Frequency locking: a distinctive feature of the coherent population trapping and the stationarity effect

Abstract: We study the case where phase modulation of the harmonic signal is used to obtain the error signal for the frequency stabilization to a reference atomic transition. High-frequency modulation, or analog of the Pound-Drever-Hall regime, is considered. We demonstrate that for coherent population trapping, the maximal error-signal slope retains at a certain level with growth in the modulation frequency, while for other types of resonances it drops steadily. The investigation of the low-frequency modulation regime reveals the stationarity effect. We show that in this case, the maximal steepness of the error signal does not depend on the modulation frequency and is reached at a fixed value of the frequency deviation.