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

TL;DR

This paper investigates how phase modulation affects frequency stabilization signals in atomic transitions, highlighting the unique behavior of coherent population trapping and the stationarity effect under different modulation regimes.

Contribution

It introduces a detailed analysis of frequency locking features, emphasizing the distinctive behavior of coherent population trapping and the stationarity effect with respect to modulation frequency.

Findings

Maximal error-signal slope remains stable at high modulation frequencies for coherent population trapping.

Error-signal slope decreases steadily for other resonances as modulation frequency increases.

In low-frequency modulation, the steepness of the error signal is independent of modulation frequency.

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.