Fast numerical analysis of the time response in coherent population trapping resonance based on Galerkin spectral method

Abstract

We propose a new algorithm to calculate the time response of coherent population trapping (CPT) resonance. The Galerkin method using a Fourier series as a basis function (Galerkin spectral method) is widely employed for the numerical analysis of piezoelectric mechanical resonators such as quartz. We attempted to apply this method to the analysis of CPT resonance. Unlike the conventional method, in which the time is digitally divided into short intervals, a continuous function can be applied to calculate the time response in the new algorithm. Therefore, not only the calculation cost can be substantially reduced, but also the behavior of CPT resonance under complicated perturbations due to laser frequency instability can be analyzed.