Light Shifts of Coherent Population Trapping Resonances in a Periodically Modulated Laser Field

The light shifts of coherent population trapping resonances in a periodically modulated laser field at the modulation frequency f varying near the fractional hyperfine splitting frequency in the ground state of atoms Δ_hfs/N, N = 1, 2, 3, …, have been studied by means of the Fourier analysis. This type of modulation usually takes place in a compact clocks with a semiconductor laser, when the injection current is harmonically modulated at the frequency f or when an electro-optical or acousto-optic modulator is used. In this case, a polychromatic equidistant spectrum is formed, where only two frequency components are most resonant to the working optical transitions in the atom, while all other frequency components are relatively non-resonant. The precise numerical calculations have shown that the widespread view that the shift in the coherent population trapping resonance is determined by the usual ac Stark shift of the lower atomic levels is, in general, essentially incorrect. The reason is that the additional contribution to the light shift of the coherent population trapping resonance, due to beats (at the frequency Δ_hfs) between different non-resonant frequency components, can be in general comparable with (or even dominant over) the standard ac Stark shift. Moreover, these beats are phase-sensitive. Therefore, even detailed information on the spectral composition of the modulated field (e.g., with the help of a spectrum analyzer) is insufficient to determine the light shift of the coherent population trapping resonance.