Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system.

Abstract

We calculate the effect of the local-field correction (LFC) on the local response at ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ and 2${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ of a medium consisting of two-level systems when subject to a pump of arbitrary intensity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ and a weak probe at ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$. The pump is considered strong if its reduced intensity I=${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}^{2}$/${\ensuremath{\gamma}}_{1}$${\ensuremath{\gamma}}_{2}$ is large compared to unity. Here ${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}$ is the Rabi frequency and ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$ are the longitudinal and transverse relaxation rates. In the weak pump case the LFC manifests itself as a fixed or static frequency shift. When the pump is strong, the response is independent of the LFC. At intermediate pump intensities the effect of LFC is dependent on the intensity of the pump. Both line-shift and line-shape distortions are present. The LFC thus gives rise to a shift in the resonance response that varies according to the intensity and frequency of the applied radiation. We call this effect the dynamic Lorentz shift.