Statistical measures on digital phase generation and transmission through alkali-metal vapours: a tutorial study

This paper explores the statistical measure features of digital phase transfer among multilevel atoms, such as alkali metals with hyperfine structures. The excitation fields constitute a train of probe pulses and a single drive field. We have provided two schemes for the mechanism of excitation dynamics. In the first scheme, the pulses are frequency swept across the upper hyperfine splitting of the excited atomic states. In the second scheme, the pulses are tuned to the upper hyperfine level with a high angular momentum, allowing strong absorption of pulses. The phases of the propagating pulses are rectangular shapes with well-separated boundaries, especially in the second scheme. We address the notion of phase entropy to study the influence of sweeping on the statistics of the generated phases and select definite phases with desired features. The estimated phase entropy exposes local maximum entropy and minimum entropy. In the second scheme, we have extended the pulses in time. Therefore, the phase distributions are rich. The features of the digital distributions of rectangular phases have not been obtained manually. We have addressed math criteria to distinguish the digital phase’s features across propagation. Randomness tests and randomness generation have been evaluated on the time-dependent discrete phase sequences. We expect the proposed generation and transmission of randomised discrete phases to be used in quantum applications.