Modulation of the shape of the photon echo pulse by a pulsed magnetic field: Zeeman splitting in LuLiF$_4$:Er$^{3+}$ and YLiF$_4$:Er$^{3+}$

A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF$_4$:Er$^{3+}$ and YLiF$_4$:Er$^{3+}$. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment р and makes it possible to determine the difference of the $g$ factors of the ground and excited $^4$F$_9/2$(I) states of the Er$^{3+}$ ion in the LuLiF$_4$ the YLiF$_4$ matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.