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

Adaptive Bayesian algorithm for achieving desired quantum transition