Optical Depth Required for Efficient Electromagnetically Induced Transparency Photon Storage

Storing a photon as a collective excitation in an atomic ensemble succeeds with a probability that rises with optical depth and falls with decoherence during the storage interval. Optical depth is therefore the first design number for an electromagnetically induced transparency memory. This study computes the quantities that follow from stated assumptions for a rubidium ensemble, control-field optimised at each optical depth, ground-state coherence times of 100 microseconds and 1 millisecond, using the relations set out in the Methods. The headline results are efficiency at d 20 = 0.9773, efficiency at d 100 = 0.9999, depth for 90pct = 8.819, eff d100 with 100us coherence = 0.8187, eff d100 with 1ms coherence = 0.9801. The central question is stated as follows: What optical depth gives ninety percent storage-and-retrieval efficiency in the standard model, and how does a finite ground-state coherence time change that requirement for a ten-microsecond storage? 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 memories report efficiencies from a few percent to above eighty percent, with the highest values in high-optical-depth cold ensembles and cavities. 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.