Transparency in two-level spin systems induced by a longitudinal field

Abstract

In an electron-spin two-level system a bichromatic radiation field, consisting of a transverse microwave field and a radio frequency field oriented parallel to the static magnetic field, can induce multiple photon transitions of the type ${\ensuremath{\sigma}}_{\text{mw}}^{+}+k{\ensuremath{\pi}}_{\text{rf}}$, with the photons ${\ensuremath{\sigma}}_{\text{mw}}^{+}$ and ${\ensuremath{\pi}}_{\text{rf}}$ absorbed from the microwave and radio frequency fields, and $k$ being an integer. The two-level spin system may become transparent under such a bichromatic radiation field. This phenomenon directly depends on the presence of the $\ensuremath{\pi}$ photons of the longitudinal radio frequency field. An analytical description of the multiple photon processes and the resulting transparency effects, based on a toggling-frame approach, is given. The effective field amplitudes of the multiple photon transitions are found to have a Bessel-function-like dependence on the radio frequency amplitude. The behavior of the magnetization vector during a bichromatic pulse is illustrated by using classical equations of motion. The theoretically predicted effects are verified experimentally. As an example for an application of the investigated type of electromagnetically induced transparency, a one-pulse echo experiment is described, where the free evolution period is created artificially.