity quality factor 20000 and emitter decay rate 1 GHz in angular-frequency units as stated, using the relations set out in the Methods. The headline results are cooperativity at V 1 lambda3 = 1.616, cooperativity at V 10 lambda3 = 0.1616, V for C1 in lambda3 = 1.616, V for C10 in lambda3 = 0.1616, V for C100 in lambda3 = 0.01616. Further computed values are g at V 1 lambda3 rad s = 4.952e+10, kappa rad s = 1.207e+11. The central question is stated as follows: What mode volume, in cubic wavelengths, is required for strong coupling and for a cooperativity of ten and of one hundred, for an emitter with a 1 GHz linewidth in a cavity of quality factor twenty thousand? 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. Cooperativities from near unity to several hundred are reported across atom, ion, quantum-dot and colour-centre platforms, which makes the threshold volume a useful common yardstick. 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.