# Coherent population trapping resonance formation delay under dynamic excitation in 87Rb

Current work describes a new effect which consists in an appearance of a delay of an electromagnetically induced transparency under conditions of quick periodical excitation of a coherent population trapping resonance. The effect was discovered by our group during work with an atomic frequency standard. The work is a part of a research which aims to study properties of a CPT resonance under dynamic excitation. The work reports on results of experimental and theoretical researches of the dependency of phase delay upon the frequency of scanning near the CPT resonance.

Excitation of a coherent population trapping resonance is a result of an interaction between a three-level energy system and a bichromatic electromagnetic field. Performing a sinusoidal modulation of the frequency difference of components of the field leads to a periodical excitation of the resonance. When the modulation frequency is low, maximums of the transmittance curve are located at zeroes of the sinusoidal modulation signal. However, increasing of the modulation frequency leads to non-zero shift of locations of transmittance curve maximums relative to zeroes of modulation signal. *Phase delay* is a delay between a CPT resonance peak and zero of the modulation signal expressed by phase of the modulation signal.

We conducted an experimental study of the dependence of phase delay upon modulation frequency, results are following (Fig. 1) : the phase delay value increases with the increase of modulation frequency linearly (modulation frequency less than 2 kHz) and reaches the saturation level of 1.7 ± 0.3 rad (at 2 kHz). In order to examine dependency of the phase delay upon relaxation properties of an active media, we conducted experiments for cases of an optical cell without an anti-relaxation coating or buffer gas (Fig. 1, (a)) and for a cell with an anti-relaxation coating (Fig. 2, (b)). Experimental results showed no dependency upon this factor. Furthermore, a theoretical study was conducted. It consisted in a numerical solution of differential equations on the elements of the density matrix of a three-level energy system. Using the numerical solution, a similar dependency was obtained. The result of modeling correspond experimental results, but there is a numerical difference (saturation value 1.4 ± 0.02 rad for the theoretical results) that can be explained by the simplicity of the mathematical model used for theoretical study.

**Fig. 1. Dependency of the phase delay of the CPT resonance excitation upon the frequency of modulation of the difference frequency of the bichromatic field components: а) optical cell without an anti-relaxation coating or buffer gas, б) optical cell with an anti-relaxation coating.**

This work reports on a new effect which consists in an appearance of a coherent population trapping resonance formation delay under circumstances of a dynamic excitation. This effect was discovered by our group during work with a frequency atomic standard. The effect has a critical impact on a feedback system of the standard.