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

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 ${\chi }_{\mathrm{eff}}$ behaves as ${\chi }_{\mathrm{lin}}{e}^{2i\varphi }$ (${\chi }_{\mathrm{lin}}$ is the linear susceptibility, $\varphi$ the phase shift) allowing coherent control of the optical response. For large optical depths, ${\chi }_{\mathrm{eff}}\approx {\chi }_{\mathrm{lin}}^{*}$, turning an absorber into an amplifier without affecting the dispersion.

Figure 1

(a) The duplicated two-level system and (b) fields configurations.

Figure 2

Coherent control of the susceptibility for the probe beam. We have (${\Delta }_0={\omega }_0-\omega$).

Figure 3

Quantum paths giving rise to the coherences that modify the $\sigma$ field behavior. (a) Absorption path. (b) Cross-Kerr type path. Zeeman coherence between the ground states is induced by simultaneous action of the pump and the probe (brackets). The pump is then diffracted. This path cancels with that of absorption. (c) Phase conjugation-type path. The diffraction of the pump leads to a wave conjugate with the probe and determines the optical response.

Figure 4

Behavior of ${\chi }_{\mathrm{eff}}$ after propagation in a thick optical medium (${\alpha }_{0}L\gg 1$). Here, the effective susceptibility saturates with the phase shift for detuning such as $|{\Delta }_0|\le \Gamma$.