Comparison of the Radon–Nikodym method with a multistage relaxation model in the analysis of the fluorescence dynamics of a cold atomic ensemble

The fluorescence of cold atoms, cooled to ultra-low temperatures and excited by pulsed laser radiation, is calculated. The fluorescence of cold atoms is calculated based on the solution of the non-steady-state Schrödinger equation for a combined system of atoms and an electromagnetic field. A universal function is proposed in the work showing the deviation of the fluorescence decay at the end of the pulse from the single-exponential model. To analyze the dynamics of fluorescence, a Radon–Nikodym method has been used based on the studies on the eigenvalues of a matrix constructed on the basis of the fluorescence signal. It is shown that a correlation exists between the parameter of distribution asymmetry inherent in signal matrix eigenvalues, and the temporal law of fluorescence decay. As an alternative method of fluorescence analysis, a multistage relaxation model is used, caused by collective multiatomic effects. The values of characteristic amplitude and relaxation time both at short times (“superradiance”) and at long times (“subradiance”) have been found.