Adaptive Bayesian algorithm for achieving a desired magneto-sensitive transition

Bayesian methods which utilize Bayes' theorem to update the knowledge of desired parameters after each measurement, are used in a wide range quantum science. For various applications science, efficiently and accurately determining transition frequency is essential. However, exact relation between controllable experimental usually absent. Here, we propose an efficient scheme search suitable conditions for via adaptive algorithm, experimentally demonstrate it by using coherent population trapping ensemble laser-cooled $^{87}$Rb atoms. The controlled external magnetic field, can be tuned realtime applying d.c. voltage. Through voltage automatically converge one from random initial value only few iterations. In particular, when target applied nonlinear, our algorithm shows significant advantages over traditional methods. This work provides simple way determine frequency, widely fields precision spectroscopy, such as atomic clocks, magnetometers, nuclear resonance.