Coherent Control of the Effective Susceptibility through Wave Mixing in a Duplicated Two-Level System

Abstract

We theoretically demonstrate the coherent control of the effective susceptibility of a duplicated two-level system. The control is obtained for a linearly polarized weak field in the presence of a much stronger orthogonally polarized field. For small optical depths, the effective susceptibility ${\ensuremath{\chi}}_{\mathrm{eff}}$ behaves as ${\ensuremath{\chi}}_{\mathrm{lin}}{e}^{2i\ensuremath{\phi}}$ (${\ensuremath{\chi}}_{\mathrm{lin}}$ is the linear susceptibility, $\ensuremath{\phi}$ the phase shift) allowing coherent control of the optical response. For large optical depths, ${\ensuremath{\chi}}_{\mathrm{eff}}\ensuremath{\approx}{\ensuremath{\chi}}_{\mathrm{lin}}^{*}$, turning an absorber into an amplifier without affecting the dispersion.